Solving ../../benchmarks/smtlib/true/length_append_le_z.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}  ;  nat -> {s, z}
}
definition:
{
(le, P:
{
le(z, s(nn2)) <= True
le(s(nn1), s(nn2)) <= le(nn1, nn2)
le(nn1, nn2) <= le(s(nn1), s(nn2))
False <= le(s(nn1), z)
False <= le(z, z)
}
)
(length, F:
{
length(nil, z) <= True
length(cons(x, ll), s(_fda)) <= length(ll, _fda)
}
eq_nat(_hda, _ida) <= length(_gda, _hda) /\ length(_gda, _ida)
)
(append, F:
{
append(nil, l2, l2) <= True
append(cons(h1, t1), l2, cons(h1, _jda)) <= append(t1, l2, _jda)
}
eq_eltlist(_mda, _nda) <= append(_kda, _lda, _mda) /\ append(_kda, _lda, _nda)
)
}

properties:
{
le(z, _qda) <= append(l1, l2, _pda) /\ le(z, _oda) /\ length(_pda, _qda) /\ length(l1, _oda)
}


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

Clause system for inference is:

{
append(nil, l2, l2) <= True -> 0
le(z, s(nn2)) <= True -> 0
length(nil, z) <= True -> 0
le(z, _qda) <= append(l1, l2, _pda) /\ le(z, _oda) /\ length(_pda, _qda) /\ length(l1, _oda) -> 0
append(cons(h1, t1), l2, cons(h1, _jda)) <= append(t1, l2, _jda) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
length(cons(x, ll), s(_fda)) <= length(ll, _fda) -> 0
}


Solving took 0.066973 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
}
]


;
le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
}
]


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



--
Equality automata are defined for: {elt, eltlist, nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005932 s (model generation: 0.005862,  model checking: 0.000070):

Clauses:
{
append(nil, l2, l2) <= True -> 0
le(z, s(nn2)) <= True -> 0
length(nil, z) <= True -> 0
le(z, _qda) <= append(l1, l2, _pda) /\ le(z, _oda) /\ length(_pda, _qda) /\ length(l1, _oda) -> 0
append(cons(h1, t1), l2, cons(h1, _jda)) <= append(t1, l2, _jda) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
length(cons(x, ll), s(_fda)) <= length(ll, _fda) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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


;
le ->
[
le : <nat * nat>
{
  
}
]


;
length ->
[
length : <eltlist * nat>
{
  
}
]



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




Answer of teacher:

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

le(z, s(nn2)) <= True  :
Yes: {

}

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

}

le(z, _qda) <= append(l1, l2, _pda) /\ le(z, _oda) /\ length(_pda, _qda) /\ length(l1, _oda)  :
No: ()

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

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
No: ()

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


-------------------------------------------
Step 1, which took 0.006365 s (model generation: 0.006283,  model checking: 0.000082):

Clauses:
{
append(nil, l2, l2) <= True -> 0
le(z, s(nn2)) <= True -> 0
length(nil, z) <= True -> 0
le(z, _qda) <= append(l1, l2, _pda) /\ le(z, _oda) /\ length(_pda, _qda) /\ length(l1, _oda) -> 0
append(cons(h1, t1), l2, cons(h1, _jda)) <= append(t1, l2, _jda) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
length(cons(x, ll), s(_fda)) <= length(ll, _fda) -> 0
}

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

Current best model:
|_
name: None

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


;
le ->
[
le : <nat * nat>
{
  le(z, s(x_1_0)) <= True
}
]


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



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




Answer of teacher:

append(nil, l2, l2) <= True  :
Yes: {
l2 -> cons(_jxbq_0, _jxbq_1)
}

le(z, s(nn2)) <= True  :
No: ()

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

le(z, _qda) <= append(l1, l2, _pda) /\ le(z, _oda) /\ length(_pda, _qda) /\ length(l1, _oda)  :
No: ()

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

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
Yes: {
nn1 -> z  ;  nn2 -> s(_oxbq_0)
}

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
No: ()

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


-------------------------------------------
Step 2, which took 0.013558 s (model generation: 0.013462,  model checking: 0.000096):

Clauses:
{
append(nil, l2, l2) <= True -> 0
le(z, s(nn2)) <= True -> 0
length(nil, z) <= True -> 0
le(z, _qda) <= append(l1, l2, _pda) /\ le(z, _oda) /\ length(_pda, _qda) /\ length(l1, _oda) -> 0
append(cons(h1, t1), l2, cons(h1, _jda)) <= append(t1, l2, _jda) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
length(cons(x, ll), s(_fda)) <= length(ll, _fda) -> 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
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= 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
}
]


;
le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= True
  le(z, s(x_1_0)) <= True
}
]


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



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




Answer of teacher:

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

le(z, s(nn2)) <= True  :
No: ()

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

le(z, _qda) <= append(l1, l2, _pda) /\ le(z, _oda) /\ length(_pda, _qda) /\ length(l1, _oda)  :
No: ()

append(cons(h1, t1), l2, cons(h1, _jda)) <= append(t1, l2, _jda)  :
Yes: {
_jda -> cons(_rxbq_0, _rxbq_1)  ;  l2 -> cons(_sxbq_0, _sxbq_1)  ;  t1 -> nil
}

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
Yes: {
nn1 -> z  ;  nn2 -> z
}

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
No: ()

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


-------------------------------------------
Step 3, which took 0.016443 s (model generation: 0.016345,  model checking: 0.000098):

Clauses:
{
append(nil, l2, l2) <= True -> 0
le(z, s(nn2)) <= True -> 0
length(nil, z) <= True -> 0
le(z, _qda) <= append(l1, l2, _pda) /\ le(z, _oda) /\ length(_pda, _qda) /\ length(l1, _oda) -> 0
append(cons(h1, t1), l2, cons(h1, _jda)) <= append(t1, l2, _jda) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
length(cons(x, ll), s(_fda)) <= length(ll, _fda) -> 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
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
le(z, z) <= le(s(z), s(z))
}

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
}
]


;
le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= True
  le(z, s(x_1_0)) <= True
  le(z, z) <= True
}
]


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



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




Answer of teacher:

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

le(z, s(nn2)) <= True  :
No: ()

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

le(z, _qda) <= append(l1, l2, _pda) /\ le(z, _oda) /\ length(_pda, _qda) /\ length(l1, _oda)  :
No: ()

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

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_yxbq_0)  ;  nn2 -> z
}

False <= le(s(nn1), z)  :
No: ()

False <= le(z, z)  :
Yes: {

}

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


-------------------------------------------
Step 4, which took 0.012091 s (model generation: 0.011965,  model checking: 0.000126):

Clauses:
{
append(nil, l2, l2) <= True -> 0
le(z, s(nn2)) <= True -> 0
length(nil, z) <= True -> 0
le(z, _qda) <= append(l1, l2, _pda) /\ le(z, _oda) /\ length(_pda, _qda) /\ length(l1, _oda) -> 0
append(cons(h1, t1), l2, cons(h1, _jda)) <= append(t1, l2, _jda) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
False <= le(s(nn1), z) -> 0
False <= le(z, z) -> 0
length(cons(x, ll), s(_fda)) <= length(ll, _fda) -> 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
le(s(z), s(s(z))) <= True
le(z, s(z)) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
le(s(z), z) <= le(s(s(z)), s(z))
False <= le(s(z), s(z))
False <= le(z, z)
}

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
}
]


;
le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(s(x_0_0), z) <= True
  le(z, s(x_1_0)) <= True
}
]


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



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




Answer of teacher:

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

le(z, s(nn2)) <= True  :
No: ()

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

le(z, _qda) <= append(l1, l2, _pda) /\ le(z, _oda) /\ length(_pda, _qda) /\ length(l1, _oda)  :
No: ()

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

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
No: ()

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
No: ()

False <= le(s(nn1), z)  :
Yes: {

}

False <= le(z, z)  :
No: ()

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


Total time: 0.066973
Learner time: 0.053917
Teacher time: 0.000472
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
}
]


;
le ->
[
le : <nat * nat>
{
  le(s(x_0_0), s(x_1_0)) <= le(x_0_0, x_1_0)
  le(z, s(x_1_0)) <= True
}
]


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



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