Solving ../../benchmarks/smtlib/true/prefix_nil.smt2...

Inference procedure has parameters:
Ice fuel: 200
Timeout: Some(60.) (sec)
Teacher_type: Checks all clauses every time
Approximation method: remove every clause that can be safely removed



Learning problem is:

env: {
elist -> {econs, enil}  ;  elt -> {a, b}  ;  nat -> {s, z}
}
definition:
{
(prefix_elt, P:
{
prefix_elt(enil, l) <= True
prefix_elt(econs(y2, zs), econs(y2, ys)) <= prefix_elt(zs, ys)
prefix_elt(zs, ys) <= prefix_elt(econs(y2, zs), econs(y2, ys))
eq_elt(z, y2) <= prefix_elt(econs(z, zs), econs(y2, ys))
False <= prefix_elt(econs(z, zs), enil)
}
)
}

properties:
{
prefix_elt(enil, l) <= True
}


over-approximation: {}
under-approximation: {prefix_elt}

Clause system for inference is:

{
prefix_elt(enil, l) <= True -> 0
prefix_elt(econs(y2, zs), econs(y2, ys)) <= prefix_elt(zs, ys) -> 0
prefix_elt(zs, ys) <= prefix_elt(econs(y2, zs), econs(y2, ys)) -> 0
eq_elt(z, y2) <= prefix_elt(econs(z, zs), econs(y2, ys)) -> 0
False <= prefix_elt(econs(z, zs), enil) -> 0
}


Solving took 0.053758 seconds.
Yes: |_
name: None

prefix_elt ->
[
prefix_elt : <elist * elist>
{
  _r_1(a, a) <= True
  _r_1(b, b) <= True
  prefix_elt(econs(x_0_0, x_0_1), econs(x_1_0, x_1_1)) <= _r_1(x_0_0, x_1_0) /\ prefix_elt(x_0_1, x_1_1)
  prefix_elt(enil, econs(x_1_0, x_1_1)) <= True
  prefix_elt(enil, enil) <= True
}
]



--
Equality automata are defined for: {elist, elt, nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006041 s (model generation: 0.005990,  model checking: 0.000051):

Clauses:
{
prefix_elt(enil, l) <= True -> 0
prefix_elt(econs(y2, zs), econs(y2, ys)) <= prefix_elt(zs, ys) -> 0
prefix_elt(zs, ys) <= prefix_elt(econs(y2, zs), econs(y2, ys)) -> 0
eq_elt(z, y2) <= prefix_elt(econs(z, zs), econs(y2, ys)) -> 0
False <= prefix_elt(econs(z, zs), enil) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

prefix_elt ->
[
prefix_elt : <elist * elist>
{
  
}
]



--
Equality automata are defined for: {elist, elt, nat}
_|




Answer of teacher:

prefix_elt(enil, l) <= True  :
Yes: {
l -> enil
}

prefix_elt(econs(y2, zs), econs(y2, ys)) <= prefix_elt(zs, ys)  :
No: ()

prefix_elt(zs, ys) <= prefix_elt(econs(y2, zs), econs(y2, ys))  :
No: ()

eq_elt(z, y2) <= prefix_elt(econs(z, zs), econs(y2, ys))  :
No: ()

False <= prefix_elt(econs(z, zs), enil)  :
No: ()


-------------------------------------------
Step 1, which took 0.005998 s (model generation: 0.005948,  model checking: 0.000050):

Clauses:
{
prefix_elt(enil, l) <= True -> 0
prefix_elt(econs(y2, zs), econs(y2, ys)) <= prefix_elt(zs, ys) -> 0
prefix_elt(zs, ys) <= prefix_elt(econs(y2, zs), econs(y2, ys)) -> 0
eq_elt(z, y2) <= prefix_elt(econs(z, zs), econs(y2, ys)) -> 0
False <= prefix_elt(econs(z, zs), enil) -> 0
}

Accumulated learning constraints:
{
prefix_elt(enil, enil) <= True
}

Current best model:
|_
name: None

prefix_elt ->
[
prefix_elt : <elist * elist>
{
  prefix_elt(enil, enil) <= True
}
]



--
Equality automata are defined for: {elist, elt, nat}
_|




Answer of teacher:

prefix_elt(enil, l) <= True  :
Yes: {
l -> econs(_jrjca_0, _jrjca_1)
}

prefix_elt(econs(y2, zs), econs(y2, ys)) <= prefix_elt(zs, ys)  :
Yes: {
ys -> enil  ;  zs -> enil
}

prefix_elt(zs, ys) <= prefix_elt(econs(y2, zs), econs(y2, ys))  :
No: ()

eq_elt(z, y2) <= prefix_elt(econs(z, zs), econs(y2, ys))  :
No: ()

False <= prefix_elt(econs(z, zs), enil)  :
No: ()


-------------------------------------------
Step 2, which took 0.006636 s (model generation: 0.006591,  model checking: 0.000045):

Clauses:
{
prefix_elt(enil, l) <= True -> 0
prefix_elt(econs(y2, zs), econs(y2, ys)) <= prefix_elt(zs, ys) -> 0
prefix_elt(zs, ys) <= prefix_elt(econs(y2, zs), econs(y2, ys)) -> 0
eq_elt(z, y2) <= prefix_elt(econs(z, zs), econs(y2, ys)) -> 0
False <= prefix_elt(econs(z, zs), enil) -> 0
}

Accumulated learning constraints:
{
prefix_elt(econs(a, enil), econs(a, enil)) <= True
prefix_elt(enil, econs(a, enil)) <= True
prefix_elt(enil, enil) <= True
}

Current best model:
|_
name: None

prefix_elt ->
[
prefix_elt : <elist * elist>
{
  prefix_elt(econs(x_0_0, x_0_1), econs(x_1_0, x_1_1)) <= True
  prefix_elt(enil, econs(x_1_0, x_1_1)) <= True
  prefix_elt(enil, enil) <= True
}
]



--
Equality automata are defined for: {elist, elt, nat}
_|




Answer of teacher:

prefix_elt(enil, l) <= True  :
No: ()

prefix_elt(econs(y2, zs), econs(y2, ys)) <= prefix_elt(zs, ys)  :
No: ()

prefix_elt(zs, ys) <= prefix_elt(econs(y2, zs), econs(y2, ys))  :
Yes: {
ys -> enil  ;  zs -> econs(_nrjca_0, _nrjca_1)
}

eq_elt(z, y2) <= prefix_elt(econs(z, zs), econs(y2, ys))  :
Yes: {
y2 -> b  ;  z -> a
}

False <= prefix_elt(econs(z, zs), enil)  :
No: ()


-------------------------------------------
Step 3, which took 0.018526 s (model generation: 0.018311,  model checking: 0.000215):

Clauses:
{
prefix_elt(enil, l) <= True -> 0
prefix_elt(econs(y2, zs), econs(y2, ys)) <= prefix_elt(zs, ys) -> 0
prefix_elt(zs, ys) <= prefix_elt(econs(y2, zs), econs(y2, ys)) -> 0
eq_elt(z, y2) <= prefix_elt(econs(z, zs), econs(y2, ys)) -> 0
False <= prefix_elt(econs(z, zs), enil) -> 0
}

Accumulated learning constraints:
{
prefix_elt(econs(a, enil), econs(a, enil)) <= True
prefix_elt(enil, econs(a, enil)) <= True
prefix_elt(enil, enil) <= True
prefix_elt(econs(a, enil), enil) <= prefix_elt(econs(a, econs(a, enil)), econs(a, enil))
False <= prefix_elt(econs(a, enil), econs(b, enil))
}

Current best model:
|_
name: None

prefix_elt ->
[
prefix_elt : <elist * elist>
{
  _r_1(a) <= True
  prefix_elt(econs(x_0_0, x_0_1), econs(x_1_0, x_1_1)) <= _r_1(x_1_0)
  prefix_elt(econs(x_0_0, x_0_1), enil) <= True
  prefix_elt(enil, econs(x_1_0, x_1_1)) <= True
  prefix_elt(enil, enil) <= True
}
]



--
Equality automata are defined for: {elist, elt, nat}
_|




Answer of teacher:

prefix_elt(enil, l) <= True  :
No: ()

prefix_elt(econs(y2, zs), econs(y2, ys)) <= prefix_elt(zs, ys)  :
Yes: {
y2 -> b  ;  ys -> enil  ;  zs -> enil
}

prefix_elt(zs, ys) <= prefix_elt(econs(y2, zs), econs(y2, ys))  :
Yes: {
y2 -> a  ;  ys -> econs(b, _asjca_1)  ;  zs -> econs(_bsjca_0, _bsjca_1)
}

eq_elt(z, y2) <= prefix_elt(econs(z, zs), econs(y2, ys))  :
Yes: {
y2 -> a  ;  z -> b
}

False <= prefix_elt(econs(z, zs), enil)  :
Yes: {

}


Total time: 0.053758
Learner time: 0.036840
Teacher time: 0.000361
Reasons for stopping: Yes: |_
name: None

prefix_elt ->
[
prefix_elt : <elist * elist>
{
  _r_1(a, a) <= True
  _r_1(b, b) <= True
  prefix_elt(econs(x_0_0, x_0_1), econs(x_1_0, x_1_1)) <= _r_1(x_0_0, x_1_0) /\ prefix_elt(x_0_1, x_1_1)
  prefix_elt(enil, econs(x_1_0, x_1_1)) <= True
  prefix_elt(enil, enil) <= True
}
]



--
Equality automata are defined for: {elist, elt, nat}
_|