Solving ../../benchmarks/smtlib/true/length_cons_s.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: {
nat -> {s, z}  ;  natlist -> {cons, nil}
}
definition:
{
(length, F:
{
length(nil, z) <= True
length(cons(x, ll), s(_ppa)) <= length(ll, _ppa)
}
eq_nat(_rpa, _spa) <= length(_qpa, _rpa) /\ length(_qpa, _spa)
)
}

properties:
{
eq_nat(_tpa, s(s(_upa))) <= length(l, _upa) /\ length(cons(z, cons(z, l)), _tpa)
}


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

Clause system for inference is:

{
length(nil, z) <= True -> 0
eq_nat(_tpa, s(s(_upa))) <= length(l, _upa) /\ length(cons(z, cons(z, l)), _tpa) -> 0
length(cons(x, ll), s(_ppa)) <= length(ll, _ppa) -> 0
}


Solving took 0.062005 seconds.
Yes: |_
name: None

length ->
[
length : <natlist * nat>
{
  length(cons(x_0_0, x_0_1), s(x_1_0)) <= length(x_0_1, x_1_0)
  length(nil, z) <= True
}
]



--
Equality automata are defined for: {nat, natlist}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.009356 s (model generation: 0.009302,  model checking: 0.000054):

Clauses:
{
length(nil, z) <= True -> 0
eq_nat(_tpa, s(s(_upa))) <= length(l, _upa) /\ length(cons(z, cons(z, l)), _tpa) -> 0
length(cons(x, ll), s(_ppa)) <= length(ll, _ppa) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

length ->
[
length : <natlist * nat>
{
  
}
]



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




Answer of teacher:

length(nil, z) <= True  :
Yes: {

}

eq_nat(_tpa, s(s(_upa))) <= length(l, _upa) /\ length(cons(z, cons(z, l)), _tpa)  :
No: ()

length(cons(x, ll), s(_ppa)) <= length(ll, _ppa)  :
No: ()


-------------------------------------------
Step 1, which took 0.014730 s (model generation: 0.014624,  model checking: 0.000106):

Clauses:
{
length(nil, z) <= True -> 0
eq_nat(_tpa, s(s(_upa))) <= length(l, _upa) /\ length(cons(z, cons(z, l)), _tpa) -> 0
length(cons(x, ll), s(_ppa)) <= length(ll, _ppa) -> 0
}

Accumulated learning constraints:
{
length(nil, z) <= True
}

Current best model:
|_
name: None

length ->
[
length : <natlist * nat>
{
  length(nil, z) <= True
}
]



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




Answer of teacher:

length(nil, z) <= True  :
No: ()

eq_nat(_tpa, s(s(_upa))) <= length(l, _upa) /\ length(cons(z, cons(z, l)), _tpa)  :
No: ()

length(cons(x, ll), s(_ppa)) <= length(ll, _ppa)  :
Yes: {
_ppa -> z  ;  ll -> nil
}


-------------------------------------------
Step 2, which took 0.018731 s (model generation: 0.018618,  model checking: 0.000113):

Clauses:
{
length(nil, z) <= True -> 0
eq_nat(_tpa, s(s(_upa))) <= length(l, _upa) /\ length(cons(z, cons(z, l)), _tpa) -> 0
length(cons(x, ll), s(_ppa)) <= length(ll, _ppa) -> 0
}

Accumulated learning constraints:
{
length(cons(z, nil), s(z)) <= True
length(nil, z) <= True
}

Current best model:
|_
name: None

length ->
[
length : <natlist * nat>
{
  length(cons(x_0_0, x_0_1), s(x_1_0)) <= True
  length(nil, z) <= True
}
]



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




Answer of teacher:

length(nil, z) <= True  :
No: ()

eq_nat(_tpa, s(s(_upa))) <= length(l, _upa) /\ length(cons(z, cons(z, l)), _tpa)  :
Yes: {
_tpa -> s(z)  ;  _upa -> s(_ishq_0)  ;  l -> cons(_jshq_0, _jshq_1)
}

length(cons(x, ll), s(_ppa)) <= length(ll, _ppa)  :
No: ()


Total time: 0.062005
Learner time: 0.042544
Teacher time: 0.000273
Reasons for stopping: Yes: |_
name: None

length ->
[
length : <natlist * nat>
{
  length(cons(x_0_0, x_0_1), s(x_1_0)) <= length(x_0_1, x_1_0)
  length(nil, z) <= True
}
]



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