Solving ../../benchmarks/true/length_delete.smt2...

Inference procedure has parameters:
Ice fuel: 200
Timeout: 30s
Convolution: complete


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
definition:
{
(leq, P:
{() -> leq([z, s(nn2)])
() -> leq([z, z])
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)])
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2])
(leq([s(nn1), z])) -> BOT}
)
(length, F:
{() -> length([nil, z])
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)])}
(length([_uv, _vv]) /\ length([_uv, _wv])) -> eq_nat([_vv, _wv])
)
(delete, F:
{() -> delete([x, nil, nil])
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv])
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)])}
(delete([_zv, _aw, _bw]) /\ delete([_zv, _aw, _cw])) -> eq_eltlist([_bw, _cw])
)
}

properties:
{(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw])}


over-approximation: {delete, length}
under-approximation: {leq}

Clause system for inference is:

{
() -> delete([x, nil, nil]) -> 0  ;  () -> length([nil, z]) -> 0  ;  () -> leq([z, s(nn2)]) -> 0  ;  () -> leq([z, z]) -> 0  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 0  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 0  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 0  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 0  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 0  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 0  ;  (leq([s(nn1), z])) -> BOT -> 0
}


Solving took 0.376270 seconds.
Proved
Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164, q_gen_3166, q_gen_3167},
Q_f={q_gen_3156},
Delta=
{
<cons>(q_gen_3167, q_gen_3166) -> q_gen_3166
<nil>() -> q_gen_3166
<a>() -> q_gen_3167
<b>() -> q_gen_3167
<cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3161
<cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3161
<nil, nil>() -> q_gen_3161
<cons, a>(q_gen_3167, q_gen_3166) -> q_gen_3162
<cons, b>(q_gen_3167, q_gen_3166) -> q_gen_3162
<nil, a>() -> q_gen_3162
<nil, b>() -> q_gen_3162
<a, cons>(q_gen_3167, q_gen_3166) -> q_gen_3163
<a, nil>() -> q_gen_3163
<b, cons>(q_gen_3167, q_gen_3166) -> q_gen_3163
<b, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<a, b>() -> q_gen_3164
<b, a>() -> q_gen_3164
<b, b>() -> q_gen_3164
<a, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<a, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<a, nil, nil>() -> q_gen_3156
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159, q_gen_3181},
Q_f={q_gen_3155},
Delta=
{
<s>(q_gen_3181) -> q_gen_3181
<z>() -> q_gen_3181
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<a, s>(q_gen_3181) -> q_gen_3159
<a, z>() -> q_gen_3159
<b, s>(q_gen_3181) -> q_gen_3159
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<s>(q_gen_3154) -> q_gen_3154
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.010570 s (model generation: 0.009740,  model checking: 0.000830):

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 0  ;  () -> length([nil, z]) -> 0  ;  () -> leq([z, s(nn2)]) -> 0  ;  () -> leq([z, z]) -> 3  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 1  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 1  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 1  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 1  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1  ;  (leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Yes: (() -> leq([z, z]), {

})

-------------------------------------------
Step 1, which took 0.010170 s (model generation: 0.010036,  model checking: 0.000134):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152},
Q_f={q_gen_3152},
Delta=
{
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 0  ;  () -> length([nil, z]) -> 0  ;  () -> leq([z, s(nn2)]) -> 3  ;  () -> leq([z, z]) -> 3  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 1  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 1  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 1  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 1  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1  ;  (leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Yes: (() -> leq([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.006483 s (model generation: 0.006229,  model checking: 0.000254):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<z>() -> q_gen_3154
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 0  ;  () -> length([nil, z]) -> 3  ;  () -> leq([z, s(nn2)]) -> 3  ;  () -> leq([z, z]) -> 3  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 1  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 1  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 1  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 1  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1  ;  (leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Yes: (() -> length([nil, z]), {

})

-------------------------------------------
Step 3, which took 0.003637 s (model generation: 0.003538,  model checking: 0.000099):

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

}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155},
Q_f={q_gen_3155},
Delta=
{
<nil, z>() -> q_gen_3155
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<z>() -> q_gen_3154
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> leq([z, s(nn2)]) -> 3  ;  () -> leq([z, z]) -> 3  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 1  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 1  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 1  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 1  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1  ;  (leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Yes: (() -> delete([x, nil, nil]), {
x -> b
})

-------------------------------------------
Step 4, which took 0.005757 s (model generation: 0.005411,  model checking: 0.000346):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156},
Q_f={q_gen_3156},
Delta=
{
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155},
Q_f={q_gen_3155},
Delta=
{
<nil, z>() -> q_gen_3155
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<z>() -> q_gen_3154
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> leq([z, s(nn2)]) -> 3  ;  () -> leq([z, z]) -> 3  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 1  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 1  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 1  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 1  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2  ;  (leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Yes: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 5, which took 0.011226 s (model generation: 0.010981,  model checking: 0.000245):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156},
Q_f={q_gen_3156},
Delta=
{
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155},
Q_f={q_gen_3155},
Delta=
{
<nil, z>() -> q_gen_3155
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> leq([z, s(nn2)]) -> 3  ;  () -> leq([z, z]) -> 3  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 1  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 1  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 1  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 4  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2  ;  (leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Yes: ((length([ll, _tv])) -> length([cons(x, ll), s(_tv)]), {
_tv -> z  ;  ll -> nil  ;  x -> b
})

-------------------------------------------
Step 6, which took 0.012167 s (model generation: 0.011019,  model checking: 0.001148):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156},
Q_f={q_gen_3156},
Delta=
{
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159},
Q_f={q_gen_3155},
Delta=
{
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> leq([z, s(nn2)]) -> 3  ;  () -> leq([z, z]) -> 3  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 1  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 1  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 4  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 4  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2  ;  (leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Yes: ((delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]), {
_yv -> nil  ;  h -> a  ;  t -> nil  ;  x -> b
})

-------------------------------------------
Step 7, which took 0.013435 s (model generation: 0.011557,  model checking: 0.001878):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164},
Q_f={q_gen_3156},
Delta=
{
<nil, nil>() -> q_gen_3161
<nil, a>() -> q_gen_3162
<a, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159},
Q_f={q_gen_3155},
Delta=
{
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> leq([z, s(nn2)]) -> 3  ;  () -> leq([z, z]) -> 3  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 4  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 2  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 4  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 4  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2  ;  (leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Yes: ((delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]), {
_xv -> nil  ;  h -> b  ;  t -> nil
})

-------------------------------------------
Step 8, which took 0.012600 s (model generation: 0.011947,  model checking: 0.000653):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164, q_gen_3166, q_gen_3167},
Q_f={q_gen_3156},
Delta=
{
<nil>() -> q_gen_3166
<b>() -> q_gen_3167
<nil, nil>() -> q_gen_3161
<nil, a>() -> q_gen_3162
<a, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159},
Q_f={q_gen_3155},
Delta=
{
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3  ;  () -> length([nil, z]) -> 3  ;  () -> leq([z, s(nn2)]) -> 6  ;  () -> leq([z, z]) -> 4  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 4  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 3  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 4  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 4  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 3  ;  (leq([s(nn1), z])) -> BOT -> 3
}
Sat witness: Yes: (() -> leq([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 9, which took 0.014078 s (model generation: 0.012548,  model checking: 0.001530):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164, q_gen_3166, q_gen_3167},
Q_f={q_gen_3156},
Delta=
{
<nil>() -> q_gen_3166
<b>() -> q_gen_3167
<nil, nil>() -> q_gen_3161
<nil, a>() -> q_gen_3162
<a, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159},
Q_f={q_gen_3155},
Delta=
{
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<s>(q_gen_3154) -> q_gen_3154
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 6  ;  () -> length([nil, z]) -> 4  ;  () -> leq([z, s(nn2)]) -> 6  ;  () -> leq([z, z]) -> 4  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 4  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 4  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 4  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 4  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4  ;  (leq([s(nn1), z])) -> BOT -> 4
}
Sat witness: Yes: (() -> delete([x, nil, nil]), {
x -> a
})

-------------------------------------------
Step 10, which took 0.013016 s (model generation: 0.012439,  model checking: 0.000577):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164, q_gen_3166, q_gen_3167},
Q_f={q_gen_3156},
Delta=
{
<nil>() -> q_gen_3166
<b>() -> q_gen_3167
<nil, nil>() -> q_gen_3161
<nil, a>() -> q_gen_3162
<a, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<a, nil, nil>() -> q_gen_3156
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159},
Q_f={q_gen_3155},
Delta=
{
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<s>(q_gen_3154) -> q_gen_3154
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 6  ;  () -> length([nil, z]) -> 4  ;  () -> leq([z, s(nn2)]) -> 6  ;  () -> leq([z, z]) -> 4  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 4  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 4  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 4  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 7  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5  ;  (leq([s(nn1), z])) -> BOT -> 5
}
Sat witness: Yes: ((length([ll, _tv])) -> length([cons(x, ll), s(_tv)]), {
_tv -> z  ;  ll -> nil  ;  x -> a
})

-------------------------------------------
Step 11, which took 0.016487 s (model generation: 0.012742,  model checking: 0.003745):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164, q_gen_3166, q_gen_3167},
Q_f={q_gen_3156},
Delta=
{
<nil>() -> q_gen_3166
<b>() -> q_gen_3167
<nil, nil>() -> q_gen_3161
<nil, a>() -> q_gen_3162
<a, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<a, nil, nil>() -> q_gen_3156
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159},
Q_f={q_gen_3155},
Delta=
{
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<a, z>() -> q_gen_3159
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<s>(q_gen_3154) -> q_gen_3154
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 6  ;  () -> length([nil, z]) -> 4  ;  () -> leq([z, s(nn2)]) -> 6  ;  () -> leq([z, z]) -> 4  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 4  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 4  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 7  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 7  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5  ;  (leq([s(nn1), z])) -> BOT -> 5
}
Sat witness: Yes: ((delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]), {
_yv -> nil  ;  h -> b  ;  t -> nil  ;  x -> a
})

-------------------------------------------
Step 12, which took 0.015497 s (model generation: 0.012781,  model checking: 0.002716):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164, q_gen_3166, q_gen_3167},
Q_f={q_gen_3156},
Delta=
{
<nil>() -> q_gen_3166
<b>() -> q_gen_3167
<nil, nil>() -> q_gen_3161
<nil, a>() -> q_gen_3162
<nil, b>() -> q_gen_3162
<a, nil>() -> q_gen_3163
<b, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<b, b>() -> q_gen_3164
<a, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<a, nil, nil>() -> q_gen_3156
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159},
Q_f={q_gen_3155},
Delta=
{
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<a, z>() -> q_gen_3159
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<s>(q_gen_3154) -> q_gen_3154
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 6  ;  () -> length([nil, z]) -> 4  ;  () -> leq([z, s(nn2)]) -> 6  ;  () -> leq([z, z]) -> 4  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 7  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 5  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 7  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 7  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5  ;  (leq([s(nn1), z])) -> BOT -> 5
}
Sat witness: Yes: ((delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]), {
_xv -> nil  ;  h -> a  ;  t -> nil
})

-------------------------------------------
Step 13, which took 0.015502 s (model generation: 0.013396,  model checking: 0.002106):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164, q_gen_3166, q_gen_3167},
Q_f={q_gen_3156},
Delta=
{
<nil>() -> q_gen_3166
<a>() -> q_gen_3167
<b>() -> q_gen_3167
<nil, nil>() -> q_gen_3161
<nil, a>() -> q_gen_3162
<nil, b>() -> q_gen_3162
<a, nil>() -> q_gen_3163
<b, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<b, b>() -> q_gen_3164
<a, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<a, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<a, nil, nil>() -> q_gen_3156
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159},
Q_f={q_gen_3155},
Delta=
{
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<a, z>() -> q_gen_3159
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<s>(q_gen_3154) -> q_gen_3154
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 7  ;  () -> length([nil, z]) -> 5  ;  () -> leq([z, s(nn2)]) -> 7  ;  () -> leq([z, z]) -> 5  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 7  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 6  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 7  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 10  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 6  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 6  ;  (leq([s(nn1), z])) -> BOT -> 6
}
Sat witness: Yes: ((length([ll, _tv])) -> length([cons(x, ll), s(_tv)]), {
_tv -> s(z)  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 14, which took 0.019123 s (model generation: 0.014068,  model checking: 0.005055):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164, q_gen_3166, q_gen_3167},
Q_f={q_gen_3156},
Delta=
{
<nil>() -> q_gen_3166
<a>() -> q_gen_3167
<b>() -> q_gen_3167
<nil, nil>() -> q_gen_3161
<nil, a>() -> q_gen_3162
<nil, b>() -> q_gen_3162
<a, nil>() -> q_gen_3163
<b, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<b, b>() -> q_gen_3164
<a, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<a, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<a, nil, nil>() -> q_gen_3156
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159, q_gen_3181},
Q_f={q_gen_3155},
Delta=
{
<z>() -> q_gen_3181
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<a, z>() -> q_gen_3159
<b, s>(q_gen_3181) -> q_gen_3159
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<s>(q_gen_3154) -> q_gen_3154
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 7  ;  () -> length([nil, z]) -> 6  ;  () -> leq([z, s(nn2)]) -> 7  ;  () -> leq([z, z]) -> 6  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 7  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 7  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 10  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 10  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 7  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 7  ;  (leq([s(nn1), z])) -> BOT -> 7
}
Sat witness: Yes: ((delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]), {
_yv -> nil  ;  h -> b  ;  t -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 15, which took 0.010499 s (model generation: 0.009484,  model checking: 0.001015):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164, q_gen_3166, q_gen_3167},
Q_f={q_gen_3156},
Delta=
{
<nil>() -> q_gen_3166
<a>() -> q_gen_3167
<b>() -> q_gen_3167
<cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3161
<nil, nil>() -> q_gen_3161
<cons, b>(q_gen_3167, q_gen_3166) -> q_gen_3162
<nil, a>() -> q_gen_3162
<nil, b>() -> q_gen_3162
<a, nil>() -> q_gen_3163
<b, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<b, b>() -> q_gen_3164
<a, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<a, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<a, nil, nil>() -> q_gen_3156
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159, q_gen_3181},
Q_f={q_gen_3155},
Delta=
{
<z>() -> q_gen_3181
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<a, z>() -> q_gen_3159
<b, s>(q_gen_3181) -> q_gen_3159
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<s>(q_gen_3154) -> q_gen_3154
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 7  ;  () -> length([nil, z]) -> 7  ;  () -> leq([z, s(nn2)]) -> 7  ;  () -> leq([z, z]) -> 7  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 10  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 8  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 10  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 10  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 8  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 8  ;  (leq([s(nn1), z])) -> BOT -> 8
}
Sat witness: Yes: ((delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]), {
_xv -> nil  ;  h -> b  ;  t -> cons(b, nil)
})

-------------------------------------------
Step 16, which took 0.010375 s (model generation: 0.009677,  model checking: 0.000698):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164, q_gen_3166, q_gen_3167},
Q_f={q_gen_3156},
Delta=
{
<cons>(q_gen_3167, q_gen_3166) -> q_gen_3166
<nil>() -> q_gen_3166
<a>() -> q_gen_3167
<b>() -> q_gen_3167
<cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3161
<nil, nil>() -> q_gen_3161
<cons, b>(q_gen_3167, q_gen_3166) -> q_gen_3162
<nil, a>() -> q_gen_3162
<nil, b>() -> q_gen_3162
<a, nil>() -> q_gen_3163
<b, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<b, b>() -> q_gen_3164
<a, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<a, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<a, nil, nil>() -> q_gen_3156
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159, q_gen_3181},
Q_f={q_gen_3155},
Delta=
{
<z>() -> q_gen_3181
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<a, z>() -> q_gen_3159
<b, s>(q_gen_3181) -> q_gen_3159
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<s>(q_gen_3154) -> q_gen_3154
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 8  ;  () -> length([nil, z]) -> 8  ;  () -> leq([z, s(nn2)]) -> 8  ;  () -> leq([z, z]) -> 8  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 10  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 9  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 10  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 13  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 9  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 9  ;  (leq([s(nn1), z])) -> BOT -> 9
}
Sat witness: Yes: ((length([ll, _tv])) -> length([cons(x, ll), s(_tv)]), {
_tv -> s(z)  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 17, which took 0.019316 s (model generation: 0.012338,  model checking: 0.006978):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164, q_gen_3166, q_gen_3167},
Q_f={q_gen_3156},
Delta=
{
<cons>(q_gen_3167, q_gen_3166) -> q_gen_3166
<nil>() -> q_gen_3166
<a>() -> q_gen_3167
<b>() -> q_gen_3167
<cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3161
<nil, nil>() -> q_gen_3161
<cons, b>(q_gen_3167, q_gen_3166) -> q_gen_3162
<nil, a>() -> q_gen_3162
<nil, b>() -> q_gen_3162
<a, nil>() -> q_gen_3163
<b, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<b, b>() -> q_gen_3164
<a, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<a, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<a, nil, nil>() -> q_gen_3156
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159, q_gen_3181},
Q_f={q_gen_3155},
Delta=
{
<z>() -> q_gen_3181
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<a, s>(q_gen_3181) -> q_gen_3159
<a, z>() -> q_gen_3159
<b, s>(q_gen_3181) -> q_gen_3159
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<s>(q_gen_3154) -> q_gen_3154
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 9  ;  () -> length([nil, z]) -> 9  ;  () -> leq([z, s(nn2)]) -> 9  ;  () -> leq([z, z]) -> 9  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 10  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 10  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 13  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 13  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 10  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 10  ;  (leq([s(nn1), z])) -> BOT -> 10
}
Sat witness: Yes: ((delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]), {
_yv -> nil  ;  h -> a  ;  t -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 18, which took 0.021002 s (model generation: 0.017873,  model checking: 0.003129):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164, q_gen_3166, q_gen_3167},
Q_f={q_gen_3156},
Delta=
{
<cons>(q_gen_3167, q_gen_3166) -> q_gen_3166
<nil>() -> q_gen_3166
<a>() -> q_gen_3167
<b>() -> q_gen_3167
<cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3161
<nil, nil>() -> q_gen_3161
<cons, a>(q_gen_3167, q_gen_3166) -> q_gen_3162
<cons, b>(q_gen_3167, q_gen_3166) -> q_gen_3162
<nil, a>() -> q_gen_3162
<nil, b>() -> q_gen_3162
<a, nil>() -> q_gen_3163
<b, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<b, b>() -> q_gen_3164
<a, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<a, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<a, nil, nil>() -> q_gen_3156
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159, q_gen_3181},
Q_f={q_gen_3155},
Delta=
{
<z>() -> q_gen_3181
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<a, s>(q_gen_3181) -> q_gen_3159
<a, z>() -> q_gen_3159
<b, s>(q_gen_3181) -> q_gen_3159
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<s>(q_gen_3154) -> q_gen_3154
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 10  ;  () -> length([nil, z]) -> 10  ;  () -> leq([z, s(nn2)]) -> 10  ;  () -> leq([z, z]) -> 10  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 13  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 11  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 13  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 13  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 11  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 11  ;  (leq([s(nn1), z])) -> BOT -> 11
}
Sat witness: Yes: ((delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]), {
_xv -> cons(b, nil)  ;  h -> a  ;  t -> cons(b, nil)
})

-------------------------------------------
Step 19, which took 0.021203 s (model generation: 0.019482,  model checking: 0.001721):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164, q_gen_3166, q_gen_3167},
Q_f={q_gen_3156},
Delta=
{
<cons>(q_gen_3167, q_gen_3166) -> q_gen_3166
<nil>() -> q_gen_3166
<a>() -> q_gen_3167
<b>() -> q_gen_3167
<cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3161
<nil, nil>() -> q_gen_3161
<cons, a>(q_gen_3167, q_gen_3166) -> q_gen_3162
<cons, b>(q_gen_3167, q_gen_3166) -> q_gen_3162
<nil, a>() -> q_gen_3162
<nil, b>() -> q_gen_3162
<a, nil>() -> q_gen_3163
<b, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<a, b>() -> q_gen_3164
<b, b>() -> q_gen_3164
<a, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<a, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<a, nil, nil>() -> q_gen_3156
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159, q_gen_3181},
Q_f={q_gen_3155},
Delta=
{
<z>() -> q_gen_3181
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<a, s>(q_gen_3181) -> q_gen_3159
<a, z>() -> q_gen_3159
<b, s>(q_gen_3181) -> q_gen_3159
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<s>(q_gen_3154) -> q_gen_3154
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 11  ;  () -> length([nil, z]) -> 11  ;  () -> leq([z, s(nn2)]) -> 11  ;  () -> leq([z, z]) -> 11  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 13  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 12  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 13  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 16  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 12  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 12  ;  (leq([s(nn1), z])) -> BOT -> 12
}
Sat witness: Yes: ((length([ll, _tv])) -> length([cons(x, ll), s(_tv)]), {
_tv -> s(s(z))  ;  ll -> cons(b, cons(b, nil))  ;  x -> b
})

-------------------------------------------
Step 20, which took 0.025709 s (model generation: 0.020292,  model checking: 0.005417):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164, q_gen_3166, q_gen_3167},
Q_f={q_gen_3156},
Delta=
{
<cons>(q_gen_3167, q_gen_3166) -> q_gen_3166
<nil>() -> q_gen_3166
<a>() -> q_gen_3167
<b>() -> q_gen_3167
<cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3161
<nil, nil>() -> q_gen_3161
<cons, a>(q_gen_3167, q_gen_3166) -> q_gen_3162
<cons, b>(q_gen_3167, q_gen_3166) -> q_gen_3162
<nil, a>() -> q_gen_3162
<nil, b>() -> q_gen_3162
<a, nil>() -> q_gen_3163
<b, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<a, b>() -> q_gen_3164
<b, b>() -> q_gen_3164
<a, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<a, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<a, nil, nil>() -> q_gen_3156
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159, q_gen_3181},
Q_f={q_gen_3155},
Delta=
{
<s>(q_gen_3181) -> q_gen_3181
<z>() -> q_gen_3181
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<a, s>(q_gen_3181) -> q_gen_3159
<a, z>() -> q_gen_3159
<b, s>(q_gen_3181) -> q_gen_3159
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<s>(q_gen_3154) -> q_gen_3154
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 12  ;  () -> length([nil, z]) -> 12  ;  () -> leq([z, s(nn2)]) -> 12  ;  () -> leq([z, z]) -> 12  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 13  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 13  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 16  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 16  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 13  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 13  ;  (leq([s(nn1), z])) -> BOT -> 13
}
Sat witness: Yes: ((delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]), {
_yv -> cons(b, nil)  ;  h -> a  ;  t -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 21, which took 0.023733 s (model generation: 0.021503,  model checking: 0.002230):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164, q_gen_3166, q_gen_3167},
Q_f={q_gen_3156},
Delta=
{
<cons>(q_gen_3167, q_gen_3166) -> q_gen_3166
<nil>() -> q_gen_3166
<a>() -> q_gen_3167
<b>() -> q_gen_3167
<cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3161
<cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3161
<nil, nil>() -> q_gen_3161
<cons, a>(q_gen_3167, q_gen_3166) -> q_gen_3162
<cons, b>(q_gen_3167, q_gen_3166) -> q_gen_3162
<nil, a>() -> q_gen_3162
<nil, b>() -> q_gen_3162
<a, cons>(q_gen_3167, q_gen_3166) -> q_gen_3163
<a, nil>() -> q_gen_3163
<b, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<a, b>() -> q_gen_3164
<b, b>() -> q_gen_3164
<a, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<a, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<a, nil, nil>() -> q_gen_3156
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159, q_gen_3181},
Q_f={q_gen_3155},
Delta=
{
<s>(q_gen_3181) -> q_gen_3181
<z>() -> q_gen_3181
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<a, s>(q_gen_3181) -> q_gen_3159
<a, z>() -> q_gen_3159
<b, s>(q_gen_3181) -> q_gen_3159
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<s>(q_gen_3154) -> q_gen_3154
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 13  ;  () -> length([nil, z]) -> 13  ;  () -> leq([z, s(nn2)]) -> 13  ;  () -> leq([z, z]) -> 13  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 16  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 14  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 16  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 16  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 14  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 14  ;  (leq([s(nn1), z])) -> BOT -> 14
}
Sat witness: Yes: ((delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]), {
_xv -> cons(a, nil)  ;  h -> b  ;  t -> cons(a, nil)
})

-------------------------------------------
Step 22, which took 0.025057 s (model generation: 0.022156,  model checking: 0.002901):

Model:
|_
{
delete -> 
{{{
Q={q_gen_3156, q_gen_3161, q_gen_3162, q_gen_3163, q_gen_3164, q_gen_3166, q_gen_3167},
Q_f={q_gen_3156},
Delta=
{
<cons>(q_gen_3167, q_gen_3166) -> q_gen_3166
<nil>() -> q_gen_3166
<a>() -> q_gen_3167
<b>() -> q_gen_3167
<cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3161
<cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3161
<nil, nil>() -> q_gen_3161
<cons, a>(q_gen_3167, q_gen_3166) -> q_gen_3162
<cons, b>(q_gen_3167, q_gen_3166) -> q_gen_3162
<nil, a>() -> q_gen_3162
<nil, b>() -> q_gen_3162
<a, cons>(q_gen_3167, q_gen_3166) -> q_gen_3163
<a, nil>() -> q_gen_3163
<b, nil>() -> q_gen_3163
<a, a>() -> q_gen_3164
<a, b>() -> q_gen_3164
<b, a>() -> q_gen_3164
<b, b>() -> q_gen_3164
<a, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<a, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<a, nil, nil>() -> q_gen_3156
<b, cons, cons>(q_gen_3164, q_gen_3163, q_gen_3162, q_gen_3161) -> q_gen_3156
<b, cons, nil>(q_gen_3167, q_gen_3166) -> q_gen_3156
<b, nil, nil>() -> q_gen_3156
}

Datatype: <elt, eltlist, eltlist>
Convolution form: complete
}}}
  ;  length -> 
{{{
Q={q_gen_3155, q_gen_3159, q_gen_3181},
Q_f={q_gen_3155},
Delta=
{
<s>(q_gen_3181) -> q_gen_3181
<z>() -> q_gen_3181
<cons, s>(q_gen_3159, q_gen_3155) -> q_gen_3155
<nil, z>() -> q_gen_3155
<a, s>(q_gen_3181) -> q_gen_3159
<a, z>() -> q_gen_3159
<b, s>(q_gen_3181) -> q_gen_3159
<b, z>() -> q_gen_3159
}

Datatype: <eltlist, nat>
Convolution form: complete
}}}
  ;  leq -> 
{{{
Q={q_gen_3152, q_gen_3154},
Q_f={q_gen_3152},
Delta=
{
<s>(q_gen_3154) -> q_gen_3154
<z>() -> q_gen_3154
<s, s>(q_gen_3152) -> q_gen_3152
<z, s>(q_gen_3154) -> q_gen_3152
<z, z>() -> q_gen_3152
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 14  ;  () -> length([nil, z]) -> 14  ;  () -> leq([z, s(nn2)]) -> 14  ;  () -> leq([z, z]) -> 14  ;  (delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 16  ;  (delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 15  ;  (delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 19  ;  (length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 17  ;  (leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 15  ;  (leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 15  ;  (leq([s(nn1), z])) -> BOT -> 15
}
Sat witness: Yes: ((delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]), {
_yv -> cons(b, nil)  ;  h -> b  ;  t -> cons(b, nil)  ;  x -> a
})

Total time: 0.376270
Reason for stopping: Proved