Solving ../../benchmarks/smtlib/true/length_count.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(_zaa)) <= length(ll, _zaa)
}
eq_nat(_bba, _cba) <= length(_aba, _bba) /\ length(_aba, _cba)
)
(count, F:
{
count(x, nil, z) <= True
count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba)
eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba)
}
eq_nat(_hba, _iba) <= count(_fba, _gba, _hba) /\ count(_fba, _gba, _iba)
)
}

properties:
{
leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba)
}


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

Clause system for inference is:

{
count(x, nil, z) <= True -> 0
length(nil, z) <= True -> 0
leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba) -> 0
count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba) -> 0
eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba) -> 0
length(cons(x, ll), s(_zaa)) <= length(ll, _zaa) -> 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 0.275215 seconds.
Yes: |_
name: None

count ->
[
count : <elt * eltlist * nat>
{
  _r_1(cons(x_0_0, x_0_1), s(x_1_0)) <= _r_1(x_0_1, x_1_0)
  _r_1(cons(x_0_0, x_0_1), z) <= True
  _r_1(nil, z) <= True
  count(a, cons(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_1_1, x_2_0)
  count(a, cons(x_1_0, x_1_1), z) <= True
  count(a, nil, z) <= True
  count(b, cons(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_1_1, x_2_0)
  count(b, cons(x_1_0, x_1_1), z) <= True
  count(b, nil, z) <= 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 0.018385 s (model generation: 0.018199,  model checking: 0.000186):

Clauses:
{
count(x, nil, z) <= True -> 0
length(nil, z) <= True -> 0
leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba) -> 0
count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba) -> 0
eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba) -> 0
length(cons(x, ll), s(_zaa)) <= length(ll, _zaa) -> 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

count ->
[
count : <elt * eltlist * nat>
{
  
}
]


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


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



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




Answer of teacher:

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

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

}

leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba)  :
No: ()

count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba)  :
No: ()

eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba)  :
No: ()

length(cons(x, ll), s(_zaa)) <= length(ll, _zaa)  :
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 0.017450 s (model generation: 0.017283,  model checking: 0.000167):

Clauses:
{
count(x, nil, z) <= True -> 0
length(nil, z) <= True -> 0
leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba) -> 0
count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba) -> 0
eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba) -> 0
length(cons(x, ll), s(_zaa)) <= length(ll, _zaa) -> 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:
{
count(b, nil, z) <= True
length(nil, z) <= True
}

Current best model:
|_
name: None

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


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


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



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




Answer of teacher:

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

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

leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba)  :
Yes: {
_jba -> z  ;  _kba -> z  ;  l -> nil  ;  x -> b
}

count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba)  :
Yes: {
_dba -> z  ;  t1 -> nil  ;  x -> b
}

eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba)  :
Yes: {
_eba -> z  ;  h1 -> a  ;  t1 -> nil  ;  x -> b
}

length(cons(x, ll), s(_zaa)) <= length(ll, _zaa)  :
Yes: {
_zaa -> 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 0.020007 s (model generation: 0.018754,  model checking: 0.001253):

Clauses:
{
count(x, nil, z) <= True -> 0
length(nil, z) <= True -> 0
leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba) -> 0
count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba) -> 0
eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba) -> 0
length(cons(x, ll), s(_zaa)) <= length(ll, _zaa) -> 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:
{
count(a, nil, z) <= True
count(b, cons(a, nil), z) <= True
count(b, cons(b, nil), s(z)) <= True
count(b, nil, z) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(z, z) <= True
}

Current best model:
|_
name: None

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



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




Answer of teacher:

count(x, nil, z) <= True  :
No: ()

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

leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba)  :
Yes: {
_jba -> z  ;  _kba -> s(_iuhq_0)  ;  l -> cons(_juhq_0, _juhq_1)  ;  x -> b
}

count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba)  :
Yes: {
_dba -> z  ;  t1 -> nil  ;  x -> a
}

eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba)  :
Yes: {
_eba -> z  ;  h1 -> b  ;  t1 -> nil  ;  x -> a
}

length(cons(x, ll), s(_zaa)) <= length(ll, _zaa)  :
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 0.018844 s (model generation: 0.018770,  model checking: 0.000074):

Clauses:
{
count(x, nil, z) <= True -> 0
length(nil, z) <= True -> 0
leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba) -> 0
count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba) -> 0
eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba) -> 0
length(cons(x, ll), s(_zaa)) <= length(ll, _zaa) -> 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:
{
count(a, cons(a, nil), s(z)) <= True
count(a, cons(b, nil), z) <= True
count(a, nil, z) <= True
count(b, cons(a, nil), z) <= True
count(b, cons(b, nil), s(z)) <= True
count(b, nil, z) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
}

Current best model:
|_
name: None

count ->
[
count : <elt * eltlist * nat>
{
  count(a, cons(x_1_0, x_1_1), s(x_2_0)) <= True
  count(a, cons(x_1_0, x_1_1), z) <= True
  count(a, nil, z) <= True
  count(b, cons(x_1_0, x_1_1), s(x_2_0)) <= True
  count(b, cons(x_1_0, x_1_1), z) <= True
  count(b, nil, 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 : <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:

count(x, nil, z) <= True  :
No: ()

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

leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba)  :
No: ()

count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba)  :
No: ()

eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba)  :
No: ()

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

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

leq(nn1, nn2) <= leq(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_uuhq_0)  ;  nn2 -> z
}

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


-------------------------------------------
Step 4, which took 0.015163 s (model generation: 0.015043,  model checking: 0.000120):

Clauses:
{
count(x, nil, z) <= True -> 0
length(nil, z) <= True -> 0
leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba) -> 0
count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba) -> 0
eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba) -> 0
length(cons(x, ll), s(_zaa)) <= length(ll, _zaa) -> 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:
{
count(a, cons(a, nil), s(z)) <= True
count(a, cons(b, nil), z) <= True
count(a, nil, z) <= True
count(b, cons(a, nil), z) <= True
count(b, cons(b, nil), s(z)) <= True
count(b, nil, z) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
leq(s(z), z) <= leq(s(s(z)), s(z))
}

Current best model:
|_
name: None

count ->
[
count : <elt * eltlist * nat>
{
  count(a, cons(x_1_0, x_1_1), s(x_2_0)) <= True
  count(a, cons(x_1_0, x_1_1), z) <= True
  count(a, nil, z) <= True
  count(b, cons(x_1_0, x_1_1), s(x_2_0)) <= True
  count(b, cons(x_1_0, x_1_1), z) <= True
  count(b, nil, 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 : <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:

count(x, nil, z) <= True  :
No: ()

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

leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba)  :
No: ()

count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba)  :
No: ()

eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba)  :
No: ()

length(cons(x, ll), s(_zaa)) <= length(ll, _zaa)  :
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 0.024117 s (model generation: 0.023881,  model checking: 0.000236):

Clauses:
{
count(x, nil, z) <= True -> 0
length(nil, z) <= True -> 0
leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba) -> 0
count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba) -> 0
eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba) -> 0
length(cons(x, ll), s(_zaa)) <= length(ll, _zaa) -> 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:
{
count(a, cons(a, nil), s(z)) <= True
count(a, cons(b, nil), z) <= True
count(a, nil, z) <= True
count(b, cons(a, nil), z) <= True
count(b, cons(b, nil), s(z)) <= True
count(b, nil, z) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
False <= leq(s(s(z)), s(z))
False <= leq(s(z), z)
}

Current best model:
|_
name: None

count ->
[
count : <elt * eltlist * nat>
{
  count(a, cons(x_1_0, x_1_1), s(x_2_0)) <= True
  count(a, cons(x_1_0, x_1_1), z) <= True
  count(a, nil, z) <= True
  count(b, cons(x_1_0, x_1_1), s(x_2_0)) <= True
  count(b, cons(x_1_0, x_1_1), z) <= True
  count(b, nil, 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 : <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:

count(x, nil, z) <= True  :
No: ()

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

leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba)  :
Yes: {
_jba -> s(s(_qvhq_0))  ;  _kba -> s(z)  ;  l -> cons(_yuhq_0, _yuhq_1)  ;  x -> a
}

count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba)  :
No: ()

eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba)  :
No: ()

length(cons(x, ll), s(_zaa)) <= length(ll, _zaa)  :
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 0.020927 s (model generation: 0.020529,  model checking: 0.000398):

Clauses:
{
count(x, nil, z) <= True -> 0
length(nil, z) <= True -> 0
leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba) -> 0
count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba) -> 0
eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba) -> 0
length(cons(x, ll), s(_zaa)) <= length(ll, _zaa) -> 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:
{
count(a, cons(a, nil), s(z)) <= True
count(a, cons(b, nil), z) <= True
count(a, nil, z) <= True
count(b, cons(a, nil), z) <= True
count(b, cons(b, nil), s(z)) <= True
count(b, nil, z) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
False <= count(a, cons(a, nil), s(s(z)))
False <= leq(s(s(z)), s(z))
False <= leq(s(z), z)
}

Current best model:
|_
name: None

count ->
[
count : <elt * eltlist * nat>
{
  count(a, cons(x_1_0, x_1_1), s(x_2_0)) <= length(x_1_1, x_2_0)
  count(a, cons(x_1_0, x_1_1), z) <= True
  count(a, nil, z) <= True
  count(b, cons(x_1_0, x_1_1), s(x_2_0)) <= True
  count(b, cons(x_1_0, x_1_1), z) <= True
  count(b, nil, z) <= True
  length(cons(x_0_0, x_0_1), s(x_1_0)) <= True
  length(nil, 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 : <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:

count(x, nil, z) <= True  :
No: ()

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

leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba)  :
Yes: {
_jba -> s(s(_zwhq_0))  ;  _kba -> s(z)  ;  l -> cons(_yvhq_0, _yvhq_1)  ;  x -> b
}

count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba)  :
Yes: {
_dba -> z  ;  t1 -> cons(_ewhq_0, _ewhq_1)  ;  x -> a
}

eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba)  :
Yes: {
_eba -> s(z)  ;  h1 -> b  ;  t1 -> cons(_lwhq_0, nil)  ;  x -> a
}

length(cons(x, ll), s(_zaa)) <= length(ll, _zaa)  :
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 0.024011 s (model generation: 0.023372,  model checking: 0.000639):

Clauses:
{
count(x, nil, z) <= True -> 0
length(nil, z) <= True -> 0
leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba) -> 0
count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba) -> 0
eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba) -> 0
length(cons(x, ll), s(_zaa)) <= length(ll, _zaa) -> 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:
{
count(a, cons(a, nil), s(z)) <= True
count(a, cons(b, cons(a, nil)), s(z)) <= True
count(a, cons(b, nil), z) <= True
count(a, nil, z) <= True
count(b, cons(a, nil), z) <= True
count(b, cons(b, nil), s(z)) <= True
count(b, nil, z) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
False <= count(a, cons(a, nil), s(s(z)))
count(a, cons(a, cons(a, nil)), s(z)) <= count(a, cons(a, nil), z)
False <= count(b, cons(a, nil), s(s(z)))
False <= leq(s(s(z)), s(z))
False <= leq(s(z), z)
}

Current best model:
|_
name: None

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


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

count(x, nil, z) <= True  :
No: ()

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

leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba)  :
Yes: {
_jba -> s(z)  ;  _kba -> z  ;  l -> cons(_rxhq_0, nil)  ;  x -> b
}

count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba)  :
No: ()

eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba)  :
No: ()

length(cons(x, ll), s(_zaa)) <= length(ll, _zaa)  :
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 8, which took 0.024947 s (model generation: 0.024716,  model checking: 0.000231):

Clauses:
{
count(x, nil, z) <= True -> 0
length(nil, z) <= True -> 0
leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba) -> 0
count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba) -> 0
eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba) -> 0
length(cons(x, ll), s(_zaa)) <= length(ll, _zaa) -> 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:
{
count(a, cons(a, nil), s(z)) <= True
count(a, cons(b, cons(a, nil)), s(z)) <= True
count(a, cons(b, nil), z) <= True
count(a, nil, z) <= True
count(b, cons(a, nil), z) <= True
count(b, cons(b, nil), s(z)) <= True
count(b, nil, z) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
False <= count(a, cons(a, nil), s(s(z)))
count(a, cons(a, cons(a, nil)), s(z)) <= count(a, cons(a, nil), z)
False <= count(b, cons(a, nil), s(s(z)))
False <= count(b, cons(a, nil), s(z)) /\ length(cons(a, nil), z)
False <= leq(s(s(z)), s(z))
False <= leq(s(z), z)
}

Current best model:
|_
name: None

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



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




Answer of teacher:

count(x, nil, z) <= True  :
No: ()

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

leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba)  :
No: ()

count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba)  :
Yes: {
_dba -> s(z)  ;  t1 -> cons(_szhq_0, _szhq_1)  ;  x -> a
}

eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba)  :
No: ()

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

leq(s(nn1), s(nn2)) <= leq(nn1, nn2)  :
Yes: {
nn1 -> s(z)  ;  nn2 -> s(_saiq_0)
}

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

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


-------------------------------------------
Step 9, which took 0.024694 s (model generation: 0.024518,  model checking: 0.000176):

Clauses:
{
count(x, nil, z) <= True -> 0
length(nil, z) <= True -> 0
leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba) -> 0
count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba) -> 0
eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba) -> 0
length(cons(x, ll), s(_zaa)) <= length(ll, _zaa) -> 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:
{
count(a, cons(a, cons(a, nil)), s(s(z))) <= True
count(a, cons(a, nil), s(z)) <= True
count(a, cons(b, cons(a, nil)), s(z)) <= True
count(a, cons(b, nil), z) <= True
count(a, nil, z) <= True
count(b, cons(a, nil), z) <= True
count(b, cons(b, nil), s(z)) <= True
count(b, nil, z) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(s(s(z)), s(s(z))) <= True
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
False <= count(a, cons(a, nil), s(s(z)))
count(a, cons(a, cons(a, nil)), s(z)) <= count(a, cons(a, nil), z)
False <= count(b, cons(a, nil), s(s(z)))
False <= count(b, cons(a, nil), s(z)) /\ length(cons(a, nil), z)
False <= leq(s(s(z)), s(z))
False <= leq(s(z), z)
}

Current best model:
|_
name: None

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

count(x, nil, z) <= True  :
No: ()

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

leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba)  :
Yes: {
_jba -> s(s(_zciq_0))  ;  _kba -> s(z)  ;  l -> cons(_jbiq_0, cons(_yciq_0, _yciq_1))  ;  x -> b
}

count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba)  :
No: ()

eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba)  :
No: ()

length(cons(x, ll), s(_zaa)) <= length(ll, _zaa)  :
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 10, which took 0.018081 s (model generation: 0.017815,  model checking: 0.000266):

Clauses:
{
count(x, nil, z) <= True -> 0
length(nil, z) <= True -> 0
leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba) -> 0
count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba) -> 0
eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba) -> 0
length(cons(x, ll), s(_zaa)) <= length(ll, _zaa) -> 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:
{
count(a, cons(a, cons(a, nil)), s(s(z))) <= True
count(a, cons(a, nil), s(z)) <= True
count(a, cons(b, cons(a, nil)), s(z)) <= True
count(a, cons(b, nil), z) <= True
count(a, nil, z) <= True
count(b, cons(a, nil), z) <= True
count(b, cons(b, nil), s(z)) <= True
count(b, nil, z) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(s(s(z)), s(s(z))) <= True
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
False <= count(a, cons(a, nil), s(s(z)))
count(a, cons(a, cons(a, nil)), s(z)) <= count(a, cons(a, nil), z)
False <= count(b, cons(a, cons(a, nil)), s(s(z))) /\ length(cons(a, cons(a, nil)), s(z))
False <= count(b, cons(a, nil), s(s(z)))
False <= count(b, cons(a, nil), s(z)) /\ length(cons(a, nil), z)
False <= leq(s(s(z)), s(z))
False <= leq(s(z), z)
}

Current best model:
|_
name: None

count ->
[
count : <elt * eltlist * nat>
{
  _r_1(cons(x_0_0, x_0_1), z) <= True
  _r_1(nil, z) <= True
  count(a, cons(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_1_1, x_2_0)
  count(a, cons(x_1_0, x_1_1), s(x_2_0)) <= length(x_1_1, x_2_0)
  count(a, cons(x_1_0, x_1_1), z) <= True
  count(a, nil, z) <= True
  count(b, cons(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_1_1, x_2_0)
  count(b, cons(x_1_0, x_1_1), z) <= True
  count(b, nil, z) <= True
  length(cons(x_0_0, x_0_1), s(x_1_0)) <= True
  length(nil, 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 : <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:

count(x, nil, z) <= True  :
No: ()

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

leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba)  :
Yes: {
_jba -> s(s(_ifiq_0))  ;  _kba -> s(z)  ;  l -> cons(_hdiq_0, cons(_hfiq_0, _hfiq_1))  ;  x -> a
}

count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba)  :
Yes: {
_dba -> s(z)  ;  t1 -> cons(_aeiq_0, nil)  ;  x -> b
}

eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba)  :
No: ()

length(cons(x, ll), s(_zaa)) <= length(ll, _zaa)  :
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 0.020515 s (model generation: 0.020269,  model checking: 0.000246):

Clauses:
{
count(x, nil, z) <= True -> 0
length(nil, z) <= True -> 0
leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba) -> 0
count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba) -> 0
eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba) -> 0
length(cons(x, ll), s(_zaa)) <= length(ll, _zaa) -> 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:
{
count(a, cons(a, cons(a, nil)), s(s(z))) <= True
count(a, cons(a, nil), s(z)) <= True
count(a, cons(b, cons(a, nil)), s(z)) <= True
count(a, cons(b, nil), z) <= True
count(a, nil, z) <= True
count(b, cons(a, nil), z) <= True
count(b, cons(b, nil), s(z)) <= True
count(b, nil, z) <= True
length(cons(a, nil), s(z)) <= True
length(nil, z) <= True
leq(s(s(z)), s(s(z))) <= True
leq(s(z), s(z)) <= True
leq(z, s(z)) <= True
leq(z, z) <= True
False <= count(a, cons(a, nil), s(s(z)))
count(a, cons(a, cons(a, nil)), s(z)) <= count(a, cons(a, nil), z)
False <= count(b, cons(a, nil), s(s(z)))
count(b, cons(b, cons(a, nil)), s(s(z))) <= count(b, cons(a, nil), s(z))
False <= count(b, cons(a, nil), s(z)) /\ length(cons(a, nil), z)
False <= length(cons(a, cons(a, nil)), s(z))
False <= leq(s(s(z)), s(z))
False <= leq(s(z), z)
}

Current best model:
|_
name: None

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

count(x, nil, z) <= True  :
No: ()

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

leq(_jba, _kba) <= count(x, l, _jba) /\ length(l, _kba)  :
Yes: {
_jba -> s(s(s(_shiq_0)))  ;  _kba -> s(s(z))  ;  l -> cons(_ufiq_0, cons(_khiq_0, nil))  ;  x -> b
}

count(x, cons(x, t1), s(_dba)) <= count(x, t1, _dba)  :
No: ()

eq_elt(h1, x) \/ count(x, cons(h1, t1), _eba) <= count(x, t1, _eba)  :
No: ()

length(cons(x, ll), s(_zaa)) <= length(ll, _zaa)  :
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: 0.275215
Learner time: 0.243148
Teacher time: 0.003993
Reasons for stopping: Yes: |_
name: None

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