Solving ../../benchmarks/false/list_delete_all_count.smt2...

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


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
definition:
{
(delete_one, F:
{() -> delete_one([x, nil, nil])
() -> delete_one([y, cons(y, r), r])
(delete_one([x, r, _cma]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _cma)])}
(delete_one([_dma, _ema, _fma]) /\ delete_one([_dma, _ema, _gma])) -> eq_eltlist([_fma, _gma])
)
(delete_all, F:
{() -> delete_all([x, nil, nil])
(delete_all([x, r, _ima]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _ima)])
(delete_all([y, r, _hma])) -> delete_all([y, cons(y, r), _hma])}
(delete_all([_jma, _kma, _lma]) /\ delete_all([_jma, _kma, _mma])) -> eq_eltlist([_lma, _mma])
)
(count, F:
{() -> count([x, nil, z])
(count([x, r, _oma]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _oma])
(count([y, r, _nma])) -> count([y, cons(y, r), s(_nma)])}
(count([_pma, _qma, _rma]) /\ count([_pma, _qma, _sma])) -> eq_nat([_rma, _sma])
)
}

properties:
{(count([x, l, _vma]) /\ delete_all([x, l, _uma]) /\ delete_one([x, l, _uma])) -> eq_nat([_vma, s(z)])}


over-approximation: {count, delete_all, delete_one}
under-approximation: {}

Clause system for inference is:

{
() -> count([x, nil, z]) -> 0
() -> delete_all([x, nil, nil]) -> 0
() -> delete_one([x, nil, nil]) -> 0
() -> delete_one([y, cons(y, r), r]) -> 0
(count([x, l, _vma]) /\ delete_all([x, l, _uma]) /\ delete_one([x, l, _uma])) -> eq_nat([_vma, s(z)]) -> 0
(count([x, r, _oma]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _oma]) -> 0
(count([y, r, _nma])) -> count([y, cons(y, r), s(_nma)]) -> 0
(delete_all([x, r, _ima]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _ima)]) -> 0
(delete_all([y, r, _hma])) -> delete_all([y, cons(y, r), _hma]) -> 0
(delete_one([x, r, _cma]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _cma)]) -> 0
}


Solving took 0.209259 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.017381 s (model generation: 0.015932,  model checking: 0.001449):

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 0
() -> delete_all([x, nil, nil]) -> 0
() -> delete_one([x, nil, nil]) -> 0
() -> delete_one([y, cons(y, r), r]) -> 3
(count([x, l, _vma]) /\ delete_all([x, l, _uma]) /\ delete_one([x, l, _uma])) -> eq_nat([_vma, s(z)]) -> 1
(count([x, r, _oma]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _oma]) -> 1
(count([y, r, _nma])) -> count([y, cons(y, r), s(_nma)]) -> 1
(delete_all([x, r, _ima]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _ima)]) -> 1
(delete_all([y, r, _hma])) -> delete_all([y, cons(y, r), _hma]) -> 1
(delete_one([x, r, _cma]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _cma)]) -> 1
}
Sat witness: Found: (() -> delete_one([y, cons(y, r), r]), {
r -> nil  ;  y -> b
})

-------------------------------------------
Step 1, which took 0.016991 s (model generation: 0.016524,  model checking: 0.000467):

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

}

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

}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  delete_one -> 
{{{
Q={q_gen_9050, q_gen_9051, q_gen_9052},
Q_f={q_gen_9050},
Delta=
{
<nil>() -> q_gen_9051
<b>() -> q_gen_9052
<b, cons, nil>(q_gen_9052, q_gen_9051) -> q_gen_9050
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 0
() -> delete_all([x, nil, nil]) -> 0
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
(count([x, l, _vma]) /\ delete_all([x, l, _uma]) /\ delete_one([x, l, _uma])) -> eq_nat([_vma, s(z)]) -> 1
(count([x, r, _oma]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _oma]) -> 1
(count([y, r, _nma])) -> count([y, cons(y, r), s(_nma)]) -> 1
(delete_all([x, r, _ima]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _ima)]) -> 1
(delete_all([y, r, _hma])) -> delete_all([y, cons(y, r), _hma]) -> 1
(delete_one([x, r, _cma]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _cma)]) -> 1
}
Sat witness: Found: (() -> delete_one([x, nil, nil]), {
x -> b
})

-------------------------------------------
Step 2, which took 0.017397 s (model generation: 0.017165,  model checking: 0.000232):

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

}

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

}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  delete_one -> 
{{{
Q={q_gen_9050, q_gen_9051, q_gen_9052},
Q_f={q_gen_9050},
Delta=
{
<nil>() -> q_gen_9051
<b>() -> q_gen_9052
<b, cons, nil>(q_gen_9052, q_gen_9051) -> q_gen_9050
<b, nil, nil>() -> q_gen_9050
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 0
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
(count([x, l, _vma]) /\ delete_all([x, l, _uma]) /\ delete_one([x, l, _uma])) -> eq_nat([_vma, s(z)]) -> 1
(count([x, r, _oma]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _oma]) -> 1
(count([y, r, _nma])) -> count([y, cons(y, r), s(_nma)]) -> 1
(delete_all([x, r, _ima]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _ima)]) -> 1
(delete_all([y, r, _hma])) -> delete_all([y, cons(y, r), _hma]) -> 1
(delete_one([x, r, _cma]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _cma)]) -> 1
}
Sat witness: Found: (() -> delete_all([x, nil, nil]), {
x -> b
})

-------------------------------------------
Step 3, which took 0.017586 s (model generation: 0.017383,  model checking: 0.000203):

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

}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  delete_all -> 
{{{
Q={q_gen_9054},
Q_f={q_gen_9054},
Delta=
{
<b, nil, nil>() -> q_gen_9054
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  delete_one -> 
{{{
Q={q_gen_9050, q_gen_9051, q_gen_9052},
Q_f={q_gen_9050},
Delta=
{
<nil>() -> q_gen_9051
<b>() -> q_gen_9052
<b, cons, nil>(q_gen_9052, q_gen_9051) -> q_gen_9050
<b, nil, nil>() -> q_gen_9050
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
(count([x, l, _vma]) /\ delete_all([x, l, _uma]) /\ delete_one([x, l, _uma])) -> eq_nat([_vma, s(z)]) -> 1
(count([x, r, _oma]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _oma]) -> 1
(count([y, r, _nma])) -> count([y, cons(y, r), s(_nma)]) -> 1
(delete_all([x, r, _ima]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _ima)]) -> 1
(delete_all([y, r, _hma])) -> delete_all([y, cons(y, r), _hma]) -> 1
(delete_one([x, r, _cma]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _cma)]) -> 1
}
Sat witness: Found: (() -> count([x, nil, z]), {
x -> b
})

-------------------------------------------
Step 4, which took 0.018504 s (model generation: 0.018001,  model checking: 0.000503):

Model:
|_
{
count -> 
{{{
Q={q_gen_9055},
Q_f={q_gen_9055},
Delta=
{
<b, nil, z>() -> q_gen_9055
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  delete_all -> 
{{{
Q={q_gen_9054},
Q_f={q_gen_9054},
Delta=
{
<b, nil, nil>() -> q_gen_9054
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  delete_one -> 
{{{
Q={q_gen_9050, q_gen_9051, q_gen_9052},
Q_f={q_gen_9050},
Delta=
{
<nil>() -> q_gen_9051
<b>() -> q_gen_9052
<b, cons, nil>(q_gen_9052, q_gen_9051) -> q_gen_9050
<b, nil, nil>() -> q_gen_9050
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
(count([x, l, _vma]) /\ delete_all([x, l, _uma]) /\ delete_one([x, l, _uma])) -> eq_nat([_vma, s(z)]) -> 1
(count([x, r, _oma]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _oma]) -> 1
(count([y, r, _nma])) -> count([y, cons(y, r), s(_nma)]) -> 1
(delete_all([x, r, _ima]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _ima)]) -> 1
(delete_all([y, r, _hma])) -> delete_all([y, cons(y, r), _hma]) -> 1
(delete_one([x, r, _cma]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _cma)]) -> 4
}
Sat witness: Found: ((delete_one([x, r, _cma]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _cma)]), {
_cma -> nil  ;  r -> nil  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 5, which took 0.018311 s (model generation: 0.017914,  model checking: 0.000397):

Model:
|_
{
count -> 
{{{
Q={q_gen_9055},
Q_f={q_gen_9055},
Delta=
{
<b, nil, z>() -> q_gen_9055
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  delete_all -> 
{{{
Q={q_gen_9054},
Q_f={q_gen_9054},
Delta=
{
<b, nil, nil>() -> q_gen_9054
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  delete_one -> 
{{{
Q={q_gen_9050, q_gen_9051, q_gen_9052, q_gen_9057, q_gen_9058},
Q_f={q_gen_9050},
Delta=
{
<nil>() -> q_gen_9051
<b>() -> q_gen_9052
<nil, nil>() -> q_gen_9057
<a, a>() -> q_gen_9058
<b, cons, cons>(q_gen_9058, q_gen_9057) -> q_gen_9050
<b, cons, nil>(q_gen_9052, q_gen_9051) -> q_gen_9050
<b, nil, nil>() -> q_gen_9050
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
(count([x, l, _vma]) /\ delete_all([x, l, _uma]) /\ delete_one([x, l, _uma])) -> eq_nat([_vma, s(z)]) -> 1
(count([x, r, _oma]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _oma]) -> 1
(count([y, r, _nma])) -> count([y, cons(y, r), s(_nma)]) -> 1
(delete_all([x, r, _ima]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _ima)]) -> 1
(delete_all([y, r, _hma])) -> delete_all([y, cons(y, r), _hma]) -> 4
(delete_one([x, r, _cma]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _cma)]) -> 4
}
Sat witness: Found: ((delete_all([y, r, _hma])) -> delete_all([y, cons(y, r), _hma]), {
_hma -> nil  ;  r -> nil  ;  y -> b
})

-------------------------------------------
Step 6, which took 0.019945 s (model generation: 0.019455,  model checking: 0.000490):

Model:
|_
{
count -> 
{{{
Q={q_gen_9055},
Q_f={q_gen_9055},
Delta=
{
<b, nil, z>() -> q_gen_9055
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  delete_all -> 
{{{
Q={q_gen_9054, q_gen_9060, q_gen_9061},
Q_f={q_gen_9054},
Delta=
{
<nil>() -> q_gen_9060
<b>() -> q_gen_9061
<b, cons, nil>(q_gen_9061, q_gen_9060) -> q_gen_9054
<b, nil, nil>() -> q_gen_9054
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  delete_one -> 
{{{
Q={q_gen_9050, q_gen_9051, q_gen_9052, q_gen_9057, q_gen_9058},
Q_f={q_gen_9050},
Delta=
{
<nil>() -> q_gen_9051
<b>() -> q_gen_9052
<nil, nil>() -> q_gen_9057
<a, a>() -> q_gen_9058
<b, cons, cons>(q_gen_9058, q_gen_9057) -> q_gen_9050
<b, cons, nil>(q_gen_9052, q_gen_9051) -> q_gen_9050
<b, nil, nil>() -> q_gen_9050
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
(count([x, l, _vma]) /\ delete_all([x, l, _uma]) /\ delete_one([x, l, _uma])) -> eq_nat([_vma, s(z)]) -> 1
(count([x, r, _oma]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _oma]) -> 1
(count([y, r, _nma])) -> count([y, cons(y, r), s(_nma)]) -> 1
(delete_all([x, r, _ima]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _ima)]) -> 4
(delete_all([y, r, _hma])) -> delete_all([y, cons(y, r), _hma]) -> 4
(delete_one([x, r, _cma]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _cma)]) -> 4
}
Sat witness: Found: ((delete_all([x, r, _ima]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _ima)]), {
_ima -> nil  ;  r -> nil  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 7, which took 0.020598 s (model generation: 0.020312,  model checking: 0.000286):

Model:
|_
{
count -> 
{{{
Q={q_gen_9055},
Q_f={q_gen_9055},
Delta=
{
<b, nil, z>() -> q_gen_9055
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  delete_all -> 
{{{
Q={q_gen_9054, q_gen_9060, q_gen_9061, q_gen_9063, q_gen_9064},
Q_f={q_gen_9054},
Delta=
{
<nil>() -> q_gen_9060
<b>() -> q_gen_9061
<nil, nil>() -> q_gen_9063
<a, a>() -> q_gen_9064
<b, cons, cons>(q_gen_9064, q_gen_9063) -> q_gen_9054
<b, cons, nil>(q_gen_9061, q_gen_9060) -> q_gen_9054
<b, nil, nil>() -> q_gen_9054
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  delete_one -> 
{{{
Q={q_gen_9050, q_gen_9051, q_gen_9052, q_gen_9057, q_gen_9058},
Q_f={q_gen_9050},
Delta=
{
<nil>() -> q_gen_9051
<b>() -> q_gen_9052
<nil, nil>() -> q_gen_9057
<a, a>() -> q_gen_9058
<b, cons, cons>(q_gen_9058, q_gen_9057) -> q_gen_9050
<b, cons, nil>(q_gen_9052, q_gen_9051) -> q_gen_9050
<b, nil, nil>() -> q_gen_9050
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
(count([x, l, _vma]) /\ delete_all([x, l, _uma]) /\ delete_one([x, l, _uma])) -> eq_nat([_vma, s(z)]) -> 1
(count([x, r, _oma]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _oma]) -> 1
(count([y, r, _nma])) -> count([y, cons(y, r), s(_nma)]) -> 4
(delete_all([x, r, _ima]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _ima)]) -> 4
(delete_all([y, r, _hma])) -> delete_all([y, cons(y, r), _hma]) -> 4
(delete_one([x, r, _cma]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _cma)]) -> 4
}
Sat witness: Found: ((count([y, r, _nma])) -> count([y, cons(y, r), s(_nma)]), {
_nma -> z  ;  r -> nil  ;  y -> b
})

-------------------------------------------
Step 8, which took 0.020693 s (model generation: 0.020039,  model checking: 0.000654):

Model:
|_
{
count -> 
{{{
Q={q_gen_9055, q_gen_9066, q_gen_9067},
Q_f={q_gen_9055},
Delta=
{
<nil>() -> q_gen_9066
<b, z>() -> q_gen_9067
<b, cons, s>(q_gen_9067, q_gen_9066) -> q_gen_9055
<b, nil, z>() -> q_gen_9055
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  delete_all -> 
{{{
Q={q_gen_9054, q_gen_9060, q_gen_9061, q_gen_9063, q_gen_9064},
Q_f={q_gen_9054},
Delta=
{
<nil>() -> q_gen_9060
<b>() -> q_gen_9061
<nil, nil>() -> q_gen_9063
<a, a>() -> q_gen_9064
<b, cons, cons>(q_gen_9064, q_gen_9063) -> q_gen_9054
<b, cons, nil>(q_gen_9061, q_gen_9060) -> q_gen_9054
<b, nil, nil>() -> q_gen_9054
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  delete_one -> 
{{{
Q={q_gen_9050, q_gen_9051, q_gen_9052, q_gen_9057, q_gen_9058},
Q_f={q_gen_9050},
Delta=
{
<nil>() -> q_gen_9051
<b>() -> q_gen_9052
<nil, nil>() -> q_gen_9057
<a, a>() -> q_gen_9058
<b, cons, cons>(q_gen_9058, q_gen_9057) -> q_gen_9050
<b, cons, nil>(q_gen_9052, q_gen_9051) -> q_gen_9050
<b, nil, nil>() -> q_gen_9050
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
(count([x, l, _vma]) /\ delete_all([x, l, _uma]) /\ delete_one([x, l, _uma])) -> eq_nat([_vma, s(z)]) -> 1
(count([x, r, _oma]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _oma]) -> 4
(count([y, r, _nma])) -> count([y, cons(y, r), s(_nma)]) -> 4
(delete_all([x, r, _ima]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _ima)]) -> 4
(delete_all([y, r, _hma])) -> delete_all([y, cons(y, r), _hma]) -> 4
(delete_one([x, r, _cma]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _cma)]) -> 4
}
Sat witness: Found: ((count([x, r, _oma]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _oma]), {
_oma -> z  ;  r -> nil  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 9, which took 0.021204 s (model generation: 0.020877,  model checking: 0.000327):

Model:
|_
{
count -> 
{{{
Q={q_gen_9055, q_gen_9066, q_gen_9067, q_gen_9069},
Q_f={q_gen_9055},
Delta=
{
<nil>() -> q_gen_9066
<a>() -> q_gen_9069
<b, z>() -> q_gen_9067
<b, cons, s>(q_gen_9067, q_gen_9066) -> q_gen_9055
<b, cons, z>(q_gen_9069, q_gen_9066) -> q_gen_9055
<b, nil, z>() -> q_gen_9055
}

Datatype: <elt, eltlist, nat>
Convolution form: left
}}}
  ;  delete_all -> 
{{{
Q={q_gen_9054, q_gen_9060, q_gen_9061, q_gen_9063, q_gen_9064},
Q_f={q_gen_9054},
Delta=
{
<nil>() -> q_gen_9060
<b>() -> q_gen_9061
<nil, nil>() -> q_gen_9063
<a, a>() -> q_gen_9064
<b, cons, cons>(q_gen_9064, q_gen_9063) -> q_gen_9054
<b, cons, nil>(q_gen_9061, q_gen_9060) -> q_gen_9054
<b, nil, nil>() -> q_gen_9054
}

Datatype: <elt, eltlist, eltlist>
Convolution form: left
}}}
  ;  delete_one -> 
{{{
Q={q_gen_9050, q_gen_9051, q_gen_9052, q_gen_9057, q_gen_9058},
Q_f={q_gen_9050},
Delta=
{
<nil>() -> q_gen_9051
<b>() -> q_gen_9052
<nil, nil>() -> q_gen_9057
<a, a>() -> q_gen_9058
<b, cons, cons>(q_gen_9058, q_gen_9057) -> q_gen_9050
<b, cons, nil>(q_gen_9052, q_gen_9051) -> q_gen_9050
<b, nil, nil>() -> q_gen_9050
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> delete_all([x, nil, nil]) -> 3
() -> delete_one([x, nil, nil]) -> 3
() -> delete_one([y, cons(y, r), r]) -> 3
(count([x, l, _vma]) /\ delete_all([x, l, _uma]) /\ delete_one([x, l, _uma])) -> eq_nat([_vma, s(z)]) -> 4
(count([x, r, _oma]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _oma]) -> 4
(count([y, r, _nma])) -> count([y, cons(y, r), s(_nma)]) -> 4
(delete_all([x, r, _ima]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _ima)]) -> 4
(delete_all([y, r, _hma])) -> delete_all([y, cons(y, r), _hma]) -> 4
(delete_one([x, r, _cma]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _cma)]) -> 4
}
Sat witness: Found: ((count([x, l, _vma]) /\ delete_all([x, l, _uma]) /\ delete_one([x, l, _uma])) -> eq_nat([_vma, s(z)]), {
_uma -> nil  ;  _vma -> z  ;  l -> nil  ;  x -> b
})

Total time: 0.209259
Reason for stopping: Disproved