Solving ../../benchmarks/smtlib/true/timbuk_reverse.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: {
elt -> {a, b}  ;  eltlist -> {cons, nil}
}
definition:
{
(leq, P:
{
leq(a, y) <= True
leq(b, b) <= True
False <= leq(b, a)
}
)
(append, F:
{
append(nil, l2, l2) <= True
append(cons(h1, t1), l2, cons(h1, _ij)) <= append(t1, l2, _ij)
}
eq_eltlist(_lj, _mj) <= append(_jj, _kj, _lj) /\ append(_jj, _kj, _mj)
)
(reverse, F:
{
reverse(nil, nil) <= True
reverse(cons(h1, t1), _oj) <= append(_nj, cons(h1, nil), _oj) /\ reverse(t1, _nj)
}
eq_eltlist(_qj, _rj) <= reverse(_pj, _qj) /\ reverse(_pj, _rj)
)
(sorted, P:
{
sorted(cons(x, nil)) <= True
sorted(nil) <= True
}
)
(invsorted, P:
{
invsorted(cons(x, nil)) <= True
invsorted(nil) <= True
}
)
}

properties:
{
invsorted(_sj) <= reverse(l, _sj) /\ sorted(l)
}


over-approximation: {append, leq, reverse, sorted}
under-approximation: {invsorted, leq}

Clause system for inference is:

{
append(nil, l2, l2) <= True -> 0
reverse(nil, nil) <= True -> 0
sorted(cons(x, nil)) <= True -> 0
sorted(nil) <= True -> 0
reverse(cons(h1, t1), _oj) <= append(_nj, cons(h1, nil), _oj) /\ reverse(t1, _nj) -> 0
append(cons(h1, t1), l2, cons(h1, _ij)) <= append(t1, l2, _ij) -> 0
invsorted(_sj) <= reverse(l, _sj) /\ sorted(l) -> 0
}


Solving took 0.070223 seconds.
Yes: |_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  append(nil, nil, nil) <= True
}
]


;
invsorted ->
[
invsorted : <eltlist>
{
  invsorted(cons(x_0_0, x_0_1)) <= True
  invsorted(nil) <= True
}
]


;
reverse ->
[
reverse : <eltlist * eltlist>
{
  reverse(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1)) <= True
  reverse(nil, nil) <= True
}
]


;
sorted ->
[
sorted : <eltlist>
{
  sorted(cons(x_0_0, x_0_1)) <= True
  sorted(nil) <= True
}
]



--
Equality automata are defined for: {elt, eltlist}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006102 s (model generation: 0.006050,  model checking: 0.000052):

Clauses:
{
append(nil, l2, l2) <= True -> 0
reverse(nil, nil) <= True -> 0
sorted(cons(x, nil)) <= True -> 0
sorted(nil) <= True -> 0
reverse(cons(h1, t1), _oj) <= append(_nj, cons(h1, nil), _oj) /\ reverse(t1, _nj) -> 0
append(cons(h1, t1), l2, cons(h1, _ij)) <= append(t1, l2, _ij) -> 0
invsorted(_sj) <= reverse(l, _sj) /\ sorted(l) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  
}
]


;
invsorted ->
[
invsorted : <eltlist>
{
  
}
]


;
reverse ->
[
reverse : <eltlist * eltlist>
{
  
}
]


;
sorted ->
[
sorted : <eltlist>
{
  
}
]



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




Answer of teacher:

append(nil, l2, l2) <= True  :
Yes: {
l2 -> nil
}

reverse(nil, nil) <= True  :
Yes: {

}

sorted(cons(x, nil)) <= True  :
Yes: {

}

sorted(nil) <= True  :
Yes: {

}

reverse(cons(h1, t1), _oj) <= append(_nj, cons(h1, nil), _oj) /\ reverse(t1, _nj)  :
No: ()

append(cons(h1, t1), l2, cons(h1, _ij)) <= append(t1, l2, _ij)  :
No: ()

invsorted(_sj) <= reverse(l, _sj) /\ sorted(l)  :
No: ()


-------------------------------------------
Step 1, which took 0.007046 s (model generation: 0.006968,  model checking: 0.000078):

Clauses:
{
append(nil, l2, l2) <= True -> 0
reverse(nil, nil) <= True -> 0
sorted(cons(x, nil)) <= True -> 0
sorted(nil) <= True -> 0
reverse(cons(h1, t1), _oj) <= append(_nj, cons(h1, nil), _oj) /\ reverse(t1, _nj) -> 0
append(cons(h1, t1), l2, cons(h1, _ij)) <= append(t1, l2, _ij) -> 0
invsorted(_sj) <= reverse(l, _sj) /\ sorted(l) -> 0
}

Accumulated learning constraints:
{
append(nil, nil, nil) <= True
reverse(nil, nil) <= True
sorted(cons(a, nil)) <= True
sorted(nil) <= True
}

Current best model:
|_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  append(nil, nil, nil) <= True
}
]


;
invsorted ->
[
invsorted : <eltlist>
{
  
}
]


;
reverse ->
[
reverse : <eltlist * eltlist>
{
  reverse(nil, nil) <= True
}
]


;
sorted ->
[
sorted : <eltlist>
{
  sorted(cons(x_0_0, x_0_1)) <= True
  sorted(nil) <= True
}
]



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




Answer of teacher:

append(nil, l2, l2) <= True  :
Yes: {
l2 -> cons(_wemcd_0, _wemcd_1)
}

reverse(nil, nil) <= True  :
No: ()

sorted(cons(x, nil)) <= True  :
No: ()

sorted(nil) <= True  :
No: ()

reverse(cons(h1, t1), _oj) <= append(_nj, cons(h1, nil), _oj) /\ reverse(t1, _nj)  :
No: ()

append(cons(h1, t1), l2, cons(h1, _ij)) <= append(t1, l2, _ij)  :
Yes: {
_ij -> nil  ;  l2 -> nil  ;  t1 -> nil
}

invsorted(_sj) <= reverse(l, _sj) /\ sorted(l)  :
Yes: {
_sj -> nil  ;  l -> nil
}


-------------------------------------------
Step 2, which took 0.013190 s (model generation: 0.013123,  model checking: 0.000067):

Clauses:
{
append(nil, l2, l2) <= True -> 0
reverse(nil, nil) <= True -> 0
sorted(cons(x, nil)) <= True -> 0
sorted(nil) <= True -> 0
reverse(cons(h1, t1), _oj) <= append(_nj, cons(h1, nil), _oj) /\ reverse(t1, _nj) -> 0
append(cons(h1, t1), l2, cons(h1, _ij)) <= append(t1, l2, _ij) -> 0
invsorted(_sj) <= reverse(l, _sj) /\ sorted(l) -> 0
}

Accumulated learning constraints:
{
append(cons(a, nil), nil, cons(a, nil)) <= True
append(nil, cons(a, nil), cons(a, nil)) <= True
append(nil, nil, nil) <= True
invsorted(nil) <= True
reverse(nil, nil) <= True
sorted(cons(a, nil)) <= True
sorted(nil) <= True
}

Current best model:
|_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  append(nil, nil, nil) <= True
}
]


;
invsorted ->
[
invsorted : <eltlist>
{
  invsorted(nil) <= True
}
]


;
reverse ->
[
reverse : <eltlist * eltlist>
{
  reverse(nil, nil) <= True
}
]


;
sorted ->
[
sorted : <eltlist>
{
  sorted(cons(x_0_0, x_0_1)) <= True
  sorted(nil) <= True
}
]



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




Answer of teacher:

append(nil, l2, l2) <= True  :
No: ()

reverse(nil, nil) <= True  :
No: ()

sorted(cons(x, nil)) <= True  :
No: ()

sorted(nil) <= True  :
No: ()

reverse(cons(h1, t1), _oj) <= append(_nj, cons(h1, nil), _oj) /\ reverse(t1, _nj)  :
Yes: {
_nj -> nil  ;  _oj -> cons(_dfmcd_0, _dfmcd_1)  ;  t1 -> nil
}

append(cons(h1, t1), l2, cons(h1, _ij)) <= append(t1, l2, _ij)  :
Yes: {
_ij -> cons(_ffmcd_0, _ffmcd_1)  ;  l2 -> cons(_gfmcd_0, _gfmcd_1)  ;  t1 -> nil
}

invsorted(_sj) <= reverse(l, _sj) /\ sorted(l)  :
No: ()


-------------------------------------------
Step 3, which took 0.025578 s (model generation: 0.025511,  model checking: 0.000067):

Clauses:
{
append(nil, l2, l2) <= True -> 0
reverse(nil, nil) <= True -> 0
sorted(cons(x, nil)) <= True -> 0
sorted(nil) <= True -> 0
reverse(cons(h1, t1), _oj) <= append(_nj, cons(h1, nil), _oj) /\ reverse(t1, _nj) -> 0
append(cons(h1, t1), l2, cons(h1, _ij)) <= append(t1, l2, _ij) -> 0
invsorted(_sj) <= reverse(l, _sj) /\ sorted(l) -> 0
}

Accumulated learning constraints:
{
append(cons(a, nil), cons(a, nil), cons(a, cons(a, nil))) <= True
append(cons(a, nil), nil, cons(a, nil)) <= True
append(nil, cons(a, nil), cons(a, nil)) <= True
append(nil, nil, nil) <= True
invsorted(nil) <= True
reverse(cons(a, nil), cons(a, nil)) <= True
reverse(nil, nil) <= True
sorted(cons(a, nil)) <= True
sorted(nil) <= True
}

Current best model:
|_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  append(nil, nil, nil) <= True
}
]


;
invsorted ->
[
invsorted : <eltlist>
{
  invsorted(nil) <= True
}
]


;
reverse ->
[
reverse : <eltlist * eltlist>
{
  reverse(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1)) <= True
  reverse(nil, nil) <= True
}
]


;
sorted ->
[
sorted : <eltlist>
{
  sorted(cons(x_0_0, x_0_1)) <= True
  sorted(nil) <= True
}
]



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




Answer of teacher:

append(nil, l2, l2) <= True  :
No: ()

reverse(nil, nil) <= True  :
No: ()

sorted(cons(x, nil)) <= True  :
No: ()

sorted(nil) <= True  :
No: ()

reverse(cons(h1, t1), _oj) <= append(_nj, cons(h1, nil), _oj) /\ reverse(t1, _nj)  :
No: ()

append(cons(h1, t1), l2, cons(h1, _ij)) <= append(t1, l2, _ij)  :
No: ()

invsorted(_sj) <= reverse(l, _sj) /\ sorted(l)  :
Yes: {
_sj -> cons(_ifmcd_0, _ifmcd_1)  ;  l -> cons(_jfmcd_0, _jfmcd_1)
}


Total time: 0.070223
Learner time: 0.051652
Teacher time: 0.000264
Reasons for stopping: Yes: |_
name: None

append ->
[
append : <eltlist * eltlist * eltlist>
{
  append(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  append(cons(x_0_0, x_0_1), nil, cons(x_2_0, x_2_1)) <= True
  append(nil, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  append(nil, nil, nil) <= True
}
]


;
invsorted ->
[
invsorted : <eltlist>
{
  invsorted(cons(x_0_0, x_0_1)) <= True
  invsorted(nil) <= True
}
]


;
reverse ->
[
reverse : <eltlist * eltlist>
{
  reverse(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1)) <= True
  reverse(nil, nil) <= True
}
]


;
sorted ->
[
sorted : <eltlist>
{
  sorted(cons(x_0_0, x_0_1)) <= True
  sorted(nil) <= True
}
]



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