Solving ../../benchmarks/smtlib/true/length_delete_leq.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(z, s(nn2)) <= True
leq(z, z) <= True
leq(s(nn1), s(nn2)) <= leq(nn1, nn2)
leq(nn1, nn2) <= leq(s(nn1), s(nn2))
False <= leq(s(nn1), z)
}
)
(length, F:
{
length(nil, z) <= True
length(cons(x, ll), s(_pva)) <= length(ll, _pva)
}
eq_nat(_rva, _sva) <= length(_qva, _rva) /\ length(_qva, _sva)
)
(delete, F:
{
delete(x, nil, nil) <= True
delete(h, cons(h, t), _tva) <= delete(h, t, _tva)
eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva)
}
eq_eltlist(_xva, _yva) <= delete(_vva, _wva, _xva) /\ delete(_vva, _wva, _yva)
)
}

properties:
{
leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa)
}


over-approximation: {delete, length}
under-approximation: {leq}

Clause system for inference is:

{
delete(x, nil, nil) <= True -> 0
length(nil, z) <= True -> 0
delete(h, cons(h, t), _tva) <= delete(h, t, _tva) -> 0
leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa) -> 0
eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva) -> 0
length(cons(x, ll), s(_pva)) <= length(ll, _pva) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
}


Solving took 0.188647 seconds.
Yes: |_
name: None

delete ->
[
delete : <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(cons(x_0_0, x_0_1), nil) <= True
  _r_1(nil, nil) <= True
  delete(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_1, x_2_1)
  delete(a, cons(x_1_0, x_1_1), nil) <= True
  delete(a, nil, nil) <= True
  delete(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_1, x_2_1)
  delete(b, cons(x_1_0, x_1_1), nil) <= True
  delete(b, nil, nil) <= 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 : <nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
}
]



--
Equality automata are defined for: {elt, eltlist, nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005556 s (model generation: 0.005507,  model checking: 0.000049):

Clauses:
{
delete(x, nil, nil) <= True -> 0
length(nil, z) <= True -> 0
delete(h, cons(h, t), _tva) <= delete(h, t, _tva) -> 0
leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa) -> 0
eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva) -> 0
length(cons(x, ll), s(_pva)) <= length(ll, _pva) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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


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


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



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




Answer of teacher:

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

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

}

delete(h, cons(h, t), _tva) <= delete(h, t, _tva)  :
No: ()

leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa)  :
No: ()

eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva)  :
No: ()

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

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

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

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


-------------------------------------------
Step 1, which took 0.007612 s (model generation: 0.007436,  model checking: 0.000176):

Clauses:
{
delete(x, nil, nil) <= True -> 0
length(nil, z) <= True -> 0
delete(h, cons(h, t), _tva) <= delete(h, t, _tva) -> 0
leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa) -> 0
eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva) -> 0
length(cons(x, ll), s(_pva)) <= length(ll, _pva) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
}

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

Current best model:
|_
name: None

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


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


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



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




Answer of teacher:

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

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

delete(h, cons(h, t), _tva) <= delete(h, t, _tva)  :
Yes: {
_tva -> nil  ;  h -> b  ;  t -> nil
}

leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa)  :
Yes: {
_awa -> z  ;  _bwa -> z  ;  _zva -> nil  ;  i -> b  ;  l -> nil
}

eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva)  :
Yes: {
_uva -> nil  ;  h -> a  ;  t -> nil  ;  x -> b
}

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

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

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

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


-------------------------------------------
Step 2, which took 0.014347 s (model generation: 0.014230,  model checking: 0.000117):

Clauses:
{
delete(x, nil, nil) <= True -> 0
length(nil, z) <= True -> 0
delete(h, cons(h, t), _tva) <= delete(h, t, _tva) -> 0
leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa) -> 0
eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva) -> 0
length(cons(x, ll), s(_pva)) <= length(ll, _pva) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
}

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

Current best model:
|_
name: None

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


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


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



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




Answer of teacher:

delete(x, nil, nil) <= True  :
No: ()

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

delete(h, cons(h, t), _tva) <= delete(h, t, _tva)  :
Yes: {
_tva -> nil  ;  h -> a  ;  t -> nil
}

leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa)  :
Yes: {
_awa -> z  ;  _bwa -> s(_aliq_0)  ;  _zva -> nil  ;  i -> b  ;  l -> cons(_dliq_0, _dliq_1)
}

eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva)  :
Yes: {
_uva -> nil  ;  h -> b  ;  t -> nil  ;  x -> a
}

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

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

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

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


-------------------------------------------
Step 3, which took 0.010674 s (model generation: 0.010597,  model checking: 0.000077):

Clauses:
{
delete(x, nil, nil) <= True -> 0
length(nil, z) <= True -> 0
delete(h, cons(h, t), _tva) <= delete(h, t, _tva) -> 0
leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa) -> 0
eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva) -> 0
length(cons(x, ll), s(_pva)) <= length(ll, _pva) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
}

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

Current best model:
|_
name: None

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


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


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



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




Answer of teacher:

delete(x, nil, nil) <= True  :
No: ()

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

delete(h, cons(h, t), _tva) <= delete(h, t, _tva)  :
No: ()

leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa)  :
No: ()

eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva)  :
No: ()

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

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

leq(nn1, nn2) <= leq(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_kliq_0)  ;  nn2 -> z
}

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


-------------------------------------------
Step 4, which took 0.009420 s (model generation: 0.009354,  model checking: 0.000066):

Clauses:
{
delete(x, nil, nil) <= True -> 0
length(nil, z) <= True -> 0
delete(h, cons(h, t), _tva) <= delete(h, t, _tva) -> 0
leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa) -> 0
eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva) -> 0
length(cons(x, ll), s(_pva)) <= length(ll, _pva) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
}

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

Current best model:
|_
name: None

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


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


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



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




Answer of teacher:

delete(x, nil, nil) <= True  :
No: ()

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

delete(h, cons(h, t), _tva) <= delete(h, t, _tva)  :
No: ()

leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa)  :
No: ()

eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva)  :
No: ()

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

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

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

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

}


-------------------------------------------
Step 5, which took 0.008999 s (model generation: 0.008845,  model checking: 0.000154):

Clauses:
{
delete(x, nil, nil) <= True -> 0
length(nil, z) <= True -> 0
delete(h, cons(h, t), _tva) <= delete(h, t, _tva) -> 0
leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa) -> 0
eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva) -> 0
length(cons(x, ll), s(_pva)) <= length(ll, _pva) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
}

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

Current best model:
|_
name: None

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


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


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



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




Answer of teacher:

delete(x, nil, nil) <= True  :
No: ()

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

delete(h, cons(h, t), _tva) <= delete(h, t, _tva)  :
No: ()

leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa)  :
Yes: {
_awa -> s(s(_imiq_0))  ;  _bwa -> s(z)  ;  _zva -> cons(_tliq_0, _tliq_1)  ;  i -> b  ;  l -> cons(_vliq_0, _vliq_1)
}

eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva)  :
No: ()

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

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

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

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


-------------------------------------------
Step 6, which took 0.009119 s (model generation: 0.008934,  model checking: 0.000185):

Clauses:
{
delete(x, nil, nil) <= True -> 0
length(nil, z) <= True -> 0
delete(h, cons(h, t), _tva) <= delete(h, t, _tva) -> 0
leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa) -> 0
eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva) -> 0
length(cons(x, ll), s(_pva)) <= length(ll, _pva) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
}

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

Current best model:
|_
name: None

delete ->
[
delete : <elt * eltlist * eltlist>
{
  delete(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  delete(a, cons(x_1_0, x_1_1), nil) <= True
  delete(a, nil, nil) <= True
  delete(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  delete(b, cons(x_1_0, x_1_1), nil) <= True
  delete(b, nil, nil) <= 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 : <nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
}
]



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




Answer of teacher:

delete(x, nil, nil) <= True  :
No: ()

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

delete(h, cons(h, t), _tva) <= delete(h, t, _tva)  :
No: ()

leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa)  :
Yes: {
_awa -> s(s(z))  ;  _bwa -> s(z)  ;  _zva -> cons(_rmiq_0, cons(_oniq_0, nil))  ;  i -> b  ;  l -> cons(_tmiq_0, nil)
}

eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva)  :
No: ()

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

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

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

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


-------------------------------------------
Step 7, which took 0.014653 s (model generation: 0.014488,  model checking: 0.000165):

Clauses:
{
delete(x, nil, nil) <= True -> 0
length(nil, z) <= True -> 0
delete(h, cons(h, t), _tva) <= delete(h, t, _tva) -> 0
leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa) -> 0
eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva) -> 0
length(cons(x, ll), s(_pva)) <= length(ll, _pva) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
}

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

Current best model:
|_
name: None

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


;
length ->
[
length : <eltlist * nat>
{
  _r_1(a, z) <= True
  length(cons(x_0_0, x_0_1), s(x_1_0)) <= _r_1(x_0_0, x_1_0)
  length(nil, z) <= True
}
]


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



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




Answer of teacher:

delete(x, nil, nil) <= True  :
No: ()

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

delete(h, cons(h, t), _tva) <= delete(h, t, _tva)  :
No: ()

leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa)  :
No: ()

eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva)  :
No: ()

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

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

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

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


-------------------------------------------
Step 8, which took 0.017288 s (model generation: 0.017028,  model checking: 0.000260):

Clauses:
{
delete(x, nil, nil) <= True -> 0
length(nil, z) <= True -> 0
delete(h, cons(h, t), _tva) <= delete(h, t, _tva) -> 0
leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa) -> 0
eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva) -> 0
length(cons(x, ll), s(_pva)) <= length(ll, _pva) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
}

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

Current best model:
|_
name: None

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


;
length ->
[
length : <eltlist * nat>
{
  _r_1(a, z) <= True
  _r_1(b, z) <= True
  length(cons(x_0_0, x_0_1), s(x_1_0)) <= _r_1(x_0_0, x_1_0)
  length(nil, z) <= True
}
]


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



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




Answer of teacher:

delete(x, nil, nil) <= True  :
No: ()

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

delete(h, cons(h, t), _tva) <= delete(h, t, _tva)  :
No: ()

leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa)  :
No: ()

eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva)  :
No: ()

length(cons(x, ll), s(_pva)) <= length(ll, _pva)  :
Yes: {
_pva -> s(z)  ;  ll -> cons(b, _epiq_1)  ;  x -> b
}

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

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

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


-------------------------------------------
Step 9, which took 0.025905 s (model generation: 0.025687,  model checking: 0.000218):

Clauses:
{
delete(x, nil, nil) <= True -> 0
length(nil, z) <= True -> 0
delete(h, cons(h, t), _tva) <= delete(h, t, _tva) -> 0
leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa) -> 0
eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva) -> 0
length(cons(x, ll), s(_pva)) <= length(ll, _pva) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
}

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

Current best model:
|_
name: None

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


;
length ->
[
length : <eltlist * nat>
{
  _r_1(a, z) <= True
  _r_1(b, s(x_1_0)) <= True
  _r_1(b, z) <= True
  length(cons(x_0_0, x_0_1), s(x_1_0)) <= _r_1(x_0_0, x_1_0)
  length(nil, z) <= True
}
]


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



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




Answer of teacher:

delete(x, nil, nil) <= True  :
No: ()

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

delete(h, cons(h, t), _tva) <= delete(h, t, _tva)  :
No: ()

leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa)  :
Yes: {
_awa -> s(s(_mriq_0))  ;  _bwa -> s(z)  ;  _zva -> cons(b, _kqiq_1)  ;  i -> b  ;  l -> cons(b, _mqiq_1)
}

eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva)  :
No: ()

length(cons(x, ll), s(_pva)) <= length(ll, _pva)  :
Yes: {
_pva -> s(z)  ;  ll -> cons(b, _oqiq_1)  ;  x -> a
}

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

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

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


-------------------------------------------
Step 10, which took 0.018166 s (model generation: 0.017931,  model checking: 0.000235):

Clauses:
{
delete(x, nil, nil) <= True -> 0
length(nil, z) <= True -> 0
delete(h, cons(h, t), _tva) <= delete(h, t, _tva) -> 0
leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa) -> 0
eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva) -> 0
length(cons(x, ll), s(_pva)) <= length(ll, _pva) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
}

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

Current best model:
|_
name: None

delete ->
[
delete : <elt * eltlist * eltlist>
{
  _r_1(nil) <= True
  delete(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= True
  delete(a, cons(x_1_0, x_1_1), nil) <= True
  delete(a, nil, nil) <= True
  delete(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_2_1)
  delete(b, cons(x_1_0, x_1_1), nil) <= True
  delete(b, nil, nil) <= 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 : <nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
}
]



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




Answer of teacher:

delete(x, nil, nil) <= True  :
No: ()

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

delete(h, cons(h, t), _tva) <= delete(h, t, _tva)  :
No: ()

leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa)  :
Yes: {
_awa -> s(s(z))  ;  _bwa -> s(z)  ;  _zva -> cons(_bsiq_0, cons(_ptiq_0, nil))  ;  i -> a  ;  l -> cons(_dsiq_0, nil)
}

eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva)  :
Yes: {
_uva -> cons(_jsiq_0, nil)  ;  h -> a  ;  t -> cons(_lsiq_0, _lsiq_1)  ;  x -> b
}

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

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

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

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


-------------------------------------------
Step 11, which took 0.020050 s (model generation: 0.019768,  model checking: 0.000282):

Clauses:
{
delete(x, nil, nil) <= True -> 0
length(nil, z) <= True -> 0
delete(h, cons(h, t), _tva) <= delete(h, t, _tva) -> 0
leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa) -> 0
eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva) -> 0
length(cons(x, ll), s(_pva)) <= length(ll, _pva) -> 0
leq(s(nn1), s(nn2)) <= leq(nn1, nn2) -> 0
leq(nn1, nn2) <= leq(s(nn1), s(nn2)) -> 0
False <= leq(s(nn1), z) -> 0
}

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

Current best model:
|_
name: None

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



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




Answer of teacher:

delete(x, nil, nil) <= True  :
No: ()

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

delete(h, cons(h, t), _tva) <= delete(h, t, _tva)  :
Yes: {
_tva -> cons(_ztiq_0, nil)  ;  h -> b  ;  t -> cons(_buiq_0, nil)
}

leq(_awa, _bwa) <= delete(i, l, _zva) /\ length(_zva, _awa) /\ length(l, _bwa)  :
Yes: {
_awa -> s(s(s(z)))  ;  _bwa -> s(s(z))  ;  _zva -> cons(_juiq_0, cons(_bwiq_0, cons(_iwiq_0, nil)))  ;  i -> b  ;  l -> cons(_luiq_0, cons(_awiq_0, nil))
}

eq_elt(x, h) \/ delete(x, cons(h, t), cons(h, _uva)) <= delete(x, t, _uva)  :
Yes: {
_uva -> nil  ;  h -> b  ;  t -> cons(_suiq_0, _suiq_1)  ;  x -> a
}

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

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

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

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


Total time: 0.188647
Learner time: 0.159805
Teacher time: 0.001984
Reasons for stopping: Yes: |_
name: None

delete ->
[
delete : <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(cons(x_0_0, x_0_1), nil) <= True
  _r_1(nil, nil) <= True
  delete(a, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_1, x_2_1)
  delete(a, cons(x_1_0, x_1_1), nil) <= True
  delete(a, nil, nil) <= True
  delete(b, cons(x_1_0, x_1_1), cons(x_2_0, x_2_1)) <= _r_1(x_1_1, x_2_1)
  delete(b, cons(x_1_0, x_1_1), nil) <= True
  delete(b, nil, nil) <= 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 : <nat * nat>
{
  leq(s(x_0_0), s(x_1_0)) <= leq(x_0_0, x_1_0)
  leq(z, s(x_1_0)) <= True
  leq(z, z) <= True
}
]



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