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

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


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, _tha]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _tha)])}
(delete_one([_uha, _vha, _wha]) /\ delete_one([_uha, _vha, _xha])) -> eq_eltlist([_wha, _xha])
)
(delete_all, F:
{() -> delete_all([x, nil, nil])
(delete_all([x, r, _zha]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _zha)])
(delete_all([y, r, _yha])) -> delete_all([y, cons(y, r), _yha])}
(delete_all([_aia, _bia, _cia]) /\ delete_all([_aia, _bia, _dia])) -> eq_eltlist([_cia, _dia])
)
(count, F:
{() -> count([x, nil, z])
(count([x, r, _fia]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _fia])
(count([y, r, _eia])) -> count([y, cons(y, r), s(_eia)])}
(count([_gia, _hia, _iia]) /\ count([_gia, _hia, _jia])) -> eq_nat([_iia, _jia])
)
}

properties:
{(count([x, l, _mia]) /\ delete_all([x, l, _lia]) /\ delete_one([x, l, _lia])) -> eq_nat([_mia, 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, _mia]) /\ delete_all([x, l, _lia]) /\ delete_one([x, l, _lia])) -> eq_nat([_mia, s(z)]) -> 0
(count([x, r, _fia]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _fia]) -> 0
(count([y, r, _eia])) -> count([y, cons(y, r), s(_eia)]) -> 0
(delete_all([x, r, _zha]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _zha)]) -> 0
(delete_all([y, r, _yha])) -> delete_all([y, cons(y, r), _yha]) -> 0
(delete_one([x, r, _tha]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _tha)]) -> 0
}


Solving took 0.129509 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.011505 s (model generation: 0.010198,  model checking: 0.001307):

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

}

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

}

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

}

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

}
--
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, _mia]) /\ delete_all([x, l, _lia]) /\ delete_one([x, l, _lia])) -> eq_nat([_mia, s(z)]) -> 1
(count([x, r, _fia]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _fia]) -> 1
(count([y, r, _eia])) -> count([y, cons(y, r), s(_eia)]) -> 1
(delete_all([x, r, _zha]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _zha)]) -> 1
(delete_all([y, r, _yha])) -> delete_all([y, cons(y, r), _yha]) -> 1
(delete_one([x, r, _tha]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _tha)]) -> 1
}
Sat witness: Found: (() -> delete_one([y, cons(y, r), r]), {
r -> nil  ;  y -> b
})

-------------------------------------------
Step 1, which took 0.011374 s (model generation: 0.010989,  model checking: 0.000385):

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

}

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

}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_6552, q_gen_6553, q_gen_6554},
Q_f={q_gen_6552},
Delta=
{
<nil>() -> q_gen_6553
<b>() -> q_gen_6554
<b, cons, nil>(q_gen_6554, q_gen_6553) -> q_gen_6552
}

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

}
--
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, _mia]) /\ delete_all([x, l, _lia]) /\ delete_one([x, l, _lia])) -> eq_nat([_mia, s(z)]) -> 1
(count([x, r, _fia]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _fia]) -> 1
(count([y, r, _eia])) -> count([y, cons(y, r), s(_eia)]) -> 1
(delete_all([x, r, _zha]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _zha)]) -> 1
(delete_all([y, r, _yha])) -> delete_all([y, cons(y, r), _yha]) -> 1
(delete_one([x, r, _tha]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _tha)]) -> 1
}
Sat witness: Found: (() -> delete_one([x, nil, nil]), {
x -> b
})

-------------------------------------------
Step 2, which took 0.011239 s (model generation: 0.011016,  model checking: 0.000223):

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

}

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

}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_6552, q_gen_6553, q_gen_6554},
Q_f={q_gen_6552},
Delta=
{
<nil>() -> q_gen_6553
<b>() -> q_gen_6554
<b, cons, nil>(q_gen_6554, q_gen_6553) -> q_gen_6552
<b, nil, nil>() -> q_gen_6552
}

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

}
--
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, _mia]) /\ delete_all([x, l, _lia]) /\ delete_one([x, l, _lia])) -> eq_nat([_mia, s(z)]) -> 1
(count([x, r, _fia]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _fia]) -> 1
(count([y, r, _eia])) -> count([y, cons(y, r), s(_eia)]) -> 1
(delete_all([x, r, _zha]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _zha)]) -> 1
(delete_all([y, r, _yha])) -> delete_all([y, cons(y, r), _yha]) -> 1
(delete_one([x, r, _tha]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _tha)]) -> 1
}
Sat witness: Found: (() -> delete_all([x, nil, nil]), {
x -> b
})

-------------------------------------------
Step 3, which took 0.011195 s (model generation: 0.010989,  model checking: 0.000206):

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

}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_6556},
Q_f={q_gen_6556},
Delta=
{
<b, nil, nil>() -> q_gen_6556
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_6552, q_gen_6553, q_gen_6554},
Q_f={q_gen_6552},
Delta=
{
<nil>() -> q_gen_6553
<b>() -> q_gen_6554
<b, cons, nil>(q_gen_6554, q_gen_6553) -> q_gen_6552
<b, nil, nil>() -> q_gen_6552
}

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

}
--
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, _mia]) /\ delete_all([x, l, _lia]) /\ delete_one([x, l, _lia])) -> eq_nat([_mia, s(z)]) -> 1
(count([x, r, _fia]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _fia]) -> 1
(count([y, r, _eia])) -> count([y, cons(y, r), s(_eia)]) -> 1
(delete_all([x, r, _zha]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _zha)]) -> 1
(delete_all([y, r, _yha])) -> delete_all([y, cons(y, r), _yha]) -> 1
(delete_one([x, r, _tha]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _tha)]) -> 1
}
Sat witness: Found: (() -> count([x, nil, z]), {
x -> b
})

-------------------------------------------
Step 4, which took 0.011754 s (model generation: 0.011233,  model checking: 0.000521):

Model:
|_
{
count -> 
{{{
Q={q_gen_6557},
Q_f={q_gen_6557},
Delta=
{
<b, nil, z>() -> q_gen_6557
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_6556},
Q_f={q_gen_6556},
Delta=
{
<b, nil, nil>() -> q_gen_6556
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_6552, q_gen_6553, q_gen_6554},
Q_f={q_gen_6552},
Delta=
{
<nil>() -> q_gen_6553
<b>() -> q_gen_6554
<b, cons, nil>(q_gen_6554, q_gen_6553) -> q_gen_6552
<b, nil, nil>() -> q_gen_6552
}

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

}
--
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, _mia]) /\ delete_all([x, l, _lia]) /\ delete_one([x, l, _lia])) -> eq_nat([_mia, s(z)]) -> 1
(count([x, r, _fia]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _fia]) -> 1
(count([y, r, _eia])) -> count([y, cons(y, r), s(_eia)]) -> 1
(delete_all([x, r, _zha]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _zha)]) -> 1
(delete_all([y, r, _yha])) -> delete_all([y, cons(y, r), _yha]) -> 1
(delete_one([x, r, _tha]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _tha)]) -> 4
}
Sat witness: Found: ((delete_one([x, r, _tha]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _tha)]), {
_tha -> nil  ;  r -> nil  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 5, which took 0.011379 s (model generation: 0.011101,  model checking: 0.000278):

Model:
|_
{
count -> 
{{{
Q={q_gen_6557},
Q_f={q_gen_6557},
Delta=
{
<b, nil, z>() -> q_gen_6557
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_6556},
Q_f={q_gen_6556},
Delta=
{
<b, nil, nil>() -> q_gen_6556
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_6552, q_gen_6553, q_gen_6554, q_gen_6559, q_gen_6560},
Q_f={q_gen_6552},
Delta=
{
<nil>() -> q_gen_6553
<b>() -> q_gen_6554
<nil, nil>() -> q_gen_6559
<a, a>() -> q_gen_6560
<b, cons, cons>(q_gen_6560, q_gen_6559) -> q_gen_6552
<b, cons, nil>(q_gen_6554, q_gen_6553) -> q_gen_6552
<b, nil, nil>() -> q_gen_6552
}

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

}
--
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, _mia]) /\ delete_all([x, l, _lia]) /\ delete_one([x, l, _lia])) -> eq_nat([_mia, s(z)]) -> 1
(count([x, r, _fia]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _fia]) -> 1
(count([y, r, _eia])) -> count([y, cons(y, r), s(_eia)]) -> 1
(delete_all([x, r, _zha]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _zha)]) -> 1
(delete_all([y, r, _yha])) -> delete_all([y, cons(y, r), _yha]) -> 4
(delete_one([x, r, _tha]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _tha)]) -> 4
}
Sat witness: Found: ((delete_all([y, r, _yha])) -> delete_all([y, cons(y, r), _yha]), {
_yha -> nil  ;  r -> nil  ;  y -> b
})

-------------------------------------------
Step 6, which took 0.011793 s (model generation: 0.011363,  model checking: 0.000430):

Model:
|_
{
count -> 
{{{
Q={q_gen_6557},
Q_f={q_gen_6557},
Delta=
{
<b, nil, z>() -> q_gen_6557
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_6556, q_gen_6562, q_gen_6563},
Q_f={q_gen_6556},
Delta=
{
<nil>() -> q_gen_6562
<b>() -> q_gen_6563
<b, cons, nil>(q_gen_6563, q_gen_6562) -> q_gen_6556
<b, nil, nil>() -> q_gen_6556
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_6552, q_gen_6553, q_gen_6554, q_gen_6559, q_gen_6560},
Q_f={q_gen_6552},
Delta=
{
<nil>() -> q_gen_6553
<b>() -> q_gen_6554
<nil, nil>() -> q_gen_6559
<a, a>() -> q_gen_6560
<b, cons, cons>(q_gen_6560, q_gen_6559) -> q_gen_6552
<b, cons, nil>(q_gen_6554, q_gen_6553) -> q_gen_6552
<b, nil, nil>() -> q_gen_6552
}

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

}
--
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, _mia]) /\ delete_all([x, l, _lia]) /\ delete_one([x, l, _lia])) -> eq_nat([_mia, s(z)]) -> 1
(count([x, r, _fia]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _fia]) -> 1
(count([y, r, _eia])) -> count([y, cons(y, r), s(_eia)]) -> 1
(delete_all([x, r, _zha]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _zha)]) -> 4
(delete_all([y, r, _yha])) -> delete_all([y, cons(y, r), _yha]) -> 4
(delete_one([x, r, _tha]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _tha)]) -> 4
}
Sat witness: Found: ((delete_all([x, r, _zha]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _zha)]), {
_zha -> nil  ;  r -> nil  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 7, which took 0.012007 s (model generation: 0.011767,  model checking: 0.000240):

Model:
|_
{
count -> 
{{{
Q={q_gen_6557},
Q_f={q_gen_6557},
Delta=
{
<b, nil, z>() -> q_gen_6557
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_6556, q_gen_6562, q_gen_6563, q_gen_6565, q_gen_6566},
Q_f={q_gen_6556},
Delta=
{
<nil>() -> q_gen_6562
<b>() -> q_gen_6563
<nil, nil>() -> q_gen_6565
<a, a>() -> q_gen_6566
<b, cons, cons>(q_gen_6566, q_gen_6565) -> q_gen_6556
<b, cons, nil>(q_gen_6563, q_gen_6562) -> q_gen_6556
<b, nil, nil>() -> q_gen_6556
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_6552, q_gen_6553, q_gen_6554, q_gen_6559, q_gen_6560},
Q_f={q_gen_6552},
Delta=
{
<nil>() -> q_gen_6553
<b>() -> q_gen_6554
<nil, nil>() -> q_gen_6559
<a, a>() -> q_gen_6560
<b, cons, cons>(q_gen_6560, q_gen_6559) -> q_gen_6552
<b, cons, nil>(q_gen_6554, q_gen_6553) -> q_gen_6552
<b, nil, nil>() -> q_gen_6552
}

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

}
--
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, _mia]) /\ delete_all([x, l, _lia]) /\ delete_one([x, l, _lia])) -> eq_nat([_mia, s(z)]) -> 1
(count([x, r, _fia]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _fia]) -> 1
(count([y, r, _eia])) -> count([y, cons(y, r), s(_eia)]) -> 4
(delete_all([x, r, _zha]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _zha)]) -> 4
(delete_all([y, r, _yha])) -> delete_all([y, cons(y, r), _yha]) -> 4
(delete_one([x, r, _tha]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _tha)]) -> 4
}
Sat witness: Found: ((count([y, r, _eia])) -> count([y, cons(y, r), s(_eia)]), {
_eia -> z  ;  r -> nil  ;  y -> b
})

-------------------------------------------
Step 8, which took 0.012524 s (model generation: 0.012076,  model checking: 0.000448):

Model:
|_
{
count -> 
{{{
Q={q_gen_6557, q_gen_6568, q_gen_6569},
Q_f={q_gen_6557},
Delta=
{
<b>() -> q_gen_6569
<nil, z>() -> q_gen_6568
<b, cons, s>(q_gen_6569, q_gen_6568) -> q_gen_6557
<b, nil, z>() -> q_gen_6557
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_6556, q_gen_6562, q_gen_6563, q_gen_6565, q_gen_6566},
Q_f={q_gen_6556},
Delta=
{
<nil>() -> q_gen_6562
<b>() -> q_gen_6563
<nil, nil>() -> q_gen_6565
<a, a>() -> q_gen_6566
<b, cons, cons>(q_gen_6566, q_gen_6565) -> q_gen_6556
<b, cons, nil>(q_gen_6563, q_gen_6562) -> q_gen_6556
<b, nil, nil>() -> q_gen_6556
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_6552, q_gen_6553, q_gen_6554, q_gen_6559, q_gen_6560},
Q_f={q_gen_6552},
Delta=
{
<nil>() -> q_gen_6553
<b>() -> q_gen_6554
<nil, nil>() -> q_gen_6559
<a, a>() -> q_gen_6560
<b, cons, cons>(q_gen_6560, q_gen_6559) -> q_gen_6552
<b, cons, nil>(q_gen_6554, q_gen_6553) -> q_gen_6552
<b, nil, nil>() -> q_gen_6552
}

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

}
--
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, _mia]) /\ delete_all([x, l, _lia]) /\ delete_one([x, l, _lia])) -> eq_nat([_mia, s(z)]) -> 1
(count([x, r, _fia]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _fia]) -> 4
(count([y, r, _eia])) -> count([y, cons(y, r), s(_eia)]) -> 4
(delete_all([x, r, _zha]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _zha)]) -> 4
(delete_all([y, r, _yha])) -> delete_all([y, cons(y, r), _yha]) -> 4
(delete_one([x, r, _tha]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _tha)]) -> 4
}
Sat witness: Found: ((count([x, r, _fia]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _fia]), {
_fia -> z  ;  r -> nil  ;  x -> b  ;  y -> a
})

-------------------------------------------
Step 9, which took 0.012663 s (model generation: 0.012379,  model checking: 0.000284):

Model:
|_
{
count -> 
{{{
Q={q_gen_6557, q_gen_6568, q_gen_6569, q_gen_6571},
Q_f={q_gen_6557},
Delta=
{
<a>() -> q_gen_6569
<b>() -> q_gen_6569
<nil>() -> q_gen_6571
<nil, z>() -> q_gen_6568
<b, cons, s>(q_gen_6569, q_gen_6568) -> q_gen_6557
<b, cons, z>(q_gen_6569, q_gen_6571) -> q_gen_6557
<b, nil, z>() -> q_gen_6557
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  delete_all -> 
{{{
Q={q_gen_6556, q_gen_6562, q_gen_6563, q_gen_6565, q_gen_6566},
Q_f={q_gen_6556},
Delta=
{
<nil>() -> q_gen_6562
<b>() -> q_gen_6563
<nil, nil>() -> q_gen_6565
<a, a>() -> q_gen_6566
<b, cons, cons>(q_gen_6566, q_gen_6565) -> q_gen_6556
<b, cons, nil>(q_gen_6563, q_gen_6562) -> q_gen_6556
<b, nil, nil>() -> q_gen_6556
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  delete_one -> 
{{{
Q={q_gen_6552, q_gen_6553, q_gen_6554, q_gen_6559, q_gen_6560},
Q_f={q_gen_6552},
Delta=
{
<nil>() -> q_gen_6553
<b>() -> q_gen_6554
<nil, nil>() -> q_gen_6559
<a, a>() -> q_gen_6560
<b, cons, cons>(q_gen_6560, q_gen_6559) -> q_gen_6552
<b, cons, nil>(q_gen_6554, q_gen_6553) -> q_gen_6552
<b, nil, nil>() -> q_gen_6552
}

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

}
--
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, _mia]) /\ delete_all([x, l, _lia]) /\ delete_one([x, l, _lia])) -> eq_nat([_mia, s(z)]) -> 4
(count([x, r, _fia]) /\ not eq_elt([x, y])) -> count([x, cons(y, r), _fia]) -> 4
(count([y, r, _eia])) -> count([y, cons(y, r), s(_eia)]) -> 4
(delete_all([x, r, _zha]) /\ not eq_elt([x, y])) -> delete_all([x, cons(y, r), cons(y, _zha)]) -> 4
(delete_all([y, r, _yha])) -> delete_all([y, cons(y, r), _yha]) -> 4
(delete_one([x, r, _tha]) /\ not eq_elt([x, y])) -> delete_one([x, cons(y, r), cons(y, _tha)]) -> 4
}
Sat witness: Found: ((count([x, l, _mia]) /\ delete_all([x, l, _lia]) /\ delete_one([x, l, _lia])) -> eq_nat([_mia, s(z)]), {
_lia -> nil  ;  _mia -> z  ;  l -> nil  ;  x -> b
})

Total time: 0.129509
Reason for stopping: Disproved