Solving ../../benchmarks/smtlib/true/insert_length_eq.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:
{
(leq, P:
{
leq(a, y) <= True
leq(b, b) <= True
False <= leq(b, a)
}
)
(insert, F:
{
insert(x, nil, cons(x, nil)) <= True
insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt)
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)
}
eq_eltlist(_au, _bu) <= insert(_yt, _zt, _au) /\ insert(_yt, _zt, _bu)
)
(length, F:
{
length(nil, z) <= True
length(cons(x, ll), s(_cu)) <= length(ll, _cu)
}
eq_nat(_eu, _fu) <= length(_du, _eu) /\ length(_du, _fu)
)
}

properties:
{
eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu)
}


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

Clause system for inference is:

{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu) -> 0
insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt) -> 0
length(cons(x, ll), s(_cu)) <= length(ll, _cu) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
}


Solving took 0.280388 seconds.
Yes: |_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  _r_1(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1)) <= _r_1(x_0_1, x_1_1)
  _r_1(nil, cons(x_1_0, x_1_1)) <= _r_2(x_1_1)
  _r_2(nil) <= True
  insert(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_1, x_2_1)
  insert(a, nil, cons(x_2_0, x_2_1)) <= _r_2(x_2_1)
  insert(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_1, x_2_1)
  insert(b, nil, cons(x_2_0, x_2_1)) <= _r_2(x_2_1)
}
]


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


;
leq ->
[
leq : <elt * elt>
{
  leq(a, a) <= True
  leq(a, b) <= True
  leq(b, b) <= True
}
]



--
Equality automata are defined for: {elt, eltlist, nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006137 s (model generation: 0.006069,  model checking: 0.000068):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu) -> 0
insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt) -> 0
length(cons(x, ll), s(_cu)) <= length(ll, _cu) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  
}
]


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


;
leq ->
[
leq : <elt * elt>
{
  
}
]



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




Answer of teacher:

insert(x, nil, cons(x, nil)) <= True  :
Yes: {
x -> b
}

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

}

leq(a, y) <= True  :
Yes: {
y -> b
}

leq(b, b) <= True  :
Yes: {

}

eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu)  :
No: ()

insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt)  :
No: ()

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

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
No: ()

False <= leq(b, a)  :
No: ()


-------------------------------------------
Step 1, which took 0.006899 s (model generation: 0.006820,  model checking: 0.000079):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu) -> 0
insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt) -> 0
length(cons(x, ll), s(_cu)) <= length(ll, _cu) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
}

Accumulated learning constraints:
{
insert(b, nil, cons(b, nil)) <= True
length(nil, z) <= True
leq(a, b) <= True
leq(b, b) <= True
}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  insert(b, nil, cons(x_2_0, x_2_1)) <= True
}
]


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


;
leq ->
[
leq : <elt * elt>
{
  leq(a, b) <= True
  leq(b, b) <= True
}
]



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




Answer of teacher:

insert(x, nil, cons(x, nil)) <= True  :
Yes: {
x -> a
}

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

leq(a, y) <= True  :
Yes: {
y -> a
}

leq(b, b) <= True  :
No: ()

eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu)  :
No: ()

insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt)  :
Yes: {
_xt -> cons(_ecne_0, _ecne_1)  ;  x -> b  ;  y -> a  ;  z -> nil
}

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

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
Yes: {
x -> b  ;  y -> b
}

False <= leq(b, a)  :
No: ()


-------------------------------------------
Step 2, which took 0.011319 s (model generation: 0.011159,  model checking: 0.000160):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu) -> 0
insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt) -> 0
length(cons(x, ll), s(_cu)) <= length(ll, _cu) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
}

Accumulated learning constraints:
{
insert(a, nil, cons(a, nil)) <= True
insert(b, cons(b, nil), cons(b, cons(b, nil))) <= True
insert(b, nil, cons(b, nil)) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
insert(b, cons(a, nil), cons(a, cons(a, nil))) \/ leq(b, a) <= insert(b, nil, cons(a, nil))
}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  insert(a, nil, cons(x_2_0, x_2_1)) <= True
  insert(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  insert(b, nil, cons(x_2_0, x_2_1)) <= True
}
]


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


;
leq ->
[
leq : <elt * elt>
{
  leq(a, a) <= True
  leq(a, b) <= True
  leq(b, a) <= True
  leq(b, b) <= True
}
]



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




Answer of teacher:

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

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

leq(a, y) <= True  :
No: ()

leq(b, b) <= True  :
No: ()

eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu)  :
Yes: {
_gu -> s(_tcne_0)  ;  _hu -> cons(_ucne_0, _ucne_1)  ;  _iu -> s(z)  ;  l -> cons(_wcne_0, _wcne_1)  ;  x -> b
}

insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt)  :
No: ()

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

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
Yes: {
x -> a  ;  y -> b
}

False <= leq(b, a)  :
Yes: {

}


-------------------------------------------
Step 3, which took 0.022332 s (model generation: 0.022182,  model checking: 0.000150):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu) -> 0
insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt) -> 0
length(cons(x, ll), s(_cu)) <= length(ll, _cu) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
}

Accumulated learning constraints:
{
insert(a, cons(b, nil), cons(a, cons(b, nil))) <= True
insert(a, nil, cons(a, nil)) <= True
insert(b, cons(b, nil), cons(b, cons(b, nil))) <= True
insert(b, nil, cons(b, nil)) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
False <= insert(b, cons(a, nil), cons(a, nil))
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
False <= leq(b, a)
}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  _r_1(cons(x_0_0, x_0_1)) <= True
  insert(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  insert(a, nil, cons(x_2_0, x_2_1)) <= True
  insert(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_2_1)
  insert(b, nil, cons(x_2_0, x_2_1)) <= True
}
]


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


;
leq ->
[
leq : <elt * elt>
{
  leq(a, a) <= True
  leq(a, b) <= True
  leq(b, b) <= True
}
]



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




Answer of teacher:

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

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

leq(a, y) <= True  :
No: ()

leq(b, b) <= True  :
No: ()

eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu)  :
Yes: {
_gu -> s(_tdne_0)  ;  _hu -> cons(_udne_0, cons(_nene_0, _nene_1))  ;  _iu -> s(z)  ;  l -> cons(_wdne_0, _wdne_1)  ;  x -> b
}

insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt)  :
No: ()

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

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
No: ()

False <= leq(b, a)  :
No: ()


-------------------------------------------
Step 4, which took 0.019307 s (model generation: 0.019137,  model checking: 0.000170):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu) -> 0
insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt) -> 0
length(cons(x, ll), s(_cu)) <= length(ll, _cu) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
}

Accumulated learning constraints:
{
insert(a, cons(b, nil), cons(a, cons(b, nil))) <= True
insert(a, nil, cons(a, nil)) <= True
insert(b, cons(b, nil), cons(b, cons(b, nil))) <= True
insert(b, nil, cons(b, nil)) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
False <= insert(b, cons(a, nil), cons(a, cons(a, nil))) /\ length(cons(a, cons(a, nil)), s(z))
False <= insert(b, cons(a, nil), cons(a, nil))
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
False <= leq(b, a)
}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  _r_1(b) <= True
  insert(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  insert(a, nil, cons(x_2_0, x_2_1)) <= True
  insert(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_2_0)
  insert(b, nil, cons(x_2_0, x_2_1)) <= _r_1(x_2_0)
}
]


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


;
leq ->
[
leq : <elt * elt>
{
  leq(a, a) <= True
  leq(a, b) <= True
  leq(b, b) <= True
}
]



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




Answer of teacher:

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

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

leq(a, y) <= True  :
No: ()

leq(b, b) <= True  :
No: ()

eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu)  :
Yes: {
_gu -> s(_rene_0)  ;  _hu -> cons(_sene_0, _sene_1)  ;  _iu -> s(z)  ;  l -> cons(_uene_0, _uene_1)  ;  x -> a
}

insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt)  :
Yes: {
_xt -> cons(b, _pfne_1)  ;  x -> b  ;  y -> a  ;  z -> nil
}

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

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
No: ()

False <= leq(b, a)  :
No: ()


-------------------------------------------
Step 5, which took 0.024398 s (model generation: 0.024072,  model checking: 0.000326):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu) -> 0
insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt) -> 0
length(cons(x, ll), s(_cu)) <= length(ll, _cu) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
}

Accumulated learning constraints:
{
insert(a, cons(b, nil), cons(a, cons(b, nil))) <= True
insert(a, nil, cons(a, nil)) <= True
insert(b, cons(a, nil), cons(a, cons(b, nil))) <= True
insert(b, cons(b, nil), cons(b, cons(b, nil))) <= True
insert(b, nil, cons(b, nil)) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
False <= insert(a, cons(a, nil), cons(a, nil))
False <= insert(b, cons(a, nil), cons(a, cons(a, nil))) /\ length(cons(a, cons(a, nil)), s(z))
False <= insert(b, cons(a, nil), cons(a, nil))
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
False <= leq(b, a)
}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  _r_1(cons(x_0_0, x_0_1)) <= True
  insert(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_2_1)
  insert(a, nil, cons(x_2_0, x_2_1)) <= True
  insert(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_2_1)
  insert(b, nil, cons(x_2_0, x_2_1)) <= True
}
]


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


;
leq ->
[
leq : <elt * elt>
{
  leq(a, a) <= True
  leq(a, b) <= True
  leq(b, b) <= True
}
]



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




Answer of teacher:

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

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

leq(a, y) <= True  :
No: ()

leq(b, b) <= True  :
No: ()

eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu)  :
Yes: {
_gu -> z  ;  _hu -> cons(_ogne_0, cons(_khne_0, nil))  ;  _iu -> s(s(z))  ;  l -> nil  ;  x -> b
}

insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt)  :
No: ()

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

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
No: ()

False <= leq(b, a)  :
No: ()


-------------------------------------------
Step 6, which took 0.031234 s (model generation: 0.030883,  model checking: 0.000351):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu) -> 0
insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt) -> 0
length(cons(x, ll), s(_cu)) <= length(ll, _cu) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
}

Accumulated learning constraints:
{
insert(a, cons(b, nil), cons(a, cons(b, nil))) <= True
insert(a, nil, cons(a, nil)) <= True
insert(b, cons(a, nil), cons(a, cons(b, nil))) <= True
insert(b, cons(b, nil), cons(b, cons(b, nil))) <= True
insert(b, nil, cons(b, nil)) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
False <= insert(a, cons(a, nil), cons(a, nil))
False <= insert(b, cons(a, nil), cons(a, cons(a, nil))) /\ length(cons(a, cons(a, nil)), s(z))
False <= insert(b, cons(a, nil), cons(a, nil))
False <= insert(b, nil, cons(a, cons(a, nil))) /\ length(cons(a, cons(a, nil)), s(s(z)))
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
False <= leq(b, a)
}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  _r_1(cons(x_0_0, x_0_1)) <= True
  insert(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_2_1)
  insert(a, nil, cons(x_2_0, x_2_1)) <= True
  insert(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_2_1)
  insert(b, nil, cons(x_2_0, x_2_1)) <= True
}
]


;
length ->
[
length : <eltlist * nat>
{
  _r_2(nil) <= True
  length(cons(x_0_0, x_0_1), s(x_1_0)) <= _r_2(x_0_1)
  length(nil, z) <= True
}
]


;
leq ->
[
leq : <elt * elt>
{
  leq(a, a) <= True
  leq(a, b) <= True
  leq(b, b) <= True
}
]



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




Answer of teacher:

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

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

leq(a, y) <= True  :
No: ()

leq(b, b) <= True  :
No: ()

eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu)  :
Yes: {
_gu -> z  ;  _hu -> cons(_whne_0, nil)  ;  _iu -> s(s(_gjne_0))  ;  l -> nil  ;  x -> a
}

insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt)  :
No: ()

length(cons(x, ll), s(_cu)) <= length(ll, _cu)  :
Yes: {
_cu -> s(_sine_0)  ;  ll -> cons(_tine_0, nil)
}

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
No: ()

False <= leq(b, a)  :
No: ()


-------------------------------------------
Step 7, which took 0.033157 s (model generation: 0.032902,  model checking: 0.000255):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu) -> 0
insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt) -> 0
length(cons(x, ll), s(_cu)) <= length(ll, _cu) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
}

Accumulated learning constraints:
{
insert(a, cons(b, nil), cons(a, cons(b, nil))) <= True
insert(a, nil, cons(a, nil)) <= True
insert(b, cons(a, nil), cons(a, cons(b, nil))) <= True
insert(b, cons(b, nil), cons(b, cons(b, nil))) <= True
insert(b, nil, cons(b, nil)) <= True
length(cons(a, cons(a, nil)), s(s(z))) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
False <= insert(a, cons(a, nil), cons(a, nil))
False <= insert(b, cons(a, nil), cons(a, cons(a, nil))) /\ length(cons(a, cons(a, nil)), s(z))
False <= insert(b, cons(a, nil), cons(a, nil))
False <= insert(b, nil, cons(a, cons(a, nil)))
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
False <= length(cons(a, nil), s(s(z)))
False <= leq(b, a)
}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  _r_1(nil) <= True
  _r_2(cons(x_0_0, x_0_1)) <= True
  insert(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_2(x_2_1)
  insert(a, nil, cons(x_2_0, x_2_1)) <= True
  insert(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_2(x_2_1)
  insert(b, nil, cons(x_2_0, x_2_1)) <= _r_1(x_2_1)
}
]


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


;
leq ->
[
leq : <elt * elt>
{
  leq(a, a) <= True
  leq(a, b) <= True
  leq(b, b) <= True
}
]



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




Answer of teacher:

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

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

leq(a, y) <= True  :
No: ()

leq(b, b) <= True  :
No: ()

eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu)  :
Yes: {
_gu -> z  ;  _hu -> cons(_ojne_0, cons(_ukne_0, nil))  ;  _iu -> s(s(z))  ;  l -> nil  ;  x -> a
}

insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt)  :
No: ()

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

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
No: ()

False <= leq(b, a)  :
No: ()


-------------------------------------------
Step 8, which took 0.033113 s (model generation: 0.032880,  model checking: 0.000233):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu) -> 0
insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt) -> 0
length(cons(x, ll), s(_cu)) <= length(ll, _cu) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
}

Accumulated learning constraints:
{
insert(a, cons(b, nil), cons(a, cons(b, nil))) <= True
insert(a, nil, cons(a, nil)) <= True
insert(b, cons(a, nil), cons(a, cons(b, nil))) <= True
insert(b, cons(b, nil), cons(b, cons(b, nil))) <= True
insert(b, nil, cons(b, nil)) <= True
length(cons(a, cons(a, nil)), s(s(z))) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
False <= insert(a, cons(a, nil), cons(a, nil))
False <= insert(a, nil, cons(a, cons(a, nil)))
False <= insert(b, cons(a, nil), cons(a, cons(a, nil))) /\ length(cons(a, cons(a, nil)), s(z))
False <= insert(b, cons(a, nil), cons(a, nil))
False <= insert(b, nil, cons(a, cons(a, nil)))
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
False <= length(cons(a, nil), s(s(z)))
False <= leq(b, a)
}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  _r_1(nil) <= True
  _r_2(cons(x_0_0, x_0_1)) <= True
  insert(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_2(x_2_1)
  insert(a, nil, cons(x_2_0, x_2_1)) <= _r_1(x_2_1)
  insert(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_2(x_2_1)
  insert(b, nil, cons(x_2_0, x_2_1)) <= _r_1(x_2_1)
}
]


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


;
leq ->
[
leq : <elt * elt>
{
  leq(a, a) <= True
  leq(a, b) <= True
  leq(b, b) <= True
}
]



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




Answer of teacher:

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

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

leq(a, y) <= True  :
No: ()

leq(b, b) <= True  :
No: ()

eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu)  :
Yes: {
_gu -> s(z)  ;  _hu -> cons(_nlne_0, cons(_smne_0, cons(_wmne_0, nil)))  ;  _iu -> s(s(s(z)))  ;  l -> cons(_plne_0, nil)  ;  x -> b
}

insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt)  :
No: ()

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

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
No: ()

False <= leq(b, a)  :
No: ()


-------------------------------------------
Step 9, which took 0.035592 s (model generation: 0.035192,  model checking: 0.000400):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu) -> 0
insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt) -> 0
length(cons(x, ll), s(_cu)) <= length(ll, _cu) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
}

Accumulated learning constraints:
{
insert(a, cons(b, nil), cons(a, cons(b, nil))) <= True
insert(a, nil, cons(a, nil)) <= True
insert(b, cons(a, nil), cons(a, cons(b, nil))) <= True
insert(b, cons(b, nil), cons(b, cons(b, nil))) <= True
insert(b, nil, cons(b, nil)) <= True
length(cons(a, cons(a, nil)), s(s(z))) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
False <= insert(a, cons(a, nil), cons(a, nil))
False <= insert(a, nil, cons(a, cons(a, nil)))
False <= insert(b, cons(a, nil), cons(a, cons(a, cons(a, nil)))) /\ length(cons(a, cons(a, cons(a, nil))), s(s(s(z))))
False <= insert(b, cons(a, nil), cons(a, cons(a, nil))) /\ length(cons(a, cons(a, nil)), s(z))
False <= insert(b, cons(a, nil), cons(a, nil))
False <= insert(b, nil, cons(a, cons(a, nil)))
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
False <= length(cons(a, nil), s(s(z)))
False <= leq(b, a)
}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  _r_1(nil) <= True
  _r_2(cons(x_0_0, x_0_1)) <= _r_1(x_0_1)
  insert(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_2(x_2_1)
  insert(a, nil, cons(x_2_0, x_2_1)) <= _r_1(x_2_1)
  insert(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_2(x_2_1)
  insert(b, nil, cons(x_2_0, x_2_1)) <= _r_1(x_2_1)
}
]


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


;
leq ->
[
leq : <elt * elt>
{
  leq(a, a) <= True
  leq(a, b) <= True
  leq(b, b) <= True
}
]



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




Answer of teacher:

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

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

leq(a, y) <= True  :
No: ()

leq(b, b) <= True  :
No: ()

eq_nat(s(_gu), _iu) <= insert(x, l, _hu) /\ length(_hu, _iu) /\ length(l, _gu)  :
Yes: {
_gu -> s(s(z))  ;  _hu -> cons(_pnne_0, cons(_rone_0, nil))  ;  _iu -> s(s(z))  ;  l -> cons(_rnne_0, cons(_sone_0, nil))  ;  x -> b
}

insert(x, cons(y, z), cons(y, _xt)) \/ leq(x, y) <= insert(x, z, _xt)  :
Yes: {
_xt -> cons(_ynne_0, cons(_zone_0, nil))  ;  x -> b  ;  y -> a  ;  z -> cons(_bone_0, _bone_1)
}

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

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
Yes: {
x -> b  ;  y -> b  ;  z -> cons(_apne_0, _apne_1)
}

False <= leq(b, a)  :
No: ()


Total time: 0.280388
Learner time: 0.221297
Teacher time: 0.002192
Reasons for stopping: Yes: |_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  _r_1(cons(x_0_0, x_0_1), cons(x_1_0, x_1_1)) <= _r_1(x_0_1, x_1_1)
  _r_1(nil, cons(x_1_0, x_1_1)) <= _r_2(x_1_1)
  _r_2(nil) <= True
  insert(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_1, x_2_1)
  insert(a, nil, cons(x_2_0, x_2_1)) <= _r_2(x_2_1)
  insert(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_1, x_2_1)
  insert(b, nil, cons(x_2_0, x_2_1)) <= _r_2(x_2_1)
}
]


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


;
leq ->
[
leq : <elt * elt>
{
  leq(a, a) <= True
  leq(a, b) <= True
  leq(b, b) <= True
}
]



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