Solving ../../benchmarks/smtlib/true/length_cons_le.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:
{
(le, P:
{
le(z, s(nn2)) <= True
False <= le(n1, z)
le(s(nn1), s(nn2)) <= le(nn1, nn2)
le(nn1, nn2) <= le(s(nn1), s(nn2))
}
)
(length, F:
{
length(nil, z) <= True
length(cons(x, ll), s(_gs)) <= length(ll, _gs)
}
eq_nat(_is, _js) <= length(_hs, _is) /\ length(_hs, _js)
)
}

properties:
{
le(_ks, _ls) <= length(l, _ks) /\ length(cons(x, l), _ls)
}


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

Clause system for inference is:

{
length(nil, z) <= True -> 0
False <= le(n1, z) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
le(_ks, _ls) <= length(l, _ks) /\ length(cons(x, l), _ls) -> 0
length(cons(x, ll), s(_gs)) <= length(ll, _gs) -> 0
}


Solving took 0.066882 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 : <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 0.006085 s (model generation: 0.006039,  model checking: 0.000046):

Clauses:
{
length(nil, z) <= True -> 0
False <= le(n1, z) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
le(_ks, _ls) <= length(l, _ks) /\ length(cons(x, l), _ls) -> 0
length(cons(x, ll), s(_gs)) <= length(ll, _gs) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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


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



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




Answer of teacher:

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

}

False <= le(n1, z)  :
No: ()

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

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

le(_ks, _ls) <= length(l, _ks) /\ length(cons(x, l), _ls)  :
No: ()

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


-------------------------------------------
Step 1, which took 0.005933 s (model generation: 0.005884,  model checking: 0.000049):

Clauses:
{
length(nil, z) <= True -> 0
False <= le(n1, z) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
le(_ks, _ls) <= length(l, _ks) /\ length(cons(x, l), _ls) -> 0
length(cons(x, ll), s(_gs)) <= length(ll, _gs) -> 0
}

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

Current best model:
|_
name: None

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


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



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




Answer of teacher:

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

False <= le(n1, z)  :
No: ()

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

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

le(_ks, _ls) <= length(l, _ks) /\ length(cons(x, l), _ls)  :
No: ()

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


-------------------------------------------
Step 2, which took 0.006359 s (model generation: 0.006313,  model checking: 0.000046):

Clauses:
{
length(nil, z) <= True -> 0
False <= le(n1, z) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
le(_ks, _ls) <= length(l, _ks) /\ length(cons(x, l), _ls) -> 0
length(cons(x, ll), s(_gs)) <= length(ll, _gs) -> 0
}

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

Current best model:
|_
name: None

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


;
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: ()

False <= le(n1, z)  :
No: ()

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

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

le(_ks, _ls) <= length(l, _ks) /\ length(cons(x, l), _ls)  :
Yes: {
_ks -> z  ;  _ls -> s(_fygq_0)  ;  l -> nil
}

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


-------------------------------------------
Step 3, which took 0.007280 s (model generation: 0.007217,  model checking: 0.000063):

Clauses:
{
length(nil, z) <= True -> 0
False <= le(n1, z) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
le(_ks, _ls) <= length(l, _ks) /\ length(cons(x, l), _ls) -> 0
length(cons(x, ll), s(_gs)) <= length(ll, _gs) -> 0
}

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

Current best model:
|_
name: None

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


;
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: ()

False <= le(n1, z)  :
No: ()

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
Yes: {
nn1 -> z  ;  nn2 -> s(_iygq_0)
}

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

le(_ks, _ls) <= length(l, _ks) /\ length(cons(x, l), _ls)  :
Yes: {
_ks -> s(_jygq_0)  ;  _ls -> s(_kygq_0)  ;  l -> cons(_lygq_0, _lygq_1)
}

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


-------------------------------------------
Step 4, which took 0.011958 s (model generation: 0.011908,  model checking: 0.000050):

Clauses:
{
length(nil, z) <= True -> 0
False <= le(n1, z) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
le(_ks, _ls) <= length(l, _ks) /\ length(cons(x, l), _ls) -> 0
length(cons(x, ll), s(_gs)) <= length(ll, _gs) -> 0
}

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

False <= le(n1, z)  :
No: ()

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

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

le(_ks, _ls) <= length(l, _ks) /\ length(cons(x, l), _ls)  :
No: ()

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


-------------------------------------------
Step 5, which took 0.009425 s (model generation: 0.009379,  model checking: 0.000046):

Clauses:
{
length(nil, z) <= True -> 0
False <= le(n1, z) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
le(_ks, _ls) <= length(l, _ks) /\ length(cons(x, l), _ls) -> 0
length(cons(x, ll), s(_gs)) <= length(ll, _gs) -> 0
}

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

False <= le(n1, z)  :
Yes: {
n1 -> z
}

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

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_rygq_0)  ;  nn2 -> z
}

le(_ks, _ls) <= length(l, _ks) /\ length(cons(x, l), _ls)  :
No: ()

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


-------------------------------------------
Step 6, which took 0.008263 s (model generation: 0.008159,  model checking: 0.000104):

Clauses:
{
length(nil, z) <= True -> 0
False <= le(n1, z) -> 0
le(s(nn1), s(nn2)) <= le(nn1, nn2) -> 0
le(nn1, nn2) <= le(s(nn1), s(nn2)) -> 0
le(_ks, _ls) <= length(l, _ks) /\ length(cons(x, l), _ls) -> 0
length(cons(x, ll), s(_gs)) <= length(ll, _gs) -> 0
}

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




Answer of teacher:

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

False <= le(n1, z)  :
Yes: {
n1 -> s(_tygq_0)
}

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

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

le(_ks, _ls) <= length(l, _ks) /\ length(cons(x, l), _ls)  :
No: ()

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


Total time: 0.066882
Learner time: 0.054899
Teacher time: 0.000404
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 : <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}
_|