Solving ../../benchmarks/true/length_cons_s.smt2...

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


Learning problem is:

env: {
nat -> {s, z}  ;  natlist -> {cons, nil}
}
definition:
{
(length, F:
{() -> length([nil, z])
(length([ll, _yaa])) -> length([cons(x, ll), s(_yaa)])}
(length([_zaa, _aba]) /\ length([_zaa, _bba])) -> eq_nat([_aba, _bba])
)
}

properties:
{(length([l, _dba]) /\ length([cons(z, cons(z, l)), _cba])) -> eq_nat([_cba, s(s(_dba))])}


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

Clause system for inference is:

{
() -> length([nil, z]) -> 0  ;  (length([l, _dba]) /\ length([cons(z, cons(z, l)), _cba])) -> eq_nat([_cba, s(s(_dba))]) -> 0  ;  (length([ll, _yaa])) -> length([cons(x, ll), s(_yaa)]) -> 0
}


Solving took 0.063105 seconds.
Proved
Model:
|_
{
length -> 
{{{
Q={q_gen_3090, q_gen_3092, q_gen_3095},
Q_f={q_gen_3090},
Delta=
{
<s>(q_gen_3095) -> q_gen_3095
<z>() -> q_gen_3095
<cons, s>(q_gen_3092, q_gen_3090) -> q_gen_3090
<nil, z>() -> q_gen_3090
<s, s>(q_gen_3092) -> q_gen_3092
<s, z>(q_gen_3095) -> q_gen_3092
<z, s>(q_gen_3095) -> q_gen_3092
<z, z>() -> q_gen_3092
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.003168 s (model generation: 0.003091,  model checking: 0.000077):

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

}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 3  ;  (length([l, _dba]) /\ length([cons(z, cons(z, l)), _cba])) -> eq_nat([_cba, s(s(_dba))]) -> 1  ;  (length([ll, _yaa])) -> length([cons(x, ll), s(_yaa)]) -> 1
}
Sat witness: Yes: (() -> length([nil, z]), {

})

-------------------------------------------
Step 1, which took 0.003449 s (model generation: 0.003355,  model checking: 0.000094):

Model:
|_
{
length -> 
{{{
Q={q_gen_3090},
Q_f={q_gen_3090},
Delta=
{
<nil, z>() -> q_gen_3090
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 3  ;  (length([l, _dba]) /\ length([cons(z, cons(z, l)), _cba])) -> eq_nat([_cba, s(s(_dba))]) -> 1  ;  (length([ll, _yaa])) -> length([cons(x, ll), s(_yaa)]) -> 4
}
Sat witness: Yes: ((length([ll, _yaa])) -> length([cons(x, ll), s(_yaa)]), {
_yaa -> z  ;  ll -> nil  ;  x -> z
})

-------------------------------------------
Step 2, which took 0.003493 s (model generation: 0.003303,  model checking: 0.000190):

Model:
|_
{
length -> 
{{{
Q={q_gen_3090, q_gen_3092},
Q_f={q_gen_3090},
Delta=
{
<cons, s>(q_gen_3092, q_gen_3090) -> q_gen_3090
<nil, z>() -> q_gen_3090
<z, z>() -> q_gen_3092
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 4  ;  (length([l, _dba]) /\ length([cons(z, cons(z, l)), _cba])) -> eq_nat([_cba, s(s(_dba))]) -> 2  ;  (length([ll, _yaa])) -> length([cons(x, ll), s(_yaa)]) -> 7
}
Sat witness: Yes: ((length([ll, _yaa])) -> length([cons(x, ll), s(_yaa)]), {
_yaa -> z  ;  ll -> nil  ;  x -> s(z)
})

-------------------------------------------
Step 3, which took 0.004001 s (model generation: 0.003792,  model checking: 0.000209):

Model:
|_
{
length -> 
{{{
Q={q_gen_3090, q_gen_3092, q_gen_3095},
Q_f={q_gen_3090},
Delta=
{
<z>() -> q_gen_3095
<cons, s>(q_gen_3092, q_gen_3090) -> q_gen_3090
<nil, z>() -> q_gen_3090
<s, z>(q_gen_3095) -> q_gen_3092
<z, z>() -> q_gen_3092
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 5  ;  (length([l, _dba]) /\ length([cons(z, cons(z, l)), _cba])) -> eq_nat([_cba, s(s(_dba))]) -> 3  ;  (length([ll, _yaa])) -> length([cons(x, ll), s(_yaa)]) -> 10
}
Sat witness: Yes: ((length([ll, _yaa])) -> length([cons(x, ll), s(_yaa)]), {
_yaa -> z  ;  ll -> nil  ;  x -> s(s(z))
})

-------------------------------------------
Step 4, which took 0.010315 s (model generation: 0.009273,  model checking: 0.001042):

Model:
|_
{
length -> 
{{{
Q={q_gen_3090, q_gen_3092, q_gen_3095},
Q_f={q_gen_3090},
Delta=
{
<s>(q_gen_3095) -> q_gen_3095
<z>() -> q_gen_3095
<cons, s>(q_gen_3092, q_gen_3090) -> q_gen_3090
<nil, z>() -> q_gen_3090
<s, z>(q_gen_3095) -> q_gen_3092
<z, z>() -> q_gen_3092
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 6  ;  (length([l, _dba]) /\ length([cons(z, cons(z, l)), _cba])) -> eq_nat([_cba, s(s(_dba))]) -> 4  ;  (length([ll, _yaa])) -> length([cons(x, ll), s(_yaa)]) -> 13
}
Sat witness: Yes: ((length([ll, _yaa])) -> length([cons(x, ll), s(_yaa)]), {
_yaa -> s(z)  ;  ll -> cons(z, nil)  ;  x -> s(z)
})

-------------------------------------------
Step 5, which took 0.013980 s (model generation: 0.012969,  model checking: 0.001011):

Model:
|_
{
length -> 
{{{
Q={q_gen_3090, q_gen_3092, q_gen_3095},
Q_f={q_gen_3090},
Delta=
{
<s>(q_gen_3095) -> q_gen_3095
<z>() -> q_gen_3095
<cons, s>(q_gen_3092, q_gen_3090) -> q_gen_3090
<nil, z>() -> q_gen_3090
<s, s>(q_gen_3092) -> q_gen_3092
<s, z>(q_gen_3095) -> q_gen_3092
<z, z>() -> q_gen_3092
}

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

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

Teacher's answer:
New clause system:
{
() -> length([nil, z]) -> 7  ;  (length([l, _dba]) /\ length([cons(z, cons(z, l)), _cba])) -> eq_nat([_cba, s(s(_dba))]) -> 5  ;  (length([ll, _yaa])) -> length([cons(x, ll), s(_yaa)]) -> 16
}
Sat witness: Yes: ((length([ll, _yaa])) -> length([cons(x, ll), s(_yaa)]), {
_yaa -> s(z)  ;  ll -> cons(z, nil)  ;  x -> z
})

Total time: 0.063105
Reason for stopping: Proved