Solving ../../benchmarks/smtlib/true/insert_length_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(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, _db)) \/ leq(x, y) <= insert(x, z, _db)
insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)
}
eq_eltlist(_gb, _hb) <= insert(_eb, _fb, _gb) /\ insert(_eb, _fb, _hb)
)
(length, F:
{
length(nil, z) <= True
length(cons(x, ll), s(_ib)) <= length(ll, _ib)
}
eq_nat(_kb, _lb) <= length(_jb, _kb) /\ length(_jb, _lb)
)
(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)
}
)
}

properties:
{
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)
}


over-approximation: {insert, length}
under-approximation: {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
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 0
}


Solving took 0.337850 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
  _r_1(nil, 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)) <= 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
}
]


;
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>
{
  leqnat(s(x_0_0), s(x_1_0)) <= leqnat(x_0_0, x_1_0)
  leqnat(z, s(x_1_0)) <= True
  leqnat(z, z) <= True
}
]



--
Equality automata are defined for: {elt, eltlist, nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005957 s (model generation: 0.005882,  model checking: 0.000075):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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


;
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: {

}

leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)  :
No: ()

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

length(cons(x, ll), s(_ib)) <= length(ll, _ib)  :
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: ()

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


-------------------------------------------
Step 1, which took 0.006647 s (model generation: 0.006560,  model checking: 0.000087):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 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
}
]


;
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: ()

leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)  :
No: ()

insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db)  :
Yes: {
_db -> cons(_xrne_0, _xrne_1)  ;  x -> b  ;  y -> a  ;  z -> nil
}

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

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


-------------------------------------------
Step 2, which took 0.009352 s (model generation: 0.009234,  model checking: 0.000118):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 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
}
]


;
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: ()

leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)  :
Yes: {
_mb -> z  ;  _nb -> cons(_ssne_0, _ssne_1)  ;  _ob -> s(_tsne_0)  ;  l -> nil  ;  x -> b
}

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

length(cons(x, ll), s(_ib)) <= length(ll, _ib)  :
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: ()

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


-------------------------------------------
Step 3, which took 0.019070 s (model generation: 0.018874,  model checking: 0.000196):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 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
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
leqnat(z, s(z)) <= 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
}
]


;
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>
{
  leqnat(z, s(x_1_0)) <= 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: ()

leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)  :
Yes: {
_mb -> s(_ftne_0)  ;  _nb -> cons(_gtne_0, _gtne_1)  ;  _ob -> s(_htne_0)  ;  l -> cons(_itne_0, _itne_1)  ;  x -> b
}

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

length(cons(x, ll), s(_ib)) <= length(ll, _ib)  :
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)  :
Yes: {
nn1 -> z  ;  nn2 -> s(_ltne_0)
}

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

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


-------------------------------------------
Step 4, which took 0.023628 s (model generation: 0.023472,  model checking: 0.000156):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 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
leqnat(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))
leqnat(z, s(z)) <= insert(b, nil, cons(a, nil))
False <= leq(b, a)
leqnat(s(z), s(s(z))) <= leqnat(z, s(z))
}

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
}
]


;
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>
{
  leqnat(s(x_0_0), s(x_1_0)) <= True
  leqnat(z, s(x_1_0)) <= 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: ()

leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)  :
No: ()

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

length(cons(x, ll), s(_ib)) <= length(ll, _ib)  :
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))  :
Yes: {
nn1 -> z  ;  nn2 -> z
}

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


-------------------------------------------
Step 5, which took 0.020159 s (model generation: 0.020051,  model checking: 0.000108):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 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
leqnat(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))
leqnat(z, s(z)) <= insert(b, nil, cons(a, nil))
False <= leq(b, a)
leqnat(z, z) <= leqnat(s(z), s(z))
leqnat(s(z), s(s(z))) <= leqnat(z, s(z))
}

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
}
]


;
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>
{
  leqnat(s(x_0_0), s(x_1_0)) <= True
  leqnat(z, s(x_1_0)) <= True
  leqnat(z, z) <= 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: ()

leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)  :
No: ()

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

length(cons(x, ll), s(_ib)) <= length(ll, _ib)  :
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))  :
Yes: {
nn1 -> s(_qtne_0)  ;  nn2 -> z
}

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


-------------------------------------------
Step 6, which took 0.022054 s (model generation: 0.021918,  model checking: 0.000136):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 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
leqnat(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))
leqnat(z, s(z)) <= insert(b, nil, cons(a, nil))
False <= leq(b, a)
leqnat(s(z), z) <= leqnat(s(s(z)), s(z))
leqnat(z, z) <= leqnat(s(z), s(z))
leqnat(s(z), s(s(z))) <= leqnat(z, s(z))
}

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
}
]


;
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>
{
  leqnat(s(x_0_0), s(x_1_0)) <= True
  leqnat(s(x_0_0), z) <= True
  leqnat(z, s(x_1_0)) <= True
  leqnat(z, z) <= 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: ()

leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)  :
No: ()

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

length(cons(x, ll), s(_ib)) <= length(ll, _ib)  :
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: ()

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

}


-------------------------------------------
Step 7, which took 0.015185 s (model generation: 0.014932,  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
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 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
leqnat(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))
leqnat(z, s(z)) <= insert(b, nil, cons(a, nil))
False <= leq(b, a)
False <= leqnat(s(s(z)), s(z))
leqnat(z, z) <= leqnat(s(z), s(z))
False <= leqnat(s(z), z)
leqnat(s(z), s(s(z))) <= leqnat(z, s(z))
}

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
}
]


;
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>
{
  leqnat(s(x_0_0), s(x_1_0)) <= leqnat(x_0_0, x_1_0)
  leqnat(z, s(x_1_0)) <= True
  leqnat(z, z) <= 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: ()

leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)  :
Yes: {
_mb -> s(s(_oune_0))  ;  _nb -> cons(_ytne_0, _ytne_1)  ;  _ob -> s(z)  ;  l -> cons(_aune_0, _aune_1)  ;  x -> b
}

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

length(cons(x, ll), s(_ib)) <= length(ll, _ib)  :
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: ()

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


-------------------------------------------
Step 8, which took 0.011501 s (model generation: 0.011308,  model checking: 0.000193):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 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
leqnat(s(z), s(z)) <= insert(b, cons(a, nil), cons(a, nil))
False <= insert(b, cons(a, nil), cons(a, nil)) /\ length(cons(a, nil), s(s(z)))
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
leqnat(z, s(z)) <= insert(b, nil, cons(a, nil))
False <= leq(b, a)
False <= leqnat(s(s(z)), s(z))
leqnat(z, z) <= leqnat(s(z), s(z))
False <= leqnat(s(z), z)
leqnat(s(z), s(s(z))) <= leqnat(z, s(z))
}

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
}
]


;
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>
{
  leqnat(s(x_0_0), s(x_1_0)) <= leqnat(x_0_0, x_1_0)
  leqnat(z, s(x_1_0)) <= True
  leqnat(z, z) <= 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: ()

leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)  :
Yes: {
_mb -> s(s(z))  ;  _nb -> cons(_wune_0, nil)  ;  _ob -> s(z)  ;  l -> cons(_yune_0, cons(_svne_0, nil))  ;  x -> b
}

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

length(cons(x, ll), s(_ib)) <= length(ll, _ib)  :
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: ()

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


-------------------------------------------
Step 9, which took 0.018659 s (model generation: 0.018482,  model checking: 0.000177):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 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, cons(a, nil)), cons(a, nil)) /\ length(cons(a, cons(a, nil)), s(s(z)))
leqnat(s(z), s(z)) <= insert(b, cons(a, nil), cons(a, nil))
False <= insert(b, cons(a, nil), cons(a, nil)) /\ length(cons(a, nil), s(s(z)))
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
leqnat(z, s(z)) <= insert(b, nil, cons(a, nil))
False <= leq(b, a)
False <= leqnat(s(s(z)), s(z))
leqnat(z, z) <= leqnat(s(z), s(z))
False <= leqnat(s(z), z)
leqnat(s(z), s(s(z))) <= leqnat(z, s(z))
}

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
}
]


;
leqnat ->
[
leqnat : <nat * nat>
{
  leqnat(z, z) <= 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: ()

leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)  :
Yes: {
_mb -> z  ;  _nb -> cons(_hwne_0, _hwne_1)  ;  _ob -> s(_iwne_0)  ;  l -> nil  ;  x -> a
}

insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db)  :
Yes: {
_db -> cons(b, _zwne_1)  ;  x -> b  ;  y -> a  ;  z -> nil
}

length(cons(x, ll), s(_ib)) <= length(ll, _ib)  :
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)  :
Yes: {
nn1 -> z  ;  nn2 -> z
}

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

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


-------------------------------------------
Step 10, which took 0.020505 s (model generation: 0.020243,  model checking: 0.000262):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 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
leqnat(s(z), s(s(z))) <= True
leqnat(z, s(z)) <= True
False <= insert(b, cons(a, cons(a, nil)), cons(a, nil)) /\ length(cons(a, cons(a, nil)), s(s(z)))
leqnat(s(z), s(z)) <= insert(b, cons(a, nil), cons(a, nil))
False <= insert(b, cons(a, nil), cons(a, nil)) /\ length(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)
False <= leqnat(s(s(z)), s(z))
leqnat(z, z) <= leqnat(s(z), s(z))
False <= leqnat(s(z), z)
leqnat(s(z), s(z)) <= leqnat(z, z)
}

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
}
]


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


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

leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)  :
No: ()

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

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

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: ()

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


-------------------------------------------
Step 11, which took 0.022957 s (model generation: 0.022773,  model checking: 0.000184):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 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(cons(b, nil), s(z)) <= True
length(nil, z) <= True
leq(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
leqnat(s(z), s(s(z))) <= True
leqnat(z, s(z)) <= True
False <= insert(b, cons(a, cons(a, nil)), cons(a, nil)) /\ length(cons(a, cons(a, nil)), s(s(z)))
leqnat(s(z), s(z)) <= insert(b, cons(a, nil), cons(a, nil))
False <= insert(b, cons(a, nil), cons(a, nil)) /\ length(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)
False <= leqnat(s(s(z)), s(z))
leqnat(z, z) <= leqnat(s(z), s(z))
False <= leqnat(s(z), z)
leqnat(s(z), s(z)) <= leqnat(z, z)
}

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
}
]


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


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

leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)  :
No: ()

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

length(cons(x, ll), s(_ib)) <= length(ll, _ib)  :
Yes: {
_ib -> s(z)  ;  ll -> cons(b, _syne_1)  ;  x -> b
}

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: ()

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


-------------------------------------------
Step 12, which took 0.023695 s (model generation: 0.023495,  model checking: 0.000200):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 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(cons(b, cons(b, nil)), s(s(z))) <= True
length(cons(b, nil), s(z)) <= True
length(nil, z) <= True
leq(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
leqnat(s(z), s(s(z))) <= True
leqnat(z, s(z)) <= True
False <= insert(b, cons(a, cons(a, nil)), cons(a, nil)) /\ length(cons(a, cons(a, nil)), s(s(z)))
leqnat(s(z), s(z)) <= insert(b, cons(a, nil), cons(a, nil))
False <= insert(b, cons(a, nil), cons(a, nil)) /\ length(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)
False <= leqnat(s(s(z)), s(z))
leqnat(z, z) <= leqnat(s(z), s(z))
False <= leqnat(s(z), z)
leqnat(s(z), s(z)) <= leqnat(z, z)
}

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
}
]


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

leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)  :
Yes: {
_mb -> s(s(_yaoe_0))  ;  _nb -> cons(_xzne_0, cons(_vaoe_0, _vaoe_1))  ;  _ob -> s(z)  ;  l -> cons(_zzne_0, _zzne_1)  ;  x -> b
}

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

length(cons(x, ll), s(_ib)) <= length(ll, _ib)  :
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: ()

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


-------------------------------------------
Step 13, which took 0.023609 s (model generation: 0.023411,  model checking: 0.000198):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 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(cons(b, cons(b, nil)), s(s(z))) <= True
length(cons(b, nil), s(z)) <= True
length(nil, z) <= True
leq(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
leqnat(s(z), s(s(z))) <= True
leqnat(z, s(z)) <= True
False <= insert(b, cons(a, cons(a, nil)), cons(a, nil)) /\ length(cons(a, cons(a, nil)), s(s(z)))
False <= insert(b, cons(a, nil), cons(a, cons(a, nil))) /\ length(cons(a, cons(a, nil)), s(z)) /\ length(cons(a, nil), s(s(z)))
leqnat(s(z), s(z)) <= insert(b, cons(a, nil), cons(a, nil))
False <= insert(b, cons(a, nil), cons(a, nil)) /\ length(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)
False <= leqnat(s(s(z)), s(z))
leqnat(z, z) <= leqnat(s(z), s(z))
False <= leqnat(s(z), z)
leqnat(s(z), s(z)) <= leqnat(z, z)
}

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
}
]


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


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

leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)  :
Yes: {
_mb -> s(s(_zboe_0))  ;  _nb -> cons(a, _gboe_1)  ;  _ob -> s(z)  ;  l -> cons(b, _iboe_1)  ;  x -> b
}

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

length(cons(x, ll), s(_ib)) <= length(ll, _ib)  :
Yes: {
_ib -> s(z)  ;  ll -> cons(b, _lboe_1)  ;  x -> a
}

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: ()

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


-------------------------------------------
Step 14, which took 0.025516 s (model generation: 0.025036,  model checking: 0.000480):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 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(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(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
leqnat(s(z), s(s(z))) <= True
leqnat(z, s(z)) <= True
False <= insert(b, cons(a, cons(a, nil)), cons(a, nil)) /\ length(cons(a, cons(a, nil)), s(s(z)))
False <= insert(b, cons(a, nil), cons(a, cons(a, nil))) /\ length(cons(a, cons(a, nil)), s(z)) /\ length(cons(a, nil), s(s(z)))
leqnat(s(z), s(z)) <= insert(b, cons(a, nil), cons(a, nil))
False <= insert(b, cons(a, nil), cons(a, nil)) /\ length(cons(a, nil), s(s(z)))
False <= insert(b, cons(b, nil), cons(a, nil)) /\ length(cons(b, nil), s(s(z)))
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
False <= leq(b, a)
False <= leqnat(s(s(z)), s(z))
leqnat(z, z) <= leqnat(s(z), s(z))
False <= leqnat(s(z), z)
leqnat(s(z), s(z)) <= leqnat(z, z)
}

Current best model:
|_
name: None

insert ->
[
insert : <elt * eltlist * eltlist>
{
  _r_1(nil) <= 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_1_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
}
]


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

leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)  :
Yes: {
_mb -> s(s(z))  ;  _nb -> cons(_ucoe_0, nil)  ;  _ob -> s(z)  ;  l -> cons(_wcoe_0, cons(_feoe_0, nil))  ;  x -> a
}

insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db)  :
Yes: {
_db -> cons(_ddoe_0, _ddoe_1)  ;  x -> b  ;  y -> a  ;  z -> cons(_gdoe_0, nil)
}

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

insert(x, cons(y, z), cons(x, cons(y, z))) <= leq(x, y)  :
Yes: {
x -> b  ;  y -> b  ;  z -> cons(_jeoe_0, _jeoe_1)
}

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

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

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

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


-------------------------------------------
Step 15, which took 0.031565 s (model generation: 0.031232,  model checking: 0.000333):

Clauses:
{
insert(x, nil, cons(x, nil)) <= True -> 0
length(nil, z) <= True -> 0
leq(a, y) <= True -> 0
leq(b, b) <= True -> 0
leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb) -> 0
insert(x, cons(y, z), cons(y, _db)) \/ leq(x, y) <= insert(x, z, _db) -> 0
length(cons(x, ll), s(_ib)) <= length(ll, _ib) -> 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
False <= leqnat(s(nn1), z) -> 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, cons(a, nil)), cons(b, cons(b, 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, 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(a, a) <= True
leq(a, b) <= True
leq(b, b) <= True
leqnat(s(z), s(s(z))) <= True
leqnat(z, s(z)) <= True
False <= insert(a, cons(a, cons(a, nil)), cons(a, nil)) /\ length(cons(a, cons(a, nil)), s(s(z)))
False <= insert(b, cons(a, cons(a, nil)), cons(a, nil)) /\ length(cons(a, cons(a, nil)), s(s(z)))
False <= insert(b, cons(a, nil), cons(a, cons(a, nil))) /\ length(cons(a, cons(a, nil)), s(z)) /\ length(cons(a, nil), s(s(z)))
insert(b, cons(a, cons(a, nil)), cons(a, cons(a, nil))) <= insert(b, cons(a, nil), cons(a, nil))
leqnat(s(z), s(z)) <= insert(b, cons(a, nil), cons(a, nil))
False <= insert(b, cons(a, nil), cons(a, nil)) /\ length(cons(a, nil), s(s(z)))
False <= insert(b, cons(b, nil), cons(a, nil)) /\ length(cons(b, nil), s(s(z)))
insert(b, cons(a, nil), cons(a, cons(a, nil))) <= insert(b, nil, cons(a, nil))
False <= leq(b, a)
False <= leqnat(s(s(z)), s(z))
leqnat(z, z) <= leqnat(s(z), s(z))
False <= leqnat(s(z), z)
leqnat(s(z), s(z)) <= leqnat(z, z)
}

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
}
]


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

leqnat(_mb, _ob) <= insert(x, l, _nb) /\ length(_nb, _ob) /\ length(l, _mb)  :
Yes: {
_mb -> s(s(s(z)))  ;  _nb -> cons(_veoe_0, cons(_bgoe_0, nil))  ;  _ob -> s(s(z))  ;  l -> cons(_xeoe_0, cons(_cgoe_0, cons(_jgoe_0, nil)))  ;  x -> b
}

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

length(cons(x, ll), s(_ib)) <= length(ll, _ib)  :
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: ()

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


Total time: 0.337850
Learner time: 0.296903
Teacher time: 0.003156
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
  _r_1(nil, 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)) <= 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
}
]


;
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>
{
  leqnat(s(x_0_0), s(x_1_0)) <= leqnat(x_0_0, x_1_0)
  leqnat(z, s(x_1_0)) <= True
  leqnat(z, z) <= True
}
]



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