Solving ../../benchmarks/smtlib/true/length_cons_le_fun_elt.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(_ofa)) <= length(ll, _ofa)
}
eq_nat(_qfa, _rfa) <= length(_pfa, _qfa) /\ length(_pfa, _rfa)
)
(fcons, F:
{
fcons(x, l, cons(x, l)) <= True
}
eq_eltlist(_ufa, _vfa) <= fcons(_sfa, _tfa, _ufa) /\ fcons(_sfa, _tfa, _vfa)
)
}

properties:
{
le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa)
}


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

Clause system for inference is:

{
fcons(x, l, cons(x, l)) <= True -> 0
length(nil, z) <= True -> 0
le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa) -> 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(_ofa)) <= length(ll, _ofa) -> 0
}


Solving took 0.149817 seconds.
Yes: |_
name: None

fcons ->
[
fcons : <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)) <= True
  fcons(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_1, x_2_1)
  fcons(a, nil, cons(x_2_0, x_2_1)) <= True
  fcons(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_1, x_2_1)
  fcons(b, nil, cons(x_2_0, x_2_1)) <= 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)) <= length(x_0_1, x_1_0)
  length(nil, z) <= True
}
]



--
Equality automata are defined for: {elt, eltlist, nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.007668 s (model generation: 0.007533,  model checking: 0.000135):

Clauses:
{
fcons(x, l, cons(x, l)) <= True -> 0
length(nil, z) <= True -> 0
le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa) -> 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(_ofa)) <= length(ll, _ofa) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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


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


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



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




Answer of teacher:

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

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

}

le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa)  :
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(_ofa)) <= length(ll, _ofa)  :
No: ()


-------------------------------------------
Step 1, which took 0.006781 s (model generation: 0.006713,  model checking: 0.000068):

Clauses:
{
fcons(x, l, cons(x, l)) <= True -> 0
length(nil, z) <= True -> 0
le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa) -> 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(_ofa)) <= length(ll, _ofa) -> 0
}

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

Current best model:
|_
name: None

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


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


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



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




Answer of teacher:

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

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

le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa)  :
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(_ofa)) <= length(ll, _ofa)  :
Yes: {
_ofa -> z  ;  ll -> nil
}


-------------------------------------------
Step 2, which took 0.009953 s (model generation: 0.009866,  model checking: 0.000087):

Clauses:
{
fcons(x, l, cons(x, l)) <= True -> 0
length(nil, z) <= True -> 0
le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa) -> 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(_ofa)) <= length(ll, _ofa) -> 0
}

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

Current best model:
|_
name: None

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


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


;
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:

fcons(x, l, cons(x, l)) <= True  :
Yes: {
l -> cons(_uahq_0, _uahq_1)  ;  x -> b
}

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

le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa)  :
Yes: {
_wfa -> z  ;  _xfa -> cons(_xahq_0, _xahq_1)  ;  _yfa -> s(_yahq_0)  ;  l -> nil  ;  x -> a
}

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(_ofa)) <= length(ll, _ofa)  :
No: ()


-------------------------------------------
Step 3, which took 0.015623 s (model generation: 0.015508,  model checking: 0.000115):

Clauses:
{
fcons(x, l, cons(x, l)) <= True -> 0
length(nil, z) <= True -> 0
le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa) -> 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(_ofa)) <= length(ll, _ofa) -> 0
}

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

Current best model:
|_
name: None

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


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

fcons(x, l, cons(x, l)) <= True  :
Yes: {
l -> cons(_gbhq_0, _gbhq_1)  ;  x -> a
}

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

le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa)  :
Yes: {
_wfa -> s(_ibhq_0)  ;  _xfa -> cons(_jbhq_0, _jbhq_1)  ;  _yfa -> s(_kbhq_0)  ;  l -> cons(_lbhq_0, _lbhq_1)  ;  x -> b
}

le(s(nn1), s(nn2)) <= le(nn1, nn2)  :
Yes: {
nn1 -> z  ;  nn2 -> s(_obhq_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(_ofa)) <= length(ll, _ofa)  :
No: ()


-------------------------------------------
Step 4, which took 0.012326 s (model generation: 0.012265,  model checking: 0.000061):

Clauses:
{
fcons(x, l, cons(x, l)) <= True -> 0
length(nil, z) <= True -> 0
le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa) -> 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(_ofa)) <= length(ll, _ofa) -> 0
}

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

Current best model:
|_
name: None

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

fcons(x, l, cons(x, l)) <= True  :
No: ()

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

le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa)  :
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: ()

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


-------------------------------------------
Step 5, which took 0.011660 s (model generation: 0.011608,  model checking: 0.000052):

Clauses:
{
fcons(x, l, cons(x, l)) <= True -> 0
length(nil, z) <= True -> 0
le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa) -> 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(_ofa)) <= length(ll, _ofa) -> 0
}

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

Current best model:
|_
name: None

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

fcons(x, l, cons(x, l)) <= True  :
No: ()

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

le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa)  :
No: ()

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

le(nn1, nn2) <= le(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_tbhq_0)  ;  nn2 -> z
}

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

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

}

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


-------------------------------------------
Step 6, which took 0.014933 s (model generation: 0.014359,  model checking: 0.000574):

Clauses:
{
fcons(x, l, cons(x, l)) <= True -> 0
length(nil, z) <= True -> 0
le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa) -> 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(_ofa)) <= length(ll, _ofa) -> 0
}

Accumulated learning constraints:
{
fcons(a, cons(a, nil), cons(a, cons(a, nil))) <= True
fcons(a, nil, cons(a, nil)) <= True
fcons(b, cons(a, nil), cons(b, cons(a, nil))) <= True
fcons(b, nil, cons(b, 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
False <= fcons(b, cons(a, nil), cons(a, nil))
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

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

fcons(x, l, cons(x, l)) <= True  :
No: ()

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

le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa)  :
Yes: {
_wfa -> s(z)  ;  _xfa -> cons(_ybhq_0, _ybhq_1)  ;  _yfa -> s(z)  ;  l -> cons(_achq_0, _achq_1)  ;  x -> a
}

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(_ofa)) <= length(ll, _ofa)  :
No: ()


-------------------------------------------
Step 7, which took 0.014091 s (model generation: 0.013820,  model checking: 0.000271):

Clauses:
{
fcons(x, l, cons(x, l)) <= True -> 0
length(nil, z) <= True -> 0
le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa) -> 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(_ofa)) <= length(ll, _ofa) -> 0
}

Accumulated learning constraints:
{
fcons(a, cons(a, nil), cons(a, cons(a, nil))) <= True
fcons(a, nil, cons(a, nil)) <= True
fcons(b, cons(a, nil), cons(b, cons(a, nil))) <= True
fcons(b, nil, cons(b, 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
False <= fcons(a, cons(a, nil), cons(a, nil))
False <= fcons(b, cons(a, nil), cons(a, nil))
False <= le(s(s(z)), s(z))
False <= le(s(z), s(z))
False <= le(s(z), z)
False <= le(z, z)
}

Current best model:
|_
name: None

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




Answer of teacher:

fcons(x, l, cons(x, l)) <= True  :
No: ()

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

le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa)  :
Yes: {
_wfa -> s(z)  ;  _xfa -> cons(_gdhq_0, cons(_udhq_0, _udhq_1))  ;  _yfa -> s(z)  ;  l -> cons(_idhq_0, _idhq_1)  ;  x -> b
}

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(_ofa)) <= length(ll, _ofa)  :
No: ()


-------------------------------------------
Step 8, which took 0.015518 s (model generation: 0.015036,  model checking: 0.000482):

Clauses:
{
fcons(x, l, cons(x, l)) <= True -> 0
length(nil, z) <= True -> 0
le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa) -> 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(_ofa)) <= length(ll, _ofa) -> 0
}

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

Current best model:
|_
name: None

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



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




Answer of teacher:

fcons(x, l, cons(x, l)) <= True  :
No: ()

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

le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa)  :
Yes: {
_wfa -> s(s(z))  ;  _xfa -> cons(_lehq_0, cons(_dfhq_0, nil))  ;  _yfa -> s(s(z))  ;  l -> cons(_nehq_0, cons(_gfhq_0, nil))  ;  x -> b
}

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(_ofa)) <= length(ll, _ofa)  :
No: ()


-------------------------------------------
Step 9, which took 0.023357 s (model generation: 0.023171,  model checking: 0.000186):

Clauses:
{
fcons(x, l, cons(x, l)) <= True -> 0
length(nil, z) <= True -> 0
le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa) -> 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(_ofa)) <= length(ll, _ofa) -> 0
}

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

Current best model:
|_
name: None

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



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




Answer of teacher:

fcons(x, l, cons(x, l)) <= True  :
Yes: {
l -> cons(_vfhq_0, cons(_vghq_0, _vghq_1))  ;  x -> b
}

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

le(_wfa, _yfa) <= fcons(x, l, _xfa) /\ length(_xfa, _yfa) /\ length(l, _wfa)  :
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(_ofa)) <= length(ll, _ofa)  :
No: ()


Total time: 0.149817
Learner time: 0.129879
Teacher time: 0.002031
Reasons for stopping: Yes: |_
name: None

fcons ->
[
fcons : <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)) <= True
  fcons(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_1, x_2_1)
  fcons(a, nil, cons(x_2_0, x_2_1)) <= True
  fcons(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_1, x_2_1)
  fcons(b, nil, cons(x_2_0, x_2_1)) <= 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)) <= length(x_0_1, x_1_0)
  length(nil, z) <= True
}
]



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