Solving ../../benchmarks/true/nat_double_is_zero_ite.smt2...

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


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(double, F:
{() -> double([z, z])
(double([nn, _rl])) -> double([s(nn), s(s(_rl))])}
(double([_sl, _tl]) /\ double([_sl, _ul])) -> eq_nat([_tl, _ul])
)
(is_zero, P:
{(double([n, _vl]) /\ is_zero([n]) /\ not eq_nat([_vl, z])) -> BOT
(double([n, z])) -> is_zero([n])}
)
}

properties:
{() -> is_zero([z])}


over-approximation: {double}
under-approximation: {is_zero}

Clause system for inference is:

{
() -> double([z, z]) -> 0  ;  () -> is_zero([z]) -> 0  ;  (double([n, _vl]) /\ is_zero([n]) /\ not eq_nat([_vl, z])) -> BOT -> 0  ;  (double([n, z])) -> is_zero([n]) -> 0  ;  (double([nn, _rl])) -> double([s(nn), s(s(_rl))]) -> 0
}


Solving took 0.069310 seconds.
Proved
Model:
|_
{
double -> 
{{{
Q={q_gen_4756, q_gen_4758, q_gen_4759},
Q_f={q_gen_4756},
Delta=
{
<s>(q_gen_4759) -> q_gen_4759
<z>() -> q_gen_4759
<s, s>(q_gen_4756) -> q_gen_4756
<s, s>(q_gen_4758) -> q_gen_4756
<z, z>() -> q_gen_4756
<z, s>(q_gen_4759) -> q_gen_4758
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  is_zero -> 
{{{
Q={q_gen_4755},
Q_f={q_gen_4755},
Delta=
{
<z>() -> q_gen_4755
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.010331 s (model generation: 0.010166,  model checking: 0.000165):

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 0  ;  () -> is_zero([z]) -> 3  ;  (double([n, _vl]) /\ is_zero([n]) /\ not eq_nat([_vl, z])) -> BOT -> 1  ;  (double([n, z])) -> is_zero([n]) -> 1  ;  (double([nn, _rl])) -> double([s(nn), s(s(_rl))]) -> 1
}
Sat witness: Yes: (() -> is_zero([z]), {

})

-------------------------------------------
Step 1, which took 0.010270 s (model generation: 0.010191,  model checking: 0.000079):

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

}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  is_zero -> 
{{{
Q={q_gen_4755},
Q_f={q_gen_4755},
Delta=
{
<z>() -> q_gen_4755
}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 3  ;  () -> is_zero([z]) -> 3  ;  (double([n, _vl]) /\ is_zero([n]) /\ not eq_nat([_vl, z])) -> BOT -> 1  ;  (double([n, z])) -> is_zero([n]) -> 1  ;  (double([nn, _rl])) -> double([s(nn), s(s(_rl))]) -> 1
}
Sat witness: Yes: (() -> double([z, z]), {

})

-------------------------------------------
Step 2, which took 0.013372 s (model generation: 0.010331,  model checking: 0.003041):

Model:
|_
{
double -> 
{{{
Q={q_gen_4756},
Q_f={q_gen_4756},
Delta=
{
<z, z>() -> q_gen_4756
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  is_zero -> 
{{{
Q={q_gen_4755},
Q_f={q_gen_4755},
Delta=
{
<z>() -> q_gen_4755
}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 3  ;  () -> is_zero([z]) -> 3  ;  (double([n, _vl]) /\ is_zero([n]) /\ not eq_nat([_vl, z])) -> BOT -> 1  ;  (double([n, z])) -> is_zero([n]) -> 1  ;  (double([nn, _rl])) -> double([s(nn), s(s(_rl))]) -> 4
}
Sat witness: Yes: ((double([nn, _rl])) -> double([s(nn), s(s(_rl))]), {
_rl -> z  ;  nn -> z
})

-------------------------------------------
Step 3, which took 0.011324 s (model generation: 0.011163,  model checking: 0.000161):

Model:
|_
{
double -> 
{{{
Q={q_gen_4756, q_gen_4759},
Q_f={q_gen_4756},
Delta=
{
<z>() -> q_gen_4759
<s, s>(q_gen_4756) -> q_gen_4756
<z, s>(q_gen_4759) -> q_gen_4756
<z, z>() -> q_gen_4756
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  is_zero -> 
{{{
Q={q_gen_4755},
Q_f={q_gen_4755},
Delta=
{
<z>() -> q_gen_4755
}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 3  ;  () -> is_zero([z]) -> 3  ;  (double([n, _vl]) /\ is_zero([n]) /\ not eq_nat([_vl, z])) -> BOT -> 4  ;  (double([n, z])) -> is_zero([n]) -> 2  ;  (double([nn, _rl])) -> double([s(nn), s(s(_rl))]) -> 4
}
Sat witness: Yes: ((double([n, _vl]) /\ is_zero([n]) /\ not eq_nat([_vl, z])) -> BOT, {
_vl -> s(z)  ;  n -> z
})

-------------------------------------------
Step 4, which took 0.011264 s (model generation: 0.010843,  model checking: 0.000421):

Model:
|_
{
double -> 
{{{
Q={q_gen_4756, q_gen_4758, q_gen_4759},
Q_f={q_gen_4756},
Delta=
{
<z>() -> q_gen_4759
<s, s>(q_gen_4758) -> q_gen_4756
<z, z>() -> q_gen_4756
<z, s>(q_gen_4759) -> q_gen_4758
}

Datatype: <nat, nat>
Convolution form: complete
}}}
  ;  is_zero -> 
{{{
Q={q_gen_4755},
Q_f={q_gen_4755},
Delta=
{
<z>() -> q_gen_4755
}

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

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

Teacher's answer:
New clause system:
{
() -> double([z, z]) -> 4  ;  () -> is_zero([z]) -> 4  ;  (double([n, _vl]) /\ is_zero([n]) /\ not eq_nat([_vl, z])) -> BOT -> 4  ;  (double([n, z])) -> is_zero([n]) -> 3  ;  (double([nn, _rl])) -> double([s(nn), s(s(_rl))]) -> 7
}
Sat witness: Yes: ((double([nn, _rl])) -> double([s(nn), s(s(_rl))]), {
_rl -> s(s(z))  ;  nn -> s(z)
})

Total time: 0.069310
Reason for stopping: Proved