Solving ../../benchmarks/smtlib/true/length_cons_le_tsil.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}  ;  nattsil -> {nil, snoc}
}
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(snoc(ll, x), s(_gka)) <= length(ll, _gka)
}
eq_nat(_ika, _jka) <= length(_hka, _ika) /\ length(_hka, _jka)
)
}

properties:
{
le(_kka, _lka) <= length(l, _kka) /\ length(snoc(l, x), _lka)
}


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

Clause system for inference is:

{
length(nil, z) <= True -> 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
le(_kka, _lka) <= length(l, _kka) /\ length(snoc(l, x), _lka) -> 0
length(snoc(ll, x), s(_gka)) <= length(ll, _gka) -> 0
}


Solving took 0.105777 seconds.
Yes: |_
name: None

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 : <nattsil * nat>
{
  length(nil, z) <= True
  length(snoc(x_0_0, x_0_1), s(x_1_0)) <= length(x_0_0, x_1_0)
}
]



--
Equality automata are defined for: {nat, nattsil}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005712 s (model generation: 0.005668,  model checking: 0.000044):

Clauses:
{
length(nil, z) <= True -> 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
le(_kka, _lka) <= length(l, _kka) /\ length(snoc(l, x), _lka) -> 0
length(snoc(ll, x), s(_gka)) <= length(ll, _gka) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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


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



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




Answer of teacher:

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

}

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: ()

le(_kka, _lka) <= length(l, _kka) /\ length(snoc(l, x), _lka)  :
No: ()

length(snoc(ll, x), s(_gka)) <= length(ll, _gka)  :
No: ()


-------------------------------------------
Step 1, which took 0.010155 s (model generation: 0.010059,  model checking: 0.000096):

Clauses:
{
length(nil, z) <= True -> 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
le(_kka, _lka) <= length(l, _kka) /\ length(snoc(l, x), _lka) -> 0
length(snoc(ll, x), s(_gka)) <= length(ll, _gka) -> 0
}

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

Current best model:
|_
name: None

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


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



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




Answer of teacher:

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

le(_kka, _lka) <= length(l, _kka) /\ length(snoc(l, x), _lka)  :
No: ()

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


-------------------------------------------
Step 2, which took 0.017866 s (model generation: 0.017611,  model checking: 0.000255):

Clauses:
{
length(nil, z) <= True -> 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
le(_kka, _lka) <= length(l, _kka) /\ length(snoc(l, x), _lka) -> 0
length(snoc(ll, x), s(_gka)) <= length(ll, _gka) -> 0
}

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

Current best model:
|_
name: None

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


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



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




Answer of teacher:

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

le(_kka, _lka) <= length(l, _kka) /\ length(snoc(l, x), _lka)  :
Yes: {
_kka -> z  ;  _lka -> s(_kqhq_0)  ;  l -> nil
}

length(snoc(ll, x), s(_gka)) <= length(ll, _gka)  :
No: ()


-------------------------------------------
Step 3, which took 0.020680 s (model generation: 0.020542,  model checking: 0.000138):

Clauses:
{
length(nil, z) <= True -> 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
le(_kka, _lka) <= length(l, _kka) /\ length(snoc(l, x), _lka) -> 0
length(snoc(ll, x), s(_gka)) <= length(ll, _gka) -> 0
}

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

Current best model:
|_
name: None

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


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



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




Answer of teacher:

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

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
Yes: {
nn1 -> z  ;  nn2 -> s(_nqhq_0)
}

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

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

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

le(_kka, _lka) <= length(l, _kka) /\ length(snoc(l, x), _lka)  :
Yes: {
_kka -> s(_oqhq_0)  ;  _lka -> s(_pqhq_0)  ;  l -> snoc(_qqhq_0, _qqhq_1)
}

length(snoc(ll, x), s(_gka)) <= length(ll, _gka)  :
No: ()


-------------------------------------------
Step 4, which took 0.022250 s (model generation: 0.022155,  model checking: 0.000095):

Clauses:
{
length(nil, z) <= True -> 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
le(_kka, _lka) <= length(l, _kka) /\ length(snoc(l, x), _lka) -> 0
length(snoc(ll, x), s(_gka)) <= length(ll, _gka) -> 0
}

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

Current best model:
|_
name: None

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


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



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




Answer of teacher:

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

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: ()

le(_kka, _lka) <= length(l, _kka) /\ length(snoc(l, x), _lka)  :
No: ()

length(snoc(ll, x), s(_gka)) <= length(ll, _gka)  :
No: ()


-------------------------------------------
Step 5, which took 0.013620 s (model generation: 0.013566,  model checking: 0.000054):

Clauses:
{
length(nil, z) <= True -> 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
le(_kka, _lka) <= length(l, _kka) /\ length(snoc(l, x), _lka) -> 0
length(snoc(ll, x), s(_gka)) <= length(ll, _gka) -> 0
}

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

Current best model:
|_
name: None

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 : <nattsil * nat>
{
  length(nil, z) <= True
  length(snoc(x_0_0, x_0_1), s(x_1_0)) <= True
}
]



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




Answer of teacher:

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

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

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_vqhq_0)  ;  nn2 -> z
}

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

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

}

le(_kka, _lka) <= length(l, _kka) /\ length(snoc(l, x), _lka)  :
No: ()

length(snoc(ll, x), s(_gka)) <= length(ll, _gka)  :
No: ()


-------------------------------------------
Step 6, which took 0.007779 s (model generation: 0.007662,  model checking: 0.000117):

Clauses:
{
length(nil, z) <= True -> 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
le(_kka, _lka) <= length(l, _kka) /\ length(snoc(l, x), _lka) -> 0
length(snoc(ll, x), s(_gka)) <= length(ll, _gka) -> 0
}

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

Current best model:
|_
name: None

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 : <nattsil * nat>
{
  length(nil, z) <= True
  length(snoc(x_0_0, x_0_1), s(x_1_0)) <= length(x_0_0, x_1_0)
}
]



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




Answer of teacher:

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

le(_kka, _lka) <= length(l, _kka) /\ length(snoc(l, x), _lka)  :
No: ()

length(snoc(ll, x), s(_gka)) <= length(ll, _gka)  :
No: ()


Total time: 0.105777
Learner time: 0.097263
Teacher time: 0.000799
Reasons for stopping: Yes: |_
name: None

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 : <nattsil * nat>
{
  length(nil, z) <= True
  length(snoc(x_0_0, x_0_1), s(x_1_0)) <= length(x_0_0, x_1_0)
}
]



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