Solving ../../benchmarks/smtlib/true/reverse_not_null.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:
{
(append, F:
{
append(nil, l2, l2) <= True
append(cons(h1, t1), l2, cons(h1, _kc)) <= append(t1, l2, _kc)
}
eq_eltlist(_nc, _oc) <= append(_lc, _mc, _nc) /\ append(_lc, _mc, _oc)
)
(reverse, F:
{
reverse(nil, nil) <= True
reverse(cons(h1, t1), _qc) <= append(_pc, cons(h1, nil), _qc) /\ reverse(t1, _pc)
}
eq_eltlist(_sc, _tc) <= reverse(_rc, _sc) /\ reverse(_rc, _tc)
)
(not_null, P:
{
not_null(cons(x, ll)) <= True
False <= not_null(nil)
}
)
}

properties:
{
not_null(_uc) <= not_null(l1) /\ reverse(l1, _uc)
}


over-approximation: {append, reverse}
under-approximation: {}

Clause system for inference is:

{
append(nil, l2, l2) <= True -> 0
not_null(cons(x, ll)) <= True -> 0
reverse(nil, nil) <= True -> 0
reverse(cons(h1, t1), _qc) <= append(_pc, cons(h1, nil), _qc) /\ reverse(t1, _pc) -> 0
append(cons(h1, t1), l2, cons(h1, _kc)) <= append(t1, l2, _kc) -> 0
not_null(_uc) <= not_null(l1) /\ reverse(l1, _uc) -> 0
False <= not_null(nil) -> 0
}


Solving took 0.052802 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
}
]


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



--
Equality automata are defined for: {elt, eltlist}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.010023 s (model generation: 0.009978,  model checking: 0.000045):

Clauses:
{
append(nil, l2, l2) <= True -> 0
not_null(cons(x, ll)) <= True -> 0
reverse(nil, nil) <= True -> 0
reverse(cons(h1, t1), _qc) <= append(_pc, cons(h1, nil), _qc) /\ reverse(t1, _pc) -> 0
append(cons(h1, t1), l2, cons(h1, _kc)) <= append(t1, l2, _kc) -> 0
not_null(_uc) <= not_null(l1) /\ reverse(l1, _uc) -> 0
False <= not_null(nil) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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


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


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



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




Answer of teacher:

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

not_null(cons(x, ll)) <= True  :
Yes: {

}

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

}

reverse(cons(h1, t1), _qc) <= append(_pc, cons(h1, nil), _qc) /\ reverse(t1, _pc)  :
No: ()

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

not_null(_uc) <= not_null(l1) /\ reverse(l1, _uc)  :
No: ()

False <= not_null(nil)  :
No: ()


-------------------------------------------
Step 1, which took 0.009694 s (model generation: 0.009644,  model checking: 0.000050):

Clauses:
{
append(nil, l2, l2) <= True -> 0
not_null(cons(x, ll)) <= True -> 0
reverse(nil, nil) <= True -> 0
reverse(cons(h1, t1), _qc) <= append(_pc, cons(h1, nil), _qc) /\ reverse(t1, _pc) -> 0
append(cons(h1, t1), l2, cons(h1, _kc)) <= append(t1, l2, _kc) -> 0
not_null(_uc) <= not_null(l1) /\ reverse(l1, _uc) -> 0
False <= not_null(nil) -> 0
}

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

Current best model:
|_
name: None

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


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


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



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




Answer of teacher:

append(nil, l2, l2) <= True  :
Yes: {
l2 -> cons(_yvjca_0, _yvjca_1)
}

not_null(cons(x, ll)) <= True  :
No: ()

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

reverse(cons(h1, t1), _qc) <= append(_pc, cons(h1, nil), _qc) /\ reverse(t1, _pc)  :
No: ()

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

not_null(_uc) <= not_null(l1) /\ reverse(l1, _uc)  :
No: ()

False <= not_null(nil)  :
No: ()


-------------------------------------------
Step 2, which took 0.013526 s (model generation: 0.013444,  model checking: 0.000082):

Clauses:
{
append(nil, l2, l2) <= True -> 0
not_null(cons(x, ll)) <= True -> 0
reverse(nil, nil) <= True -> 0
reverse(cons(h1, t1), _qc) <= append(_pc, cons(h1, nil), _qc) /\ reverse(t1, _pc) -> 0
append(cons(h1, t1), l2, cons(h1, _kc)) <= append(t1, l2, _kc) -> 0
not_null(_uc) <= not_null(l1) /\ reverse(l1, _uc) -> 0
False <= not_null(nil) -> 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
not_null(cons(a, nil)) <= True
reverse(nil, 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
}
]


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


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



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




Answer of teacher:

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

not_null(cons(x, ll)) <= True  :
No: ()

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

reverse(cons(h1, t1), _qc) <= append(_pc, cons(h1, nil), _qc) /\ reverse(t1, _pc)  :
Yes: {
_pc -> nil  ;  _qc -> cons(_dwjca_0, _dwjca_1)  ;  t1 -> nil
}

append(cons(h1, t1), l2, cons(h1, _kc)) <= append(t1, l2, _kc)  :
Yes: {
_kc -> cons(_fwjca_0, _fwjca_1)  ;  l2 -> cons(_gwjca_0, _gwjca_1)  ;  t1 -> nil
}

not_null(_uc) <= not_null(l1) /\ reverse(l1, _uc)  :
No: ()

False <= not_null(nil)  :
No: ()


Total time: 0.052802
Learner time: 0.033066
Teacher time: 0.000177
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
}
]


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



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