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


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}
}
definition:
{
(butlast, F:
{() -> butlast([cons(y, nil), nil])
() -> butlast([nil, nil])
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)])}
(butlast([_lea, _mea]) /\ butlast([_lea, _nea])) -> eq_eltlist([_mea, _nea])
)
(append, F:
{() -> append([nil, l2, l2])
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)])}
(append([_pea, _qea, _rea]) /\ append([_pea, _qea, _sea])) -> eq_eltlist([_rea, _sea])
)
(butlastconcat, F:
{(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea])
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea])}
(butlastconcat([_wea, _xea, _yea]) /\ butlastconcat([_wea, _xea, _zea])) -> eq_eltlist([_yea, _zea])
)
}

properties:
{(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa])}


over-approximation: {append, butlast, butlastconcat}
under-approximation: {}

Clause system for inference is:

{
() -> append([nil, l2, l2]) -> 0
() -> butlast([cons(y, nil), nil]) -> 0
() -> butlast([nil, nil]) -> 0
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 0
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 0
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 0
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 0
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 0
}


Solving took 60.003842 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8259, q_gen_8260, q_gen_8261, q_gen_8264, q_gen_8265, q_gen_8266, q_gen_8273, q_gen_8276, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8285, q_gen_8286, q_gen_8290, q_gen_8291, q_gen_8298, q_gen_8299, q_gen_8300, q_gen_8303, q_gen_8304, q_gen_8305, q_gen_8309, q_gen_8310, q_gen_8311, q_gen_8314, q_gen_8317, q_gen_8318, q_gen_8319, q_gen_8322, q_gen_8323, q_gen_8324, q_gen_8325, q_gen_8326, q_gen_8329, q_gen_8330, q_gen_8331, q_gen_8341, q_gen_8342, q_gen_8343, q_gen_8344, q_gen_8345, q_gen_8346, q_gen_8352, q_gen_8355, q_gen_8356, q_gen_8357, q_gen_8361, q_gen_8362, q_gen_8363, q_gen_8365, q_gen_8373, q_gen_8374, q_gen_8376, q_gen_8377, q_gen_8378, q_gen_8379, q_gen_8381, q_gen_8383, q_gen_8384, q_gen_8385, q_gen_8386, q_gen_8387, q_gen_8388, q_gen_8389, q_gen_8392, q_gen_8394, q_gen_8395, q_gen_8396, q_gen_8397, q_gen_8398, q_gen_8400},
Q_f={},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<a>() -> q_gen_8325
<cons>(q_gen_8279, q_gen_8278) -> q_gen_8387
<nil, nil>() -> q_gen_8260
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8265
<a, a>() -> q_gen_8266
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons>(q_gen_8261, q_gen_8305) -> q_gen_8304
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8305
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8311
<nil, cons>(q_gen_8325, q_gen_8278) -> q_gen_8344
<a, b>() -> q_gen_8345
<cons, cons>(q_gen_8261, q_gen_8357) -> q_gen_8356
<cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8357
<cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8379
<b, a>() -> q_gen_8397
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8259
<nil, cons, cons>(q_gen_8266, q_gen_8265) -> q_gen_8264
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8273
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8276
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<b, b, b>() -> q_gen_8280
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8285
<cons, nil, cons>(q_gen_8266, q_gen_8260) -> q_gen_8290
<cons, nil, cons>(q_gen_8261, q_gen_8265) -> q_gen_8291
<cons, cons, cons>(q_gen_8299, q_gen_8277) -> q_gen_8298
<a, b, a>() -> q_gen_8299
<cons, cons, cons>(q_gen_8280, q_gen_8285) -> q_gen_8300
<cons, nil, cons>(q_gen_8261, q_gen_8304) -> q_gen_8303
<cons, cons, cons>(q_gen_8280, q_gen_8310) -> q_gen_8309
<cons, nil, cons>(q_gen_8261, q_gen_8311) -> q_gen_8310
<cons, nil, cons>(q_gen_8261, q_gen_8305) -> q_gen_8314
<cons, cons, cons>(q_gen_8299, q_gen_8318) -> q_gen_8317
<cons, nil, cons>(q_gen_8266, q_gen_8286) -> q_gen_8318
<cons, nil, cons>(q_gen_8266, q_gen_8305) -> q_gen_8319
<nil, cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8322
<cons, cons, cons>(q_gen_8326, q_gen_8324) -> q_gen_8323
<nil, nil, cons>(q_gen_8325, q_gen_8278) -> q_gen_8324
<b, a, b>() -> q_gen_8326
<cons, cons, cons>(q_gen_8330, q_gen_8324) -> q_gen_8329
<a, a, a>() -> q_gen_8330
<cons, cons, cons>(q_gen_8280, q_gen_8324) -> q_gen_8331
<nil, cons, cons>(q_gen_8261, q_gen_8265) -> q_gen_8341
<cons, cons, cons>(q_gen_8299, q_gen_8343) -> q_gen_8342
<nil, cons, cons>(q_gen_8345, q_gen_8344) -> q_gen_8343
<cons, nil, cons>(q_gen_8345, q_gen_8286) -> q_gen_8346
<nil, cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8352
<cons, nil, cons>(q_gen_8261, q_gen_8356) -> q_gen_8355
<cons, cons, cons>(q_gen_8299, q_gen_8362) -> q_gen_8361
<cons, nil, cons>(q_gen_8261, q_gen_8344) -> q_gen_8362
<nil, cons, cons>(q_gen_8345, q_gen_8305) -> q_gen_8363
<cons, cons, cons>(q_gen_8280, q_gen_8346) -> q_gen_8365
<cons, cons, cons>(q_gen_8280, q_gen_8362) -> q_gen_8373
<nil, cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8374
<cons, cons, cons>(q_gen_8326, q_gen_8346) -> q_gen_8376
<cons, cons, cons>(q_gen_8330, q_gen_8378) -> q_gen_8377
<cons, nil, cons>(q_gen_8261, q_gen_8379) -> q_gen_8378
<cons, cons, cons>(q_gen_8280, q_gen_8352) -> q_gen_8381
<cons, cons, cons>(q_gen_8280, q_gen_8374) -> q_gen_8383
<cons, cons, cons>(q_gen_8299, q_gen_8385) -> q_gen_8384
<cons, cons, cons>(q_gen_8326, q_gen_8386) -> q_gen_8385
<nil, nil, cons>(q_gen_8279, q_gen_8387) -> q_gen_8386
<cons, cons, cons>(q_gen_8280, q_gen_8389) -> q_gen_8388
<cons, cons, cons>(q_gen_8299, q_gen_8259) -> q_gen_8389
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8392
<nil, cons, cons>(q_gen_8266, q_gen_8305) -> q_gen_8394
<cons, cons, cons>(q_gen_8330, q_gen_8396) -> q_gen_8395
<nil, cons, cons>(q_gen_8397, q_gen_8286) -> q_gen_8396
<cons, cons, cons>(q_gen_8299, q_gen_8285) -> q_gen_8398
<nil, cons, cons>(q_gen_8261, q_gen_8305) -> q_gen_8400
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8253, q_gen_8254, q_gen_8262, q_gen_8263, q_gen_8267, q_gen_8268, q_gen_8269, q_gen_8281, q_gen_8282, q_gen_8292, q_gen_8301, q_gen_8312, q_gen_8348, q_gen_8349, q_gen_8350, q_gen_8351, q_gen_8353, q_gen_8370, q_gen_8375},
Q_f={},
Delta=
{
<nil>() -> q_gen_8250
<b>() -> q_gen_8251
<a>() -> q_gen_8263
<nil, nil>() -> q_gen_8248
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8253
<b, b>() -> q_gen_8254
<cons, nil>(q_gen_8263, q_gen_8250) -> q_gen_8262
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8269, q_gen_8267) -> q_gen_8268
<a, a>() -> q_gen_8269
<cons, cons>(q_gen_8254, q_gen_8262) -> q_gen_8281
<cons, cons>(q_gen_8254, q_gen_8281) -> q_gen_8282
<cons, cons>(q_gen_8269, q_gen_8253) -> q_gen_8292
<cons, cons>(q_gen_8254, q_gen_8253) -> q_gen_8301
<cons, cons>(q_gen_8254, q_gen_8301) -> q_gen_8312
<cons, cons>(q_gen_8254, q_gen_8349) -> q_gen_8348
<cons, cons>(q_gen_8269, q_gen_8262) -> q_gen_8349
<cons, cons>(q_gen_8254, q_gen_8348) -> q_gen_8350
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8351
<cons, cons>(q_gen_8269, q_gen_8249) -> q_gen_8353
<cons, cons>(q_gen_8254, q_gen_8353) -> q_gen_8370
<cons, cons>(q_gen_8269, q_gen_8281) -> q_gen_8375
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8274, q_gen_8275, q_gen_8283, q_gen_8284, q_gen_8287, q_gen_8288, q_gen_8289, q_gen_8293, q_gen_8294, q_gen_8295, q_gen_8296, q_gen_8297, q_gen_8302, q_gen_8306, q_gen_8307, q_gen_8308, q_gen_8313, q_gen_8315, q_gen_8316, q_gen_8320, q_gen_8321, q_gen_8327, q_gen_8328, q_gen_8332, q_gen_8333, q_gen_8334, q_gen_8335, q_gen_8336, q_gen_8337, q_gen_8338, q_gen_8339, q_gen_8340, q_gen_8347, q_gen_8354, q_gen_8358, q_gen_8359, q_gen_8360, q_gen_8364, q_gen_8366, q_gen_8367, q_gen_8368, q_gen_8369, q_gen_8371, q_gen_8372, q_gen_8380, q_gen_8382, q_gen_8390, q_gen_8391, q_gen_8393, q_gen_8399, q_gen_8401, q_gen_8402},
Q_f={},
Delta=
{
<nil>() -> q_gen_8257
<b>() -> q_gen_8258
<a>() -> q_gen_8275
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8294
<a, a>() -> q_gen_8295
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8308
<b, a>() -> q_gen_8334
<a, b>() -> q_gen_8340
<cons, cons>(q_gen_8340, q_gen_8271) -> q_gen_8360
<cons, cons>(q_gen_8295, q_gen_8288) -> q_gen_8372
<nil, nil, nil>() -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, nil>(q_gen_8275, q_gen_8257) -> q_gen_8274
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8283
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8284
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8287
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8289
<cons, nil, cons>(q_gen_8295, q_gen_8294) -> q_gen_8293
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8296
<b, b, b>() -> q_gen_8297
<cons, cons, cons>(q_gen_8297, q_gen_8283) -> q_gen_8302
<cons, cons, cons>(q_gen_8297, q_gen_8307) -> q_gen_8306
<cons, nil, cons>(q_gen_8272, q_gen_8308) -> q_gen_8307
<cons, cons, cons>(q_gen_8297, q_gen_8287) -> q_gen_8313
<cons, cons, cons>(q_gen_8316, q_gen_8270) -> q_gen_8315
<b, a, b>() -> q_gen_8316
<cons, cons, cons>(q_gen_8321, q_gen_8270) -> q_gen_8320
<a, b, a>() -> q_gen_8321
<cons, cons, cons>(q_gen_8328, q_gen_8255) -> q_gen_8327
<a, a, a>() -> q_gen_8328
<cons, cons, cons>(q_gen_8297, q_gen_8333) -> q_gen_8332
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8333
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8335
<cons, cons, cons>(q_gen_8297, q_gen_8335) -> q_gen_8336
<cons, nil, cons>(q_gen_8272, q_gen_8294) -> q_gen_8337
<cons, cons, cons>(q_gen_8297, q_gen_8339) -> q_gen_8338
<nil, cons, cons>(q_gen_8340, q_gen_8271) -> q_gen_8339
<cons, nil, nil>(q_gen_8275, q_gen_8257) -> q_gen_8347
<nil, cons, cons>(q_gen_8340, q_gen_8288) -> q_gen_8354
<cons, cons, cons>(q_gen_8297, q_gen_8359) -> q_gen_8358
<cons, nil, cons>(q_gen_8272, q_gen_8360) -> q_gen_8359
<nil, cons, cons>(q_gen_8295, q_gen_8288) -> q_gen_8364
<cons, cons, cons>(q_gen_8297, q_gen_8367) -> q_gen_8366
<cons, cons, cons>(q_gen_8369, q_gen_8368) -> q_gen_8367
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8368
<a, b, b>() -> q_gen_8369
<cons, nil, cons>(q_gen_8272, q_gen_8372) -> q_gen_8371
<cons, nil, cons>(q_gen_8340, q_gen_8288) -> q_gen_8380
<cons, cons, cons>(q_gen_8297, q_gen_8354) -> q_gen_8382
<cons, cons, cons>(q_gen_8297, q_gen_8391) -> q_gen_8390
<cons, cons, cons>(q_gen_8369, q_gen_8283) -> q_gen_8391
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8393
<cons, cons, cons>(q_gen_8369, q_gen_8270) -> q_gen_8399
<cons, nil, cons>(q_gen_8295, q_gen_8288) -> q_gen_8401
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8402
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.069506 s (model generation: 0.065034,  model checking: 0.004472):

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> butlast([cons(y, nil), nil]) -> 0
() -> butlast([nil, nil]) -> 3
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 1
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 1
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 1
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 1
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 1
}
Sat witness: Found: (() -> butlast([nil, nil]), {

})

-------------------------------------------
Step 1, which took 0.070363 s (model generation: 0.069532,  model checking: 0.000831):

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

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248},
Q_f={q_gen_8248},
Delta=
{
<nil, nil>() -> q_gen_8248
}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> butlast([cons(y, nil), nil]) -> 3
() -> butlast([nil, nil]) -> 3
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 1
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 1
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 1
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 1
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 1
}
Sat witness: Found: (() -> butlast([cons(y, nil), nil]), {
y -> b
})

-------------------------------------------
Step 2, which took 0.076344 s (model generation: 0.073667,  model checking: 0.002677):

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

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8250, q_gen_8251},
Q_f={q_gen_8248},
Delta=
{
<nil>() -> q_gen_8250
<b>() -> q_gen_8251
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8248
<nil, nil>() -> q_gen_8248
}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> butlast([cons(y, nil), nil]) -> 3
() -> butlast([nil, nil]) -> 3
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 1
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 1
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 1
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 1
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 1
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> nil
})

-------------------------------------------
Step 3, which took 0.080739 s (model generation: 0.079152,  model checking: 0.001587):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252},
Q_f={q_gen_8252},
Delta=
{
<nil, nil, nil>() -> q_gen_8252
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8250, q_gen_8251},
Q_f={q_gen_8248},
Delta=
{
<nil>() -> q_gen_8250
<b>() -> q_gen_8251
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8248
<nil, nil>() -> q_gen_8248
}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> butlast([cons(y, nil), nil]) -> 3
() -> butlast([nil, nil]) -> 3
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 1
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 1
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 1
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 1
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 4
}
Sat witness: Found: ((butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]), {
_kea -> nil  ;  x2 -> b  ;  x3 -> nil  ;  y -> b
})

-------------------------------------------
Step 4, which took 0.087220 s (model generation: 0.085564,  model checking: 0.001656):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252},
Q_f={q_gen_8252},
Delta=
{
<nil, nil, nil>() -> q_gen_8252
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8250, q_gen_8251, q_gen_8254},
Q_f={q_gen_8248},
Delta=
{
<nil>() -> q_gen_8250
<b>() -> q_gen_8251
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8248
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<b, b>() -> q_gen_8254
}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> butlast([cons(y, nil), nil]) -> 3
() -> butlast([nil, nil]) -> 3
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 1
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 1
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 1
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 4
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 4
}
Sat witness: Found: ((butlast([x, _tea])) -> butlastconcat([x, nil, _tea]), {
_tea -> nil  ;  x -> nil
})

-------------------------------------------
Step 5, which took 0.099027 s (model generation: 0.094281,  model checking: 0.004746):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252},
Q_f={q_gen_8252},
Delta=
{
<nil, nil, nil>() -> q_gen_8252
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8250, q_gen_8251, q_gen_8254},
Q_f={q_gen_8248},
Delta=
{
<nil>() -> q_gen_8250
<b>() -> q_gen_8251
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8248
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<b, b>() -> q_gen_8254
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255},
Q_f={q_gen_8255},
Delta=
{
<nil, nil, nil>() -> q_gen_8255
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> butlast([cons(y, nil), nil]) -> 3
() -> butlast([nil, nil]) -> 3
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 1
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 4
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 2
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 4
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 4
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> nil  ;  _vea -> nil  ;  x -> nil  ;  x2 -> nil  ;  z -> b
})

-------------------------------------------
Step 6, which took 0.085668 s (model generation: 0.084001,  model checking: 0.001667):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252},
Q_f={q_gen_8252},
Delta=
{
<nil, nil, nil>() -> q_gen_8252
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8250, q_gen_8251, q_gen_8254},
Q_f={q_gen_8248},
Delta=
{
<nil>() -> q_gen_8250
<b>() -> q_gen_8251
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8248
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<b, b>() -> q_gen_8254
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<b>() -> q_gen_8258
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> butlast([cons(y, nil), nil]) -> 3
() -> butlast([nil, nil]) -> 3
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 4
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 4
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 2
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 4
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 4
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> nil  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 7, which took 0.088243 s (model generation: 0.085526,  model checking: 0.002717):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261},
Q_f={q_gen_8252},
Delta=
{
<nil, nil>() -> q_gen_8260
<b, b>() -> q_gen_8261
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8250, q_gen_8251, q_gen_8254},
Q_f={q_gen_8248},
Delta=
{
<nil>() -> q_gen_8250
<b>() -> q_gen_8251
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8248
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<b, b>() -> q_gen_8254
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<b>() -> q_gen_8258
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> butlast([cons(y, nil), nil]) -> 6
() -> butlast([nil, nil]) -> 4
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 4
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 4
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 3
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 4
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 4
}
Sat witness: Found: (() -> butlast([cons(y, nil), nil]), {
y -> a
})

-------------------------------------------
Step 8, which took 0.096613 s (model generation: 0.089744,  model checking: 0.006869):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261},
Q_f={q_gen_8252},
Delta=
{
<nil, nil>() -> q_gen_8260
<b, b>() -> q_gen_8261
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8250, q_gen_8251, q_gen_8254},
Q_f={q_gen_8248},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8248
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<b, b>() -> q_gen_8254
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<b>() -> q_gen_8258
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> butlast([cons(y, nil), nil]) -> 6
() -> butlast([nil, nil]) -> 4
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 4
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 4
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 4
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 4
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 4
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 9, which took 0.094652 s (model generation: 0.092567,  model checking: 0.002085):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261},
Q_f={q_gen_8252},
Delta=
{
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8250, q_gen_8251, q_gen_8254},
Q_f={q_gen_8248},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8248
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<b, b>() -> q_gen_8254
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<b>() -> q_gen_8258
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> butlast([cons(y, nil), nil]) -> 6
() -> butlast([nil, nil]) -> 4
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 4
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 4
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 4
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 4
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 7
}
Sat witness: Found: ((butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]), {
_kea -> cons(b, nil)  ;  x2 -> b  ;  x3 -> nil  ;  y -> a
})

-------------------------------------------
Step 10, which took 0.124383 s (model generation: 0.119560,  model checking: 0.004823):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261},
Q_f={q_gen_8252},
Delta=
{
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8250, q_gen_8251, q_gen_8254},
Q_f={q_gen_8248},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8248
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<b>() -> q_gen_8258
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> butlast([cons(y, nil), nil]) -> 6
() -> butlast([nil, nil]) -> 4
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 4
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 4
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 4
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 7
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 7
}
Sat witness: Found: ((butlast([x, _tea])) -> butlastconcat([x, nil, _tea]), {
_tea -> cons(b, nil)  ;  x -> cons(b, nil)
})

-------------------------------------------
Step 11, which took 0.117041 s (model generation: 0.111506,  model checking: 0.005535):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261},
Q_f={q_gen_8252},
Delta=
{
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8250, q_gen_8251, q_gen_8254},
Q_f={q_gen_8248},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8248
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8271, q_gen_8272},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> butlast([cons(y, nil), nil]) -> 6
() -> butlast([nil, nil]) -> 4
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 4
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 4
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 7
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 7
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 7
}
Sat witness: Found: ((append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]), {
_afa -> cons(b, nil)  ;  _bfa -> cons(b, nil)  ;  _cfa -> nil  ;  xs -> nil  ;  ys -> cons(b, nil)
})

-------------------------------------------
Step 12, which took 0.111654 s (model generation: 0.107642,  model checking: 0.004012):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261},
Q_f={q_gen_8252},
Delta=
{
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8271, q_gen_8272},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> butlast([cons(y, nil), nil]) -> 6
() -> butlast([nil, nil]) -> 4
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 4
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 7
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 7
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 7
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 7
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> nil  ;  _vea -> nil  ;  x -> nil  ;  x2 -> nil  ;  z -> a
})

-------------------------------------------
Step 13, which took 0.124356 s (model generation: 0.113076,  model checking: 0.011280):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261},
Q_f={q_gen_8252},
Delta=
{
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8271, q_gen_8272},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> butlast([cons(y, nil), nil]) -> 6
() -> butlast([nil, nil]) -> 4
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 7
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 7
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 7
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 7
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 7
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> cons(b, nil)  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 14, which took 0.125945 s (model generation: 0.121179,  model checking: 0.004766):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8265, q_gen_8273, q_gen_8278, q_gen_8279, q_gen_8280},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8265
<cons, cons, cons>(q_gen_8280, q_gen_8273) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8265) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8273
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8273
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8250, q_gen_8251, q_gen_8254},
Q_f={q_gen_8248},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8248
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8271, q_gen_8272},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> butlast([cons(y, nil), nil]) -> 7
() -> butlast([nil, nil]) -> 5
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 7
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 7
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 7
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 7
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 7
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, nil)
})

-------------------------------------------
Step 15, which took 0.123800 s (model generation: 0.119218,  model checking: 0.004582):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8278, q_gen_8279, q_gen_8280},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8271, q_gen_8272},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> butlast([cons(y, nil), nil]) -> 7
() -> butlast([nil, nil]) -> 6
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 7
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 7
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 7
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 7
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 10
}
Sat witness: Found: ((butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]), {
_kea -> cons(b, nil)  ;  x2 -> b  ;  x3 -> cons(a, nil)  ;  y -> b
})

-------------------------------------------
Step 16, which took 0.132866 s (model generation: 0.127974,  model checking: 0.004892):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8278, q_gen_8279, q_gen_8280},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8271, q_gen_8272},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> butlast([cons(y, nil), nil]) -> 7
() -> butlast([nil, nil]) -> 7
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 7
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 7
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 7
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 10
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 10
}
Sat witness: Found: ((butlast([x, _tea])) -> butlastconcat([x, nil, _tea]), {
_tea -> nil  ;  x -> cons(b, nil)
})

-------------------------------------------
Step 17, which took 0.130498 s (model generation: 0.126844,  model checking: 0.003654):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8278, q_gen_8279, q_gen_8280},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8271, q_gen_8272},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> butlast([cons(y, nil), nil]) -> 7
() -> butlast([nil, nil]) -> 7
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 7
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 7
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 10
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 10
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 10
}
Sat witness: Found: ((append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]), {
_afa -> cons(b, nil)  ;  _bfa -> nil  ;  _cfa -> cons(b, nil)  ;  xs -> cons(b, nil)  ;  ys -> nil
})

-------------------------------------------
Step 18, which took 0.170108 s (model generation: 0.159307,  model checking: 0.010801):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8278, q_gen_8279, q_gen_8280},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> butlast([cons(y, nil), nil]) -> 7
() -> butlast([nil, nil]) -> 7
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 7
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 10
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 10
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 10
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 10
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> nil  ;  _vea -> cons(b, nil)  ;  x -> nil  ;  x2 -> nil  ;  z -> b
})

-------------------------------------------
Step 19, which took 0.145828 s (model generation: 0.140562,  model checking: 0.005266):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8278, q_gen_8279, q_gen_8280},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> butlast([cons(y, nil), nil]) -> 7
() -> butlast([nil, nil]) -> 7
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 10
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 10
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 10
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 10
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 10
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> cons(b, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 20, which took 0.155363 s (model generation: 0.137706,  model checking: 0.017657):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8278, q_gen_8279, q_gen_8280},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> butlast([cons(y, nil), nil]) -> 8
() -> butlast([nil, nil]) -> 8
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 10
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 10
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 10
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 13
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 11
}
Sat witness: Found: ((butlast([x, _tea])) -> butlastconcat([x, nil, _tea]), {
_tea -> cons(b, nil)  ;  x -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 21, which took 0.149066 s (model generation: 0.142715,  model checking: 0.006351):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8278, q_gen_8279, q_gen_8280},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> butlast([cons(y, nil), nil]) -> 9
() -> butlast([nil, nil]) -> 9
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 10
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 10
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 13
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 13
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 11
}
Sat witness: Found: ((append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]), {
_afa -> cons(b, cons(b, nil))  ;  _bfa -> cons(b, nil)  ;  _cfa -> nil  ;  xs -> cons(b, nil)  ;  ys -> nil
})

-------------------------------------------
Step 22, which took 0.153249 s (model generation: 0.144197,  model checking: 0.009052):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8265, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8265
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8265
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8265) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8265) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> butlast([cons(y, nil), nil]) -> 10
() -> butlast([nil, nil]) -> 10
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 10
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 13
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 13
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 13
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 11
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> cons(b, nil)  ;  _vea -> cons(b, nil)  ;  x -> nil  ;  x2 -> cons(b, nil)  ;  z -> b
})

-------------------------------------------
Step 23, which took 0.156355 s (model generation: 0.151170,  model checking: 0.005185):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8265, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8265
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8265
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8265) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8265) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> butlast([cons(y, nil), nil]) -> 10
() -> butlast([nil, nil]) -> 10
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 13
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 13
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 13
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 13
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 11
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> cons(a, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 24, which took 0.186022 s (model generation: 0.163326,  model checking: 0.022696):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> butlast([cons(y, nil), nil]) -> 11
() -> butlast([nil, nil]) -> 11
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 13
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 13
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 13
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 16
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 12
}
Sat witness: Found: ((butlast([x, _tea])) -> butlastconcat([x, nil, _tea]), {
_tea -> cons(a, cons(b, nil))  ;  x -> cons(a, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 25, which took 0.210059 s (model generation: 0.176334,  model checking: 0.033725):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12
() -> butlast([cons(y, nil), nil]) -> 12
() -> butlast([nil, nil]) -> 12
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 13
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 16
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 14
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 16
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 13
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> nil  ;  _vea -> cons(b, nil)  ;  x -> cons(b, nil)  ;  x2 -> nil  ;  z -> b
})

-------------------------------------------
Step 26, which took 0.201882 s (model generation: 0.174654,  model checking: 0.027228):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> butlast([cons(y, nil), nil]) -> 13
() -> butlast([nil, nil]) -> 13
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 16
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 16
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 14
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 16
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 14
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> cons(b, nil)  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 27, which took 0.214032 s (model generation: 0.184050,  model checking: 0.029982):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, b, a>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 14
() -> butlast([cons(y, nil), nil]) -> 14
() -> butlast([nil, nil]) -> 14
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 16
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 16
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 17
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 16
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 15
}
Sat witness: Found: ((append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]), {
_afa -> cons(b, cons(b, cons(b, nil)))  ;  _bfa -> cons(b, cons(b, nil))  ;  _cfa -> cons(b, nil)  ;  xs -> cons(b, cons(b, nil))  ;  ys -> cons(b, nil)
})

-------------------------------------------
Step 28, which took 0.216312 s (model generation: 0.207188,  model checking: 0.009124):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, b, a>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8263, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<b>() -> q_gen_8251
<a>() -> q_gen_8263
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8248
<cons, nil>(q_gen_8263, q_gen_8250) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 15
() -> butlast([cons(y, nil), nil]) -> 15
() -> butlast([nil, nil]) -> 15
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 16
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 16
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 17
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 16
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 18
}
Sat witness: Found: ((butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]), {
_kea -> nil  ;  x2 -> a  ;  x3 -> nil  ;  y -> b
})

-------------------------------------------
Step 29, which took 0.259110 s (model generation: 0.234075,  model checking: 0.025035):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8285, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8285) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, b, a>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8285
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> butlast([cons(y, nil), nil]) -> 16
() -> butlast([nil, nil]) -> 16
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 16
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 19
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 17
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 17
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 18
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> nil  ;  _vea -> cons(b, cons(b, cons(b, nil)))  ;  x -> cons(b, cons(b, cons(b, nil)))  ;  x2 -> nil  ;  z -> b
})

-------------------------------------------
Step 30, which took 0.263221 s (model generation: 0.236079,  model checking: 0.027142):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, b, a>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8256
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> butlast([cons(y, nil), nil]) -> 16
() -> butlast([nil, nil]) -> 16
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 19
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 19
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 17
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 17
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 18
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 31, which took 0.326286 s (model generation: 0.289808,  model checking: 0.036478):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, b, a>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 17
() -> butlast([cons(y, nil), nil]) -> 17
() -> butlast([nil, nil]) -> 17
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 19
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 19
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 20
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 18
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 18
}
Sat witness: Found: ((append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]), {
_afa -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _bfa -> cons(b, cons(b, cons(b, nil)))  ;  _cfa -> cons(b, cons(b, nil))  ;  xs -> cons(b, cons(b, cons(b, nil)))  ;  ys -> cons(b, nil)
})

-------------------------------------------
Step 32, which took 0.229082 s (model generation: 0.210148,  model checking: 0.018934):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, b, a>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8256
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 18
() -> butlast([cons(y, nil), nil]) -> 18
() -> butlast([nil, nil]) -> 18
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 19
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 22
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 20
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 19
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 19
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> nil  ;  _vea -> cons(b, cons(b, nil))  ;  x -> cons(b, cons(b, nil))  ;  x2 -> nil  ;  z -> a
})

-------------------------------------------
Step 33, which took 0.139331 s (model generation: 0.127621,  model checking: 0.011710):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8285, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8285) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, b, a>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8285
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 19
() -> butlast([cons(y, nil), nil]) -> 19
() -> butlast([nil, nil]) -> 19
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 22
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 22
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 20
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 20
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 20
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> cons(a, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> cons(a, nil)
})

-------------------------------------------
Step 34, which took 0.159997 s (model generation: 0.136197,  model checking: 0.023800):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, b, a>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 20
() -> butlast([cons(y, nil), nil]) -> 20
() -> butlast([nil, nil]) -> 20
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 22
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 25
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 21
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 21
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 21
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> nil  ;  _vea -> cons(a, cons(b, nil))  ;  x -> cons(a, cons(b, nil))  ;  x2 -> nil  ;  z -> b
})

-------------------------------------------
Step 35, which took 0.169418 s (model generation: 0.144489,  model checking: 0.024929):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, b, a>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 21
() -> butlast([cons(y, nil), nil]) -> 21
() -> butlast([nil, nil]) -> 21
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 25
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 25
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 22
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 22
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 22
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> cons(a, nil)  ;  h1 -> b  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 36, which took 0.190010 s (model generation: 0.167796,  model checking: 0.022214):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8283, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255, q_gen_8283},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8283) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8283
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8283
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8283
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 22
() -> butlast([cons(y, nil), nil]) -> 22
() -> butlast([nil, nil]) -> 22
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 25
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 28
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 23
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 23
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 23
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> nil  ;  _vea -> cons(a, nil)  ;  x -> cons(a, nil)  ;  x2 -> nil  ;  z -> a
})

-------------------------------------------
Step 37, which took 0.192345 s (model generation: 0.172540,  model checking: 0.019805):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8283, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255, q_gen_8283},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8283) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8283
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8283
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8283
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 23
() -> butlast([cons(y, nil), nil]) -> 23
() -> butlast([nil, nil]) -> 23
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 28
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 28
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 24
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 24
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 24
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> cons(a, nil)  ;  h1 -> a  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 38, which took 0.191043 s (model generation: 0.170385,  model checking: 0.020658):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8283, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255, q_gen_8283},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8283) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8283
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8283
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8283
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 24
() -> butlast([cons(y, nil), nil]) -> 24
() -> butlast([nil, nil]) -> 24
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 28
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 28
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 27
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 25
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 25
}
Sat witness: Found: ((append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]), {
_afa -> cons(b, cons(b, cons(b, nil)))  ;  _bfa -> cons(b, cons(b, nil))  ;  _cfa -> cons(b, nil)  ;  xs -> cons(b, cons(b, nil))  ;  ys -> nil
})

-------------------------------------------
Step 39, which took 0.198081 s (model generation: 0.175974,  model checking: 0.022107):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8283, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255, q_gen_8283},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8283) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8283
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8283
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8283
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 25
() -> butlast([cons(y, nil), nil]) -> 25
() -> butlast([nil, nil]) -> 25
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 28
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 31
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 28
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 26
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 26
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> cons(b, nil)  ;  _vea -> cons(b, cons(a, nil))  ;  x -> cons(b, nil)  ;  x2 -> cons(b, nil)  ;  z -> b
})

-------------------------------------------
Step 40, which took 0.268079 s (model generation: 0.257519,  model checking: 0.010560):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 26
() -> butlast([cons(y, nil), nil]) -> 26
() -> butlast([nil, nil]) -> 26
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 28
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 31
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 31
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 27
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 27
}
Sat witness: Found: ((append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]), {
_afa -> cons(b, cons(b, nil))  ;  _bfa -> cons(b, nil)  ;  _cfa -> cons(a, nil)  ;  xs -> cons(b, cons(b, nil))  ;  ys -> nil
})

-------------------------------------------
Step 41, which took 0.306438 s (model generation: 0.302958,  model checking: 0.003480):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8265, q_gen_8266, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8285},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<nil, nil>() -> q_gen_8260
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8265
<cons, cons>(q_gen_8261, q_gen_8265) -> q_gen_8265
<cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8265
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8265
<a, a>() -> q_gen_8266
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8266, q_gen_8265) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8285) -> q_gen_8277
<cons, nil, cons>(q_gen_8266, q_gen_8260) -> q_gen_8277
<cons, nil, cons>(q_gen_8266, q_gen_8265) -> q_gen_8277
<nil, cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
<cons, nil, cons>(q_gen_8261, q_gen_8265) -> q_gen_8285
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 29
() -> butlast([cons(y, nil), nil]) -> 27
() -> butlast([nil, nil]) -> 27
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 28
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 31
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 31
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 27
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 27
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, nil)
})

-------------------------------------------
Step 42, which took 0.320327 s (model generation: 0.309026,  model checking: 0.011301):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8265, q_gen_8266, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8285},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<nil, nil>() -> q_gen_8260
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8265
<cons, cons>(q_gen_8261, q_gen_8265) -> q_gen_8265
<cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8265
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8265
<a, a>() -> q_gen_8266
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8266, q_gen_8265) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8285) -> q_gen_8277
<cons, nil, cons>(q_gen_8266, q_gen_8260) -> q_gen_8277
<cons, nil, cons>(q_gen_8266, q_gen_8265) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
<cons, nil, cons>(q_gen_8261, q_gen_8265) -> q_gen_8285
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8288
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 29
() -> butlast([cons(y, nil), nil]) -> 28
() -> butlast([nil, nil]) -> 28
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 31
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 31
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 31
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 28
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 28
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> cons(b, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 43, which took 0.316005 s (model generation: 0.291510,  model checking: 0.024495):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8256
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 30
() -> butlast([cons(y, nil), nil]) -> 29
() -> butlast([nil, nil]) -> 29
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 31
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 31
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 34
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 29
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 29
}
Sat witness: Found: ((append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]), {
_afa -> cons(b, cons(b, cons(b, cons(b, nil))))  ;  _bfa -> cons(b, cons(b, cons(b, nil)))  ;  _cfa -> cons(b, cons(a, nil))  ;  xs -> cons(b, cons(b, cons(b, nil)))  ;  ys -> cons(b, nil)
})

-------------------------------------------
Step 44, which took 0.311906 s (model generation: 0.307054,  model checking: 0.004852):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8262, q_gen_8263, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249, q_gen_8262},
Delta=
{
<nil>() -> q_gen_8250
<b>() -> q_gen_8251
<a>() -> q_gen_8263
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8262) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, nil>(q_gen_8263, q_gen_8250) -> q_gen_8262
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 30
() -> butlast([cons(y, nil), nil]) -> 29
() -> butlast([nil, nil]) -> 29
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 31
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 31
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 34
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 29
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 32
}
Sat witness: Found: ((butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]), {
_kea -> cons(b, nil)  ;  x2 -> b  ;  x3 -> cons(b, nil)  ;  y -> b
})

-------------------------------------------
Step 45, which took 0.287483 s (model generation: 0.285775,  model checking: 0.001708):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8265, q_gen_8266, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8285},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8265) -> q_gen_8265
<cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8265
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8265
<a, a>() -> q_gen_8266
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8266, q_gen_8265) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8285) -> q_gen_8277
<cons, nil, cons>(q_gen_8266, q_gen_8260) -> q_gen_8277
<cons, nil, cons>(q_gen_8266, q_gen_8265) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
<cons, nil, cons>(q_gen_8261, q_gen_8265) -> q_gen_8285
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8295, q_gen_8297},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, a>() -> q_gen_8295
<b, a>() -> q_gen_8295
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, cons>(q_gen_8295, q_gen_8271) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8295, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8295, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 30
() -> butlast([cons(y, nil), nil]) -> 29
() -> butlast([nil, nil]) -> 29
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 31
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 31
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 34
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 32
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 32
}
Sat witness: Found: ((butlast([x, _tea])) -> butlastconcat([x, nil, _tea]), {
_tea -> cons(b, cons(b, nil))  ;  x -> cons(b, cons(b, cons(b, nil)))
})

-------------------------------------------
Step 46, which took 0.269139 s (model generation: 0.255020,  model checking: 0.014119):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8283, q_gen_8288, q_gen_8297, q_gen_8334, q_gen_8335},
Q_f={q_gen_8255, q_gen_8283},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8283) -> q_gen_8270
<cons, cons, cons>(q_gen_8297, q_gen_8335) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8283
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8283
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8335
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 31
() -> butlast([cons(y, nil), nil]) -> 30
() -> butlast([nil, nil]) -> 30
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 31
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 34
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 34
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 32
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 32
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> cons(b, nil)  ;  _vea -> cons(b, cons(b, nil))  ;  x -> cons(b, nil)  ;  x2 -> cons(a, nil)  ;  z -> b
})

-------------------------------------------
Step 47, which took 0.329064 s (model generation: 0.311640,  model checking: 0.017424):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8253, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249, q_gen_8253},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<cons, cons>(q_gen_8254, q_gen_8253) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8253
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 31
() -> butlast([cons(y, nil), nil]) -> 31
() -> butlast([nil, nil]) -> 31
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 34
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 34
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 34
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 32
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 32
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> cons(b, cons(a, nil))  ;  h1 -> a  ;  l2 -> cons(b, cons(a, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 48, which took 0.415506 s (model generation: 0.413125,  model checking: 0.002381):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8265, q_gen_8266, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8285},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, b>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8265) -> q_gen_8265
<cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8265
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8265
<a, a>() -> q_gen_8266
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8266, q_gen_8265) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8285) -> q_gen_8277
<cons, nil, cons>(q_gen_8266, q_gen_8260) -> q_gen_8277
<cons, nil, cons>(q_gen_8266, q_gen_8265) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
<cons, nil, cons>(q_gen_8261, q_gen_8265) -> q_gen_8285
<nil, cons, cons>(q_gen_8261, q_gen_8265) -> q_gen_8285
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> butlast([cons(y, nil), nil]) -> 32
() -> butlast([nil, nil]) -> 32
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 34
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 34
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 34
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 32
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 32
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 49, which took 0.430389 s (model generation: 0.415088,  model checking: 0.015301):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8266, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8285, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<b, b>() -> q_gen_8261
<a, a>() -> q_gen_8266
<a, b>() -> q_gen_8266
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<cons, nil, cons>(q_gen_8266, q_gen_8286) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8285) -> q_gen_8277
<cons, nil, cons>(q_gen_8266, q_gen_8260) -> q_gen_8277
<nil, cons, cons>(q_gen_8266, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8285
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<a, b>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> butlast([cons(y, nil), nil]) -> 33
() -> butlast([nil, nil]) -> 33
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 34
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 34
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 37
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 33
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 33
}
Sat witness: Found: ((append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]), {
_afa -> cons(b, cons(b, nil))  ;  _bfa -> cons(b, nil)  ;  _cfa -> nil  ;  xs -> cons(a, nil)  ;  ys -> nil
})

-------------------------------------------
Step 50, which took 0.449616 s (model generation: 0.444657,  model checking: 0.004959):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<a, b>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8253, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249, q_gen_8253},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<cons, cons>(q_gen_8254, q_gen_8253) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8253
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8256
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> butlast([cons(y, nil), nil]) -> 33
() -> butlast([nil, nil]) -> 33
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 34
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 34
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 37
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 33
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 36
}
Sat witness: Found: ((butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]), {
_kea -> cons(b, cons(a, nil))  ;  x2 -> b  ;  x3 -> cons(a, cons(a, nil))  ;  y -> b
})

-------------------------------------------
Step 51, which took 0.522920 s (model generation: 0.518802,  model checking: 0.004118):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<a, b>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334, q_gen_8335},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<cons, cons, cons>(q_gen_8297, q_gen_8335) -> q_gen_8335
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8335
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> butlast([cons(y, nil), nil]) -> 33
() -> butlast([nil, nil]) -> 33
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 34
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 34
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 37
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 36
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 36
}
Sat witness: Found: ((butlast([x, _tea])) -> butlastconcat([x, nil, _tea]), {
_tea -> cons(b, cons(b, nil))  ;  x -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 52, which took 0.513342 s (model generation: 0.504151,  model checking: 0.009191):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<a, b>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8302, q_gen_8334},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8256
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8302) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8302
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8302
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> butlast([cons(y, nil), nil]) -> 34
() -> butlast([nil, nil]) -> 34
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 34
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 37
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 37
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 36
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 36
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> cons(a, nil)  ;  _vea -> cons(b, nil)  ;  x -> nil  ;  x2 -> cons(b, nil)  ;  z -> a
})

-------------------------------------------
Step 53, which took 0.625638 s (model generation: 0.621603,  model checking: 0.004035):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8266, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8285, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, b>() -> q_gen_8261
<b, b>() -> q_gen_8261
<a, a>() -> q_gen_8266
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<cons, nil, cons>(q_gen_8266, q_gen_8286) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8285) -> q_gen_8277
<cons, nil, cons>(q_gen_8266, q_gen_8260) -> q_gen_8277
<nil, cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8285
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8288
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 34
() -> butlast([cons(y, nil), nil]) -> 34
() -> butlast([nil, nil]) -> 34
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 37
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 37
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 37
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 36
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 36
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> nil  ;  h1 -> a  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 54, which took 0.528782 s (model generation: 0.518657,  model checking: 0.010125):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<a, b>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8302, q_gen_8334},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8288) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8302
<cons, cons, cons>(q_gen_8297, q_gen_8302) -> q_gen_8302
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8302
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 35
() -> butlast([cons(y, nil), nil]) -> 35
() -> butlast([nil, nil]) -> 35
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 37
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 37
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 40
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 37
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 37
}
Sat witness: Found: ((append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]), {
_afa -> cons(b, nil)  ;  _bfa -> nil  ;  _cfa -> cons(b, nil)  ;  xs -> nil  ;  ys -> cons(b, nil)
})

-------------------------------------------
Step 55, which took 0.859177 s (model generation: 0.845784,  model checking: 0.013393):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8285, q_gen_8286, q_gen_8299},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<a, b>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, cons, cons>(q_gen_8299, q_gen_8277) -> q_gen_8252
<cons, cons, cons>(q_gen_8299, q_gen_8285) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8285) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<b, b, b>() -> q_gen_8280
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8285
<nil, cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8285
<a, a, a>() -> q_gen_8299
<a, b, a>() -> q_gen_8299
<b, a, b>() -> q_gen_8299
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 36
() -> butlast([cons(y, nil), nil]) -> 36
() -> butlast([nil, nil]) -> 36
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 37
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 40
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 40
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 38
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 38
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> nil  ;  _vea -> cons(b, cons(b, cons(b, nil)))  ;  x -> cons(b, cons(b, cons(a, nil)))  ;  x2 -> nil  ;  z -> b
})

-------------------------------------------
Step 56, which took 1.515971 s (model generation: 1.511546,  model checking: 0.004425):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8266, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8285, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<b, b>() -> q_gen_8261
<a, a>() -> q_gen_8266
<a, b>() -> q_gen_8266
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<cons, nil, cons>(q_gen_8266, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8285) -> q_gen_8277
<cons, nil, cons>(q_gen_8266, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8266, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8285
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<a, b>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 37
() -> butlast([cons(y, nil), nil]) -> 37
() -> butlast([nil, nil]) -> 37
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 40
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 40
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 40
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 38
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 38
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> cons(b, cons(a, nil))  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 57, which took 0.937024 s (model generation: 0.928565,  model checking: 0.008459):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<a, b>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334, q_gen_8335},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8288) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8256
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<cons, cons, cons>(q_gen_8297, q_gen_8335) -> q_gen_8335
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8335
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 38
() -> butlast([cons(y, nil), nil]) -> 38
() -> butlast([nil, nil]) -> 38
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 40
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 40
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 43
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 39
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 39
}
Sat witness: Found: ((append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]), {
_afa -> cons(b, cons(b, nil))  ;  _bfa -> cons(b, nil)  ;  _cfa -> cons(a, nil)  ;  xs -> nil  ;  ys -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 58, which took 0.745728 s (model generation: 0.731791,  model checking: 0.013937):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286, q_gen_8345},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<a, b>() -> q_gen_8345
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<cons, nil, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334, q_gen_8335},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<a, b>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<cons, cons, cons>(q_gen_8297, q_gen_8335) -> q_gen_8335
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8335
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 39
() -> butlast([cons(y, nil), nil]) -> 39
() -> butlast([nil, nil]) -> 39
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 40
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 43
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 43
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 40
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 40
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> cons(b, nil)  ;  _vea -> cons(b, cons(b, cons(b, nil)))  ;  x -> cons(b, cons(a, nil))  ;  x2 -> cons(b, nil)  ;  z -> b
})

-------------------------------------------
Step 59, which took 0.487372 s (model generation: 0.481159,  model checking: 0.006213):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8285, q_gen_8286, q_gen_8299},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<a, b>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, cons, cons>(q_gen_8299, q_gen_8277) -> q_gen_8252
<cons, cons, cons>(q_gen_8299, q_gen_8285) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8285) -> q_gen_8277
<nil, cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<b, b, b>() -> q_gen_8280
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8285
<a, a, a>() -> q_gen_8299
<a, b, a>() -> q_gen_8299
<b, a, b>() -> q_gen_8299
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8295, q_gen_8297, q_gen_8334},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, b>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, a>() -> q_gen_8295
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, cons>(q_gen_8295, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8295, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<a, b, b>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> butlast([cons(y, nil), nil]) -> 40
() -> butlast([nil, nil]) -> 40
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 40
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 43
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 43
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 43
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 41
}
Sat witness: Found: ((butlast([x, _tea])) -> butlastconcat([x, nil, _tea]), {
_tea -> cons(b, cons(a, nil))  ;  x -> cons(b, cons(a, cons(b, nil)))
})

-------------------------------------------
Step 60, which took 0.564930 s (model generation: 0.562647,  model checking: 0.002283):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8285, q_gen_8286, q_gen_8299},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<a, b>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, cons, cons>(q_gen_8299, q_gen_8277) -> q_gen_8252
<cons, cons, cons>(q_gen_8299, q_gen_8285) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8285) -> q_gen_8277
<nil, cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<b, b, b>() -> q_gen_8280
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8285
<a, a, a>() -> q_gen_8299
<a, b, a>() -> q_gen_8299
<b, a, b>() -> q_gen_8299
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267, q_gen_8269},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<cons, cons>(q_gen_8269, q_gen_8267) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
<cons, cons>(q_gen_8269, q_gen_8249) -> q_gen_8267
<a, a>() -> q_gen_8269
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8295, q_gen_8297},
Q_f={q_gen_8255},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8295, q_gen_8288) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, b>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8288
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, a>() -> q_gen_8295
<b, a>() -> q_gen_8295
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, cons>(q_gen_8295, q_gen_8271) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8295, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8295, q_gen_8288) -> q_gen_8270
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<a, b, b>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 40
() -> butlast([cons(y, nil), nil]) -> 40
() -> butlast([nil, nil]) -> 40
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 43
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 43
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 43
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 43
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 41
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> cons(b, cons(a, nil))  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 61, which took 0.625635 s (model generation: 0.619571,  model checking: 0.006064):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286, q_gen_8345},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<a, b>() -> q_gen_8345
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<cons, nil, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334, q_gen_8335},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8288) -> q_gen_8255
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8256
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<a, b, b>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<cons, cons, cons>(q_gen_8297, q_gen_8335) -> q_gen_8335
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8335
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 41
() -> butlast([cons(y, nil), nil]) -> 41
() -> butlast([nil, nil]) -> 41
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 43
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 43
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 46
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 44
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 42
}
Sat witness: Found: ((append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]), {
_afa -> cons(b, cons(b, nil))  ;  _bfa -> cons(b, nil)  ;  _cfa -> nil  ;  xs -> nil  ;  ys -> cons(a, nil)
})

-------------------------------------------
Step 62, which took 0.693837 s (model generation: 0.690975,  model checking: 0.002862):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<a, b>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8253, q_gen_8254, q_gen_8267, q_gen_8269},
Q_f={q_gen_8248, q_gen_8249, q_gen_8253},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<cons, cons>(q_gen_8254, q_gen_8253) -> q_gen_8248
<cons, cons>(q_gen_8269, q_gen_8249) -> q_gen_8248
<cons, cons>(q_gen_8269, q_gen_8267) -> q_gen_8248
<nil, nil>() -> q_gen_8248
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8253
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8253
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8269, q_gen_8253) -> q_gen_8267
<a, a>() -> q_gen_8269
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8295, q_gen_8297},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8295, q_gen_8288) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, b>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8288
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, a>() -> q_gen_8295
<b, a>() -> q_gen_8295
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, cons>(q_gen_8295, q_gen_8271) -> q_gen_8255
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8295, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8295, q_gen_8288) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<a, b, b>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 42
() -> butlast([cons(y, nil), nil]) -> 42
() -> butlast([nil, nil]) -> 42
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 43
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 43
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 46
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 44
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 45
}
Sat witness: Found: ((butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]), {
_kea -> cons(b, nil)  ;  x2 -> b  ;  x3 -> cons(a, nil)  ;  y -> a
})

-------------------------------------------
Step 63, which took 0.776435 s (model generation: 0.774489,  model checking: 0.001946):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<a, b>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8294, q_gen_8295, q_gen_8297, q_gen_8335},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, b>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8294
<cons, cons>(q_gen_8295, q_gen_8288) -> q_gen_8294
<a, a>() -> q_gen_8295
<b, a>() -> q_gen_8295
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8294) -> q_gen_8255
<cons, nil, cons>(q_gen_8295, q_gen_8294) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, cons>(q_gen_8295, q_gen_8271) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, cons, cons>(q_gen_8297, q_gen_8335) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<a, b, b>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<cons, nil, cons>(q_gen_8295, q_gen_8288) -> q_gen_8335
<nil, cons, cons>(q_gen_8295, q_gen_8288) -> q_gen_8335
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8335
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 43
() -> butlast([cons(y, nil), nil]) -> 43
() -> butlast([nil, nil]) -> 43
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 43
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 46
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 46
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 44
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 45
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> cons(a, nil)  ;  _vea -> cons(a, nil)  ;  x -> nil  ;  x2 -> cons(b, nil)  ;  z -> a
})

-------------------------------------------
Step 64, which took 0.642563 s (model generation: 0.624155,  model checking: 0.018408):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286, q_gen_8345},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<a, b>() -> q_gen_8345
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<cons, nil, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334, q_gen_8335},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, cons, cons>(q_gen_8297, q_gen_8335) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<a, b, b>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8335
<nil, cons, cons>(q_gen_8334, q_gen_8288) -> q_gen_8335
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8335
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 43
() -> butlast([cons(y, nil), nil]) -> 43
() -> butlast([nil, nil]) -> 43
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 46
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 46
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 46
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 44
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 45
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> a  ;  l2 -> cons(a, nil)  ;  t1 -> cons(b, cons(a, nil))
})

-------------------------------------------
Step 65, which took 0.600589 s (model generation: 0.595461,  model checking: 0.005128):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286, q_gen_8345},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8286
<cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<a, b>() -> q_gen_8345
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<cons, nil, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334, q_gen_8335},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<a, b>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8255
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<a, b, b>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<cons, cons, cons>(q_gen_8297, q_gen_8335) -> q_gen_8335
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8335
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 44
() -> butlast([cons(y, nil), nil]) -> 44
() -> butlast([nil, nil]) -> 44
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 46
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 46
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 49
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 45
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 46
}
Sat witness: Found: ((append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]), {
_afa -> cons(a, cons(b, nil))  ;  _bfa -> cons(a, nil)  ;  _cfa -> cons(b, nil)  ;  xs -> cons(a, cons(b, nil))  ;  ys -> nil
})

-------------------------------------------
Step 66, which took 1.531562 s (model generation: 1.525911,  model checking: 0.005651):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286, q_gen_8345},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8286
<cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<a, b>() -> q_gen_8345
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<cons, nil, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334, q_gen_8335},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8255
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8256
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<a, b, b>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<cons, cons, cons>(q_gen_8297, q_gen_8335) -> q_gen_8335
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8335
<nil, cons, cons>(q_gen_8334, q_gen_8288) -> q_gen_8335
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 45
() -> butlast([cons(y, nil), nil]) -> 45
() -> butlast([nil, nil]) -> 45
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 46
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 49
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 49
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 46
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 47
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> cons(b, cons(a, nil))  ;  _vea -> cons(b, cons(b, nil))  ;  x -> cons(b, nil)  ;  x2 -> cons(a, cons(b, nil))  ;  z -> b
})

-------------------------------------------
Step 67, which took 1.176038 s (model generation: 1.123497,  model checking: 0.052541):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286, q_gen_8345},
Q_f={q_gen_8252},
Delta=
{
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8260
<cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<a, b>() -> q_gen_8345
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<cons, nil, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334, q_gen_8335},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8288) -> q_gen_8255
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8256
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<a, b, b>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<cons, cons, cons>(q_gen_8297, q_gen_8335) -> q_gen_8335
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8335
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 46
() -> butlast([cons(y, nil), nil]) -> 46
() -> butlast([nil, nil]) -> 46
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 49
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 49
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 49
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 47
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 47
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> cons(b, cons(b, cons(b, nil)))  ;  h1 -> a  ;  l2 -> cons(b, cons(a, nil))  ;  t1 -> cons(b, nil)
})

-------------------------------------------
Step 68, which took 1.073562 s (model generation: 1.064693,  model checking: 0.008869):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286, q_gen_8345},
Q_f={q_gen_8252},
Delta=
{
<cons>(q_gen_8279, q_gen_8278) -> q_gen_8278
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<a, b>() -> q_gen_8345
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<cons, nil, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8334, q_gen_8335},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8256
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8334, q_gen_8288) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<a, b, b>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<cons, cons, cons>(q_gen_8297, q_gen_8335) -> q_gen_8335
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8335
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 47
() -> butlast([cons(y, nil), nil]) -> 47
() -> butlast([nil, nil]) -> 47
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 49
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 49
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 52
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 48
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 48
}
Sat witness: Found: ((append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]), {
_afa -> cons(b, cons(a, cons(b, nil)))  ;  _bfa -> cons(b, cons(a, nil))  ;  _cfa -> cons(b, cons(b, nil))  ;  xs -> cons(b, cons(a, cons(b, nil)))  ;  ys -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 69, which took 1.086911 s (model generation: 1.082938,  model checking: 0.003973):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286, q_gen_8345},
Q_f={q_gen_8252},
Delta=
{
<cons>(q_gen_8279, q_gen_8278) -> q_gen_8278
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8286
<cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<a, b>() -> q_gen_8345
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<cons, nil, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8256, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8288, q_gen_8297, q_gen_8302, q_gen_8334},
Q_f={q_gen_8255, q_gen_8256},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8288) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8256
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8256
<cons, cons, cons>(q_gen_8297, q_gen_8302) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8270
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<a, b, b>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<cons, cons, cons>(q_gen_8297, q_gen_8256) -> q_gen_8302
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8302
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8302
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 48
() -> butlast([cons(y, nil), nil]) -> 48
() -> butlast([nil, nil]) -> 48
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 49
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 52
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 52
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 49
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 49
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> cons(b, nil)  ;  _vea -> cons(b, nil)  ;  x -> cons(b, nil)  ;  x2 -> cons(b, nil)  ;  z -> b
})

-------------------------------------------
Step 70, which took 3.790930 s (model generation: 3.770249,  model checking: 0.020681):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286, q_gen_8345},
Q_f={q_gen_8252},
Delta=
{
<cons>(q_gen_8279, q_gen_8278) -> q_gen_8278
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8286
<cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<a, b>() -> q_gen_8345
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<cons, nil, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8283, q_gen_8288, q_gen_8297, q_gen_8302, q_gen_8334},
Q_f={q_gen_8255, q_gen_8283},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8302) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8334, q_gen_8288) -> q_gen_8270
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8283
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8283
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8283
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<a, b, b>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<cons, cons, cons>(q_gen_8297, q_gen_8283) -> q_gen_8302
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8302
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 49
() -> butlast([cons(y, nil), nil]) -> 49
() -> butlast([nil, nil]) -> 49
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 52
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 52
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 52
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 50
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 50
}
Sat witness: Found: ((append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]), {
_oea -> cons(a, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 71, which took 1.611952 s (model generation: 1.602140,  model checking: 0.009812):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286, q_gen_8345},
Q_f={q_gen_8252},
Delta=
{
<cons>(q_gen_8279, q_gen_8278) -> q_gen_8278
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<a, b>() -> q_gen_8345
<b, a>() -> q_gen_8345
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<cons, nil, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8283, q_gen_8288, q_gen_8297, q_gen_8302, q_gen_8334},
Q_f={q_gen_8255, q_gen_8283},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8302) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8270
<nil, cons, cons>(q_gen_8334, q_gen_8288) -> q_gen_8270
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8283
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8283
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8283
<a, a, a>() -> q_gen_8297
<a, b, a>() -> q_gen_8297
<a, b, b>() -> q_gen_8297
<b, a, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<cons, cons, cons>(q_gen_8297, q_gen_8283) -> q_gen_8302
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8302
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8302
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 50
() -> butlast([cons(y, nil), nil]) -> 50
() -> butlast([nil, nil]) -> 50
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 52
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 52
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 55
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 51
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 51
}
Sat witness: Found: ((append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]), {
_afa -> cons(a, cons(b, cons(b, nil)))  ;  _bfa -> cons(a, cons(b, nil))  ;  _cfa -> cons(b, cons(b, nil))  ;  xs -> cons(a, cons(b, nil))  ;  ys -> cons(b, nil)
})

-------------------------------------------
Step 72, which took 2.114645 s (model generation: 2.113729,  model checking: 0.000916):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8266, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286, q_gen_8305},
Q_f={q_gen_8252},
Delta=
{
<cons>(q_gen_8279, q_gen_8278) -> q_gen_8278
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, b>() -> q_gen_8261
<b, b>() -> q_gen_8261
<a, a>() -> q_gen_8266
<b, a>() -> q_gen_8266
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<cons, cons>(q_gen_8261, q_gen_8305) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8305
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8305) -> q_gen_8252
<cons, nil, cons>(q_gen_8266, q_gen_8260) -> q_gen_8252
<cons, nil, cons>(q_gen_8266, q_gen_8286) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8266, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8266, q_gen_8286) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<cons, nil, cons>(q_gen_8266, q_gen_8305) -> q_gen_8277
<nil, cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8261, q_gen_8305) -> q_gen_8277
<nil, cons, cons>(q_gen_8266, q_gen_8305) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8283, q_gen_8288, q_gen_8297, q_gen_8316, q_gen_8334},
Q_f={q_gen_8255, q_gen_8283},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8271
<cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8271
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, cons, cons>(q_gen_8316, q_gen_8270) -> q_gen_8255
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8270
<cons, cons, cons>(q_gen_8297, q_gen_8283) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8283
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8283
<a, a, a>() -> q_gen_8297
<a, b, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<a, b, a>() -> q_gen_8316
<b, a, b>() -> q_gen_8316
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 53
() -> butlast([cons(y, nil), nil]) -> 51
() -> butlast([nil, nil]) -> 51
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 52
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 52
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 55
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 51
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 51
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(b, cons(b, nil))
})

-------------------------------------------
Step 73, which took 3.663112 s (model generation: 3.658122,  model checking: 0.004990):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286, q_gen_8345},
Q_f={q_gen_8252},
Delta=
{
<cons>(q_gen_8279, q_gen_8278) -> q_gen_8278
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8260
<cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8260
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<a, b>() -> q_gen_8345
<b, a>() -> q_gen_8345
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<cons, nil, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8283, q_gen_8288, q_gen_8294, q_gen_8295, q_gen_8297, q_gen_8316},
Q_f={q_gen_8255, q_gen_8283},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<b, b>() -> q_gen_8272
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8294
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8294
<cons, cons>(q_gen_8295, q_gen_8271) -> q_gen_8294
<cons, cons>(q_gen_8295, q_gen_8288) -> q_gen_8294
<a, a>() -> q_gen_8295
<a, b>() -> q_gen_8295
<b, a>() -> q_gen_8295
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<cons, nil, cons>(q_gen_8272, q_gen_8294) -> q_gen_8255
<nil, cons, cons>(q_gen_8295, q_gen_8271) -> q_gen_8255
<nil, cons, cons>(q_gen_8295, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8270
<cons, cons, cons>(q_gen_8297, q_gen_8283) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8295, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, cons, cons>(q_gen_8316, q_gen_8270) -> q_gen_8283
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8283
<cons, nil, cons>(q_gen_8295, q_gen_8294) -> q_gen_8283
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8283
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8283
<a, a, a>() -> q_gen_8297
<a, b, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<a, b, a>() -> q_gen_8316
<b, a, b>() -> q_gen_8316
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 53
() -> butlast([cons(y, nil), nil]) -> 51
() -> butlast([nil, nil]) -> 51
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 52
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 52
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 55
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 54
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 52
}
Sat witness: Found: ((butlast([x, _tea])) -> butlastconcat([x, nil, _tea]), {
_tea -> cons(a, nil)  ;  x -> cons(a, cons(b, nil))
})

-------------------------------------------
Step 74, which took 6.082865 s (model generation: 6.071513,  model checking: 0.011352):

Model:
|_
{
append -> 
{{{
Q={q_gen_8252, q_gen_8260, q_gen_8261, q_gen_8265, q_gen_8277, q_gen_8278, q_gen_8279, q_gen_8280, q_gen_8286, q_gen_8345},
Q_f={q_gen_8252},
Delta=
{
<cons>(q_gen_8279, q_gen_8278) -> q_gen_8278
<nil>() -> q_gen_8278
<a>() -> q_gen_8279
<b>() -> q_gen_8279
<nil, nil>() -> q_gen_8260
<a, a>() -> q_gen_8261
<b, b>() -> q_gen_8261
<cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8265
<cons, cons>(q_gen_8261, q_gen_8265) -> q_gen_8286
<cons, cons>(q_gen_8261, q_gen_8286) -> q_gen_8286
<cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8286
<cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8286
<nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8286
<a, b>() -> q_gen_8345
<b, a>() -> q_gen_8345
<cons, cons, cons>(q_gen_8280, q_gen_8252) -> q_gen_8252
<cons, cons, cons>(q_gen_8280, q_gen_8277) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8265) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8260) -> q_gen_8252
<nil, cons, cons>(q_gen_8261, q_gen_8265) -> q_gen_8252
<nil, nil, nil>() -> q_gen_8252
<cons, nil, cons>(q_gen_8261, q_gen_8286) -> q_gen_8277
<cons, nil, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8260) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8265) -> q_gen_8277
<nil, cons, cons>(q_gen_8345, q_gen_8286) -> q_gen_8277
<nil, nil, cons>(q_gen_8279, q_gen_8278) -> q_gen_8277
<a, a, a>() -> q_gen_8280
<a, b, a>() -> q_gen_8280
<b, a, b>() -> q_gen_8280
<b, b, b>() -> q_gen_8280
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  butlast -> 
{{{
Q={q_gen_8248, q_gen_8249, q_gen_8250, q_gen_8251, q_gen_8254, q_gen_8267},
Q_f={q_gen_8248, q_gen_8249},
Delta=
{
<nil>() -> q_gen_8250
<a>() -> q_gen_8251
<b>() -> q_gen_8251
<nil, nil>() -> q_gen_8248
<cons, cons>(q_gen_8254, q_gen_8249) -> q_gen_8249
<cons, cons>(q_gen_8254, q_gen_8267) -> q_gen_8249
<cons, nil>(q_gen_8251, q_gen_8250) -> q_gen_8249
<a, a>() -> q_gen_8254
<b, b>() -> q_gen_8254
<cons, cons>(q_gen_8254, q_gen_8248) -> q_gen_8267
}

Datatype: <eltlist, eltlist>
Convolution form: left
}}}
  ;  butlastconcat -> 
{{{
Q={q_gen_8255, q_gen_8257, q_gen_8258, q_gen_8270, q_gen_8271, q_gen_8272, q_gen_8283, q_gen_8288, q_gen_8297, q_gen_8316, q_gen_8334},
Q_f={q_gen_8255, q_gen_8283},
Delta=
{
<nil>() -> q_gen_8257
<a>() -> q_gen_8258
<b>() -> q_gen_8258
<nil, nil>() -> q_gen_8271
<a, a>() -> q_gen_8272
<b, b>() -> q_gen_8272
<cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8288
<cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8288
<cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8288
<cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8288
<a, b>() -> q_gen_8334
<b, a>() -> q_gen_8334
<cons, cons, cons>(q_gen_8297, q_gen_8255) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8271) -> q_gen_8255
<nil, cons, cons>(q_gen_8334, q_gen_8288) -> q_gen_8255
<nil, cons, nil>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, cons>(q_gen_8258, q_gen_8257) -> q_gen_8255
<nil, nil, nil>() -> q_gen_8255
<cons, cons, cons>(q_gen_8297, q_gen_8270) -> q_gen_8270
<cons, cons, cons>(q_gen_8297, q_gen_8283) -> q_gen_8270
<cons, nil, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, nil, cons>(q_gen_8334, q_gen_8288) -> q_gen_8270
<nil, cons, cons>(q_gen_8272, q_gen_8271) -> q_gen_8270
<cons, cons, cons>(q_gen_8316, q_gen_8270) -> q_gen_8283
<cons, nil, cons>(q_gen_8272, q_gen_8288) -> q_gen_8283
<cons, nil, nil>(q_gen_8258, q_gen_8257) -> q_gen_8283
<nil, cons, cons>(q_gen_8272, q_gen_8288) -> q_gen_8283
<a, a, a>() -> q_gen_8297
<a, b, b>() -> q_gen_8297
<b, b, b>() -> q_gen_8297
<a, b, a>() -> q_gen_8316
<b, a, b>() -> q_gen_8316
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 53
() -> butlast([cons(y, nil), nil]) -> 52
() -> butlast([nil, nil]) -> 52
(append([t1, l2, _oea])) -> append([cons(h1, t1), l2, cons(h1, _oea)]) -> 52
(append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]) -> 55
(append([xs, ys, _afa]) /\ butlast([_afa, _bfa]) /\ butlastconcat([xs, ys, _cfa])) -> eq_eltlist([_bfa, _cfa]) -> 55
(butlast([x, _tea])) -> butlastconcat([x, nil, _tea]) -> 54
(butlast([cons(x2, x3), _kea])) -> butlast([cons(y, cons(x2, x3)), cons(y, _kea)]) -> 53
}
Sat witness: Found: ((append([x, _uea, _vea]) /\ butlast([cons(z, x2), _uea])) -> butlastconcat([x, cons(z, x2), _vea]), {
_uea -> nil  ;  _vea -> cons(b, cons(b, nil))  ;  x -> cons(b, cons(b, nil))  ;  x2 -> nil  ;  z -> b
})

Total time: 60.003842
Reason for stopping: DontKnow. Stopped because: timeout