Solving ../../benchmarks/smtlib/true/isaplanner_prop15.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, _li)) \/ leq(x, y) <= insert(x, z, _li)
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)
}
eq_eltlist(_oi, _pi) <= insert(_mi, _ni, _oi) /\ insert(_mi, _ni, _pi)
)
(length, F:
{
length(nil, z) <= True
length(cons(x, ll), s(_qi)) <= length(ll, _qi)
}
eq_nat(_si, _ti) <= length(_ri, _si) /\ length(_ri, _ti)
)
(leqnat, P:
{
leqnat(z, s(nn2)) <= True
leqnat(z, z) <= True
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2)
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2))
False <= leqnat(s(nn1), z)
}
)
(le_nat, P:
{
le_nat(z, s(nn2)) <= True
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2)
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2))
False <= le_nat(s(nn1), z)
False <= le_nat(z, z)
}
)
}

properties:
{
le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui)
}


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

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
le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui) -> 0
insert(x, cons(y, z), cons(y, _li)) \/ leq(x, y) <= insert(x, z, _li) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
length(cons(x, ll), s(_qi)) <= length(ll, _qi) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2) -> 0
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2)) -> 0
}


Solving took 0.184483 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)) <= 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)) <= True
  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)) <= True
}
]


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


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


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



--
Equality automata are defined for: {elt, eltlist, nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006158 s (model generation: 0.006056,  model checking: 0.000102):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui) -> 0
insert(x, cons(y, z), cons(y, _li)) \/ leq(x, y) <= insert(x, z, _li) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
length(cons(x, ll), s(_qi)) <= length(ll, _qi) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2) -> 0
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2)) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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


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


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


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


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



--
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: {

}

le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui)  :
No: ()

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

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

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

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

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

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

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

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

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

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


-------------------------------------------
Step 1, which took 0.006982 s (model generation: 0.006810,  model checking: 0.000172):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui) -> 0
insert(x, cons(y, z), cons(y, _li)) \/ leq(x, y) <= insert(x, z, _li) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
length(cons(x, ll), s(_qi)) <= length(ll, _qi) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2) -> 0
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2)) -> 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
}
]


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


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


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


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



--
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: ()

le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui)  :
No: ()

insert(x, cons(y, z), cons(y, _li)) \/ leq(x, y) <= insert(x, z, _li)  :
Yes: {
_li -> cons(_osre_0, _osre_1)  ;  x -> b  ;  y -> a  ;  z -> nil
}

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

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

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

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

length(cons(x, ll), s(_qi)) <= length(ll, _qi)  :
Yes: {
_qi -> 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: ()

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

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


-------------------------------------------
Step 2, which took 0.010012 s (model generation: 0.009854,  model checking: 0.000158):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui) -> 0
insert(x, cons(y, z), cons(y, _li)) \/ leq(x, y) <= insert(x, z, _li) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
length(cons(x, ll), s(_qi)) <= length(ll, _qi) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2) -> 0
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2)) -> 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
}
]


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


;
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
}
]


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



--
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: ()

le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui)  :
Yes: {
_ui -> z  ;  _vi -> cons(_zsre_0, _zsre_1)  ;  _wi -> s(_atre_0)  ;  l -> nil  ;  x -> a
}

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

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

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

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

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

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

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

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

}

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

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


-------------------------------------------
Step 3, which took 0.011281 s (model generation: 0.011146,  model checking: 0.000135):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui) -> 0
insert(x, cons(y, z), cons(y, _li)) \/ leq(x, y) <= insert(x, z, _li) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
length(cons(x, ll), s(_qi)) <= length(ll, _qi) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2) -> 0
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2)) -> 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
le_nat(z, 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
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>
{
  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)) <= True
  insert(b, nil, cons(x_2_0, x_2_1)) <= True
}
]


;
le_nat ->
[
le_nat : <nat * nat>
{
  le_nat(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
}
]


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


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



--
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: ()

le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui)  :
Yes: {
_ui -> s(_wtre_0)  ;  _vi -> cons(_xtre_0, _xtre_1)  ;  _wi -> s(_ytre_0)  ;  l -> cons(_ztre_0, _ztre_1)  ;  x -> b
}

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

le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2)  :
Yes: {
nn1 -> z  ;  nn2 -> s(_cure_0)
}

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

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

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

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

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

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

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

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


-------------------------------------------
Step 4, which took 0.011861 s (model generation: 0.011746,  model checking: 0.000115):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui) -> 0
insert(x, cons(y, z), cons(y, _li)) \/ leq(x, y) <= insert(x, z, _li) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
length(cons(x, ll), s(_qi)) <= length(ll, _qi) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2) -> 0
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2)) -> 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
le_nat(s(z), s(s(z))) <= True
le_nat(z, 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
le_nat(s(z), s(z)) <= 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>
{
  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)) <= True
  insert(b, nil, cons(x_2_0, x_2_1)) <= True
}
]


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


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


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



--
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: ()

le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui)  :
No: ()

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

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

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

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

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

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

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

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

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

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


-------------------------------------------
Step 5, which took 0.011756 s (model generation: 0.011649,  model checking: 0.000107):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui) -> 0
insert(x, cons(y, z), cons(y, _li)) \/ leq(x, y) <= insert(x, z, _li) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
length(cons(x, ll), s(_qi)) <= length(ll, _qi) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2) -> 0
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2)) -> 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
le_nat(s(z), s(s(z))) <= True
le_nat(z, 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
le_nat(s(z), s(z)) <= insert(b, cons(a, nil), cons(a, nil))
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
le_nat(z, z) <= le_nat(s(z), s(z))
False <= leq(b, a)
}

Current best model:
|_
name: None

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


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


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



--
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: ()

le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui)  :
No: ()

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

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

le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_hure_0)  ;  nn2 -> z
}

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

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

}

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

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

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

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

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


-------------------------------------------
Step 6, which took 0.018070 s (model generation: 0.017720,  model checking: 0.000350):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui) -> 0
insert(x, cons(y, z), cons(y, _li)) \/ leq(x, y) <= insert(x, z, _li) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
length(cons(x, ll), s(_qi)) <= length(ll, _qi) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2) -> 0
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2)) -> 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
le_nat(s(z), s(s(z))) <= True
le_nat(z, 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(b, cons(a, nil), cons(a, nil))
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
le_nat(s(z), z) <= le_nat(s(s(z)), s(z))
False <= le_nat(s(z), s(z))
False <= le_nat(z, z)
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
}
]


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


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


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



--
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: ()

le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui)  :
Yes: {
_ui -> s(z)  ;  _vi -> cons(_pure_0, cons(_nvre_0, _nvre_1))  ;  _wi -> s(z)  ;  l -> cons(_rure_0, _rure_1)  ;  x -> b
}

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

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

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

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

}

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

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

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

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

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

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


-------------------------------------------
Step 7, which took 0.018402 s (model generation: 0.018149,  model checking: 0.000253):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui) -> 0
insert(x, cons(y, z), cons(y, _li)) \/ leq(x, y) <= insert(x, z, _li) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
length(cons(x, ll), s(_qi)) <= length(ll, _qi) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2) -> 0
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2)) -> 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
le_nat(s(z), s(s(z))) <= True
le_nat(z, 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(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 <= le_nat(s(s(z)), s(z))
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
False <= le_nat(z, z)
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)
}
]


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


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


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



--
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: ()

le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui)  :
Yes: {
_ui -> s(z)  ;  _vi -> cons(b, _zvre_1)  ;  _wi -> s(z)  ;  l -> cons(_bwre_0, _bwre_1)  ;  x -> b
}

insert(x, cons(y, z), cons(y, _li)) \/ leq(x, y) <= insert(x, z, _li)  :
Yes: {
_li -> cons(b, _hwre_1)  ;  x -> b  ;  y -> a  ;  z -> nil
}

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

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

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

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

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

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

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

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

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


-------------------------------------------
Step 8, which took 0.020327 s (model generation: 0.019932,  model checking: 0.000395):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui) -> 0
insert(x, cons(y, z), cons(y, _li)) \/ leq(x, y) <= insert(x, z, _li) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
length(cons(x, ll), s(_qi)) <= length(ll, _qi) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2) -> 0
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2)) -> 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
le_nat(s(z), s(s(z))) <= True
le_nat(z, 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(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, cons(a, nil), cons(b, nil)) /\ length(cons(b, nil), s(z))
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
False <= le_nat(s(s(z)), s(z))
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
False <= le_nat(z, z)
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
}
]


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


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


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



--
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: ()

le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui)  :
Yes: {
_ui -> s(z)  ;  _vi -> cons(_fxre_0, nil)  ;  _wi -> s(z)  ;  l -> cons(_hxre_0, nil)  ;  x -> a
}

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

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

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

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

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

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

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

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

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

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


-------------------------------------------
Step 9, which took 0.020767 s (model generation: 0.020439,  model checking: 0.000328):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui) -> 0
insert(x, cons(y, z), cons(y, _li)) \/ leq(x, y) <= insert(x, z, _li) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
length(cons(x, ll), s(_qi)) <= length(ll, _qi) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2) -> 0
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2)) -> 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
le_nat(s(z), s(s(z))) <= True
le_nat(z, 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, cons(a, nil), cons(b, nil)) /\ length(cons(b, nil), s(z))
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
False <= le_nat(s(s(z)), s(z))
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
False <= le_nat(z, z)
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
}
]


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


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


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



--
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: ()

le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui)  :
Yes: {
_ui -> s(s(z))  ;  _vi -> cons(_zyre_0, cons(_kase_0, nil))  ;  _wi -> s(s(z))  ;  l -> cons(_bzre_0, cons(_nase_0, nil))  ;  x -> a
}

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

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

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

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

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

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

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

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

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

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


-------------------------------------------
Step 10, which took 0.022322 s (model generation: 0.022056,  model checking: 0.000266):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui) -> 0
insert(x, cons(y, z), cons(y, _li)) \/ leq(x, y) <= insert(x, z, _li) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
length(cons(x, ll), s(_qi)) <= length(ll, _qi) -> 0
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y) -> 0
False <= leq(b, a) -> 0
leqnat(s(nn1), s(nn2)) <= leqnat(nn1, nn2) -> 0
leqnat(nn1, nn2) <= leqnat(s(nn1), s(nn2)) -> 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
le_nat(s(z), s(s(z))) <= True
le_nat(z, 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
le_nat(s(s(z)), s(s(z))) <= insert(a, cons(a, cons(a, nil)), cons(a, cons(a, nil))) /\ length(cons(a, cons(a, nil)), s(s(z)))
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, cons(a, nil), cons(b, nil)) /\ length(cons(b, nil), s(z))
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
False <= le_nat(s(s(z)), s(z))
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
False <= le_nat(z, z)
False <= leq(b, a)
}

Current best model:
|_
name: None

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


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


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


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



--
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: ()

le_nat(_ui, _wi) <= insert(x, l, _vi) /\ length(_vi, _wi) /\ length(l, _ui)  :
No: ()

insert(x, cons(y, z), cons(y, _li)) \/ leq(x, y) <= insert(x, z, _li)  :
Yes: {
_li -> cons(_kbse_0, cons(_ocse_0, _ocse_1))  ;  x -> b  ;  y -> a  ;  z -> cons(_nbse_0, nil)
}

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

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

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

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

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

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
Yes: {
x -> a  ;  y -> a  ;  z -> cons(_mcse_0, _mcse_1)
}

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

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

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


Total time: 0.184483
Learner time: 0.155557
Teacher time: 0.002381
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)) <= 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)) <= True
  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)) <= True
}
]


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


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


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



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