Solving ../../benchmarks/smtlib/true/length_delete_minus_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: {
elist -> {econs, enil}  ;  elt -> {a, b}  ;  nat -> {s, z}
}
definition:
{
(length_elt, F:
{
length_elt(enil, z) <= True
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)
}
eq_nat(_oka, _pka) <= length_elt(_nka, _oka) /\ length_elt(_nka, _pka)
)
(minus, F:
{
minus(s(u), z, s(u)) <= True
minus(z, y, z) <= True
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)
}
eq_nat(_tka, _uka) <= minus(_rka, _ska, _tka) /\ minus(_rka, _ska, _uka)
)
(delete_all_elt, F:
{
delete_all_elt(x, enil, enil) <= True
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)
}
eq_elist(_zka, _ala) <= delete_all_elt(_xka, _yka, _ala) /\ delete_all_elt(_xka, _yka, _zka)
)
(count_elt, F:
{
count_elt(x, enil, z) <= True
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)
}
eq_nat(_fla, _gla) <= count_elt(_dla, _ela, _fla) /\ count_elt(_dla, _ela, _gla)
)
}

properties:
{
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)
}


over-approximation: {count_elt, delete_all_elt, length_elt, minus}
under-approximation: {}

Clause system for inference is:

{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}


Solving took 59.442734 seconds.
Maybe:  timeout during learnerLast solver state:

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, econs(a, enil)), s(s(z))) <= True
count_elt(a, econs(a, econs(b, enil)), s(z)) <= True
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, econs(a, enil))), s(s(z))) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(a, enil)), z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(a, enil)), enil) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, econs(a, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, econs(a, enil)), econs(a, econs(a, enil))) <= True
delete_all_elt(b, econs(a, econs(b, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, econs(a, enil)), s(s(z))) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, econs(a, enil)), s(s(z))) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(s(z)), z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(s(z)), z, s(s(z))) <= True
minus(s(z), s(s(z)), z) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, econs(a, enil)), s(z))
False <= count_elt(a, econs(a, enil), s(s(z)))
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, econs(a, enil)), s(s(z)))
False <= count_elt(a, econs(b, econs(a, enil)), z)
False <= count_elt(a, econs(b, enil), s(z))
False <= count_elt(b, econs(a, econs(a, enil)), s(s(z)))
count_elt(b, econs(b, econs(a, econs(a, enil))), s(s(z))) <= count_elt(b, econs(a, econs(a, enil)), s(z))
False <= count_elt(b, econs(a, enil), s(s(z)))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, econs(a, enil)), s(s(z)))
count_elt(b, econs(a, econs(b, econs(b, enil))), s(s(z))) <= count_elt(b, econs(b, econs(b, enil)), s(s(z)))
count_elt(b, econs(a, econs(b, enil)), s(s(z))) <= count_elt(b, econs(b, enil), s(s(z)))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, econs(a, enil))) <= delete_all_elt(a, econs(b, enil), econs(a, econs(a, enil)))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, econs(a, enil)), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, econs(a, enil)))
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(s(z)), s(s(z)), s(z))
False <= minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
False <= minus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_1(s(x_0_0)) <= _r_2(x_0_0)
  _r_1(z) <= True
  _r_2(s(x_0_0)) <= True
  _r_3(a) <= True
  _r_4(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= _r_4(x_0_0)
  _r_5(econs(x_0_0, x_0_1)) <= _r_6(x_0_1)
  _r_5(enil) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_2_0) /\ _r_4(x_1_0) /\ _r_6(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_2_0) /\ _r_4(x_1_0) /\ _r_5(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0) /\ length_elt(x_1_1, x_2_0)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_4(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_2_0) /\ _r_6(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_2_0) /\ _r_5(x_1_1) /\ length_elt(x_1_1, x_2_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(b, enil, z) <= True
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(a) <= True
  _r_4(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= _r_4(x_0_0)
  _r_5(econs(x_0_0, x_0_1)) <= _r_6(x_0_1)
  _r_5(enil) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_4(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_2_0) /\ _r_6(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_6(x_2_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_6(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= _r_2(x_0_0)
  _r_1(z) <= True
  _r_2(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0) /\ _r_2(x_1_0)
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ _r_2(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_2(x_1_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_2_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_2(x_0_0)
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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






-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005619 s (model generation: 0.005477,  model checking: 0.000142):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  
}
]


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



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
Yes: {
x -> b
}

delete_all_elt(x, enil, enil) <= True  :
Yes: {
x -> b
}

length_elt(enil, z) <= True  :
Yes: {

}

minus(s(u), z, s(u)) <= True  :
Yes: {

}

minus(z, y, z) <= True  :
Yes: {
y -> z
}

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
No: ()

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 1, which took 0.010094 s (model generation: 0.009871,  model checking: 0.000223):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(b, enil, z) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(enil, z) <= True
minus(s(z), z, s(z)) <= True
minus(z, z, z) <= True
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  delete_all_elt(b, enil, enil) <= True
}
]


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


;
minus ->
[
minus : <nat * nat * nat>
{
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
Yes: {
x -> a
}

delete_all_elt(x, enil, enil) <= True  :
Yes: {
x -> a
}

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
Yes: {
y -> s(_qziq_0)
}

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
No: ()

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
Yes: {
_bla -> z  ;  t1 -> enil  ;  x -> b
}

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
Yes: {
_cla -> z  ;  h1 -> a  ;  t1 -> enil  ;  x -> b
}

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
Yes: {
_vka -> enil  ;  h -> b  ;  t -> enil
}

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
Yes: {
_wka -> enil  ;  h -> a  ;  t -> enil  ;  x -> b
}

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
Yes: {
_mka -> z  ;  ll -> enil
}

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
Yes: {
_qka -> z  ;  u -> z  ;  x2 -> z
}


-------------------------------------------
Step 2, which took 0.017010 s (model generation: 0.016714,  model checking: 0.000296):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, enil, z) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= True
  count_elt(b, econs(x_1_0, x_1_1), z) <= True
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= True
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= True
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  minus(s(x_0_0), s(x_1_0), z) <= True
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> enil  ;  _ila -> z  ;  _jla -> s(_dbjq_0)  ;  _kla -> z  ;  _lla -> s(_fbjq_0)  ;  e -> b  ;  l -> econs(_hbjq_0, _hbjq_1)
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
Yes: {
_bla -> z  ;  t1 -> enil  ;  x -> a
}

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
Yes: {
_cla -> z  ;  h1 -> b  ;  t1 -> enil  ;  x -> a
}

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
Yes: {
_vka -> enil  ;  h -> a  ;  t -> enil
}

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
Yes: {
_wka -> enil  ;  h -> b  ;  t -> enil  ;  x -> a
}

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
Yes: {
_qka -> s(_wbjq_0)  ;  u -> s(_xbjq_0)  ;  x2 -> z
}


-------------------------------------------
Step 3, which took 0.023960 s (model generation: 0.023698,  model checking: 0.000262):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= delete_all_elt(b, econs(a, enil), enil)
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= True
  count_elt(a, econs(x_1_0, x_1_1), z) <= True
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= True
  count_elt(b, econs(x_1_0, x_1_1), z) <= True
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_1(b) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= True
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_1(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= True
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= True
  minus(s(x_0_0), s(x_1_0), z) <= True
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> enil  ;  _ila -> z  ;  _jla -> s(_pcjq_0)  ;  _kla -> s(_qcjq_0)  ;  _lla -> s(_rcjq_0)  ;  e -> a  ;  l -> econs(_tcjq_0, _tcjq_1)
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 4, which took 0.037337 s (model generation: 0.037072,  model checking: 0.000265):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= delete_all_elt(b, econs(a, enil), enil)
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= True
  count_elt(a, econs(x_1_0, x_1_1), z) <= True
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= True
  count_elt(b, econs(x_1_0, x_1_1), z) <= True
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_2(b) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= True
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_2(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= True
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= True
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> enil  ;  _ila -> z  ;  _jla -> s(_bgjq_0)  ;  _kla -> z  ;  _lla -> s(_dgjq_0)  ;  e -> a  ;  l -> econs(_fgjq_0, _fgjq_1)
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 5, which took 0.029031 s (model generation: 0.028754,  model checking: 0.000277):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, enil), z)
False <= delete_all_elt(b, econs(a, enil), enil)
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_2(b) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= True
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_2(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= True
  count_elt(b, econs(x_1_0, x_1_1), z) <= True
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_2(b) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= True
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_2(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= True
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= True
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(_rjjq_0, _rjjq_1)  ;  _ila -> s(_sjjq_0)  ;  _jla -> s(_tjjq_0)  ;  _kla -> s(_ujjq_0)  ;  _lla -> z  ;  e -> b  ;  l -> econs(_xjjq_0, _xjjq_1)
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 6, which took 0.027940 s (model generation: 0.027582,  model checking: 0.000358):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(b, econs(a, enil), s(z))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_2(b) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= True
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_2(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), z) <= True
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_2(b) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= True
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_2(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= True
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= True
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(_uljq_0, _uljq_1)  ;  _ila -> s(_vljq_0)  ;  _jla -> s(_wljq_0)  ;  _kla -> s(_xljq_0)  ;  _lla -> z  ;  e -> a  ;  l -> econs(_amjq_0, _amjq_1)
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
Yes: {
_cla -> s(_wojq_0)  ;  h1 -> a  ;  t1 -> econs(b, _yojq_1)  ;  x -> b
}

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 7, which took 0.048529 s (model generation: 0.048042,  model checking: 0.000487):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(b, econs(a, enil), s(z))
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_2(b) <= True
  _r_3(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= True
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_2(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= True
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_2(b) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_2(x_1_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= True
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_2(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= True
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= True
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> enil  ;  _ila -> z  ;  _jla -> s(s(_dvjq_0))  ;  _kla -> s(_eqjq_0)  ;  _lla -> s(_fqjq_0)  ;  e -> a  ;  l -> econs(_hqjq_0, _hqjq_1)
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
Yes: {
_vka -> econs(_cujq_0, _cujq_1)  ;  h -> a  ;  t -> econs(b, _eujq_1)
}

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 8, which took 0.055576 s (model generation: 0.055000,  model checking: 0.000576):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(b, econs(a, enil), s(z))
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_2(b) <= True
  _r_3(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= True
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_2(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= True
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_2(b) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_2(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= True
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_2(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= True
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> enil  ;  _ila -> z  ;  _jla -> s(z)  ;  _kla -> z  ;  _lla -> s(_qyjq_0)  ;  e -> b  ;  l -> econs(b, enil)
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 9, which took 0.088467 s (model generation: 0.087910,  model checking: 0.000557):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), z) /\ length_elt(econs(b, enil), s(z))
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_3(b) <= True
  _r_4(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= True
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= True
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(b) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= True
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  _r_2(a, z) <= True
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= _r_2(x_0_0, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0), z) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0, x_1_0)
  minus(s(x_0_0), s(x_1_0), z) <= True
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(a, _rdkq_1)  ;  _ila -> s(z)  ;  _jla -> s(z)  ;  _kla -> s(_udkq_0)  ;  _lla -> z  ;  e -> b  ;  l -> econs(a, econs(_ghkq_0, _ghkq_1))
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
Yes: {
_mka -> z  ;  ll -> enil  ;  x -> b
}

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
Yes: {
_qka -> s(_ugkq_0)  ;  u -> s(s(_ehkq_0))  ;  x2 -> s(z)
}


-------------------------------------------
Step 10, which took 0.124025 s (model generation: 0.123386,  model checking: 0.000639):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(b, econs(a, econs(a, enil)), s(z)) /\ delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil)) /\ length_elt(econs(a, econs(a, enil)), s(z))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_2(a) <= True
  _r_3(b) <= True
  _r_4(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= True
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_2(x_1_0)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(b) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= True
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= True
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> enil  ;  _ila -> z  ;  _jla -> s(z)  ;  _kla -> z  ;  _lla -> s(_oikq_0)  ;  e -> a  ;  l -> econs(b, enil)
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 11, which took 0.125493 s (model generation: 0.124808,  model checking: 0.000685):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(b, econs(a, econs(a, enil)), s(z)) /\ delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil)) /\ length_elt(econs(a, econs(a, enil)), s(z))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, enil), enil)
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_2(a) <= True
  _r_3(b) <= True
  _r_4(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= True
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_2(x_1_0)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_2(a) <= True
  _r_3(b) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_2(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= True
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(b, enil)  ;  _ila -> s(z)  ;  _jla -> s(z)  ;  _kla -> s(_bokq_0)  ;  _lla -> z  ;  e -> a  ;  l -> econs(_eokq_0, enil)
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 12, which took 0.125915 s (model generation: 0.125281,  model checking: 0.000634):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(b, econs(a, econs(a, enil)), s(z)) /\ delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil)) /\ length_elt(econs(a, econs(a, enil)), s(z))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, enil), enil)
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_2(b) <= True
  _r_3(a) <= True
  _r_4(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= True
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_2(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_2(b) <= True
  _r_3(a) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_2(x_1_0) /\ _r_2(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_2(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= True
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(_xvkq_0, enil)  ;  _ila -> s(z)  ;  _jla -> s(z)  ;  _kla -> s(_awkq_0)  ;  _lla -> z  ;  e -> b  ;  l -> econs(b, enil)
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
Yes: {
_vka -> econs(b, _ezkq_1)  ;  h -> a  ;  t -> econs(b, _gzkq_1)
}

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 13, which took 0.134839 s (model generation: 0.134015,  model checking: 0.000824):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(b, econs(a, econs(a, enil)), s(z)) /\ delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil)) /\ length_elt(econs(a, econs(a, enil)), s(z))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_2(a) <= True
  _r_3(b) <= True
  _r_4(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= True
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_2(x_1_0)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_2(a) <= True
  _r_3(b) <= True
  _r_4(econs(x_0_0, x_0_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_2(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_2(x_1_0)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= True
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(_tblq_0, enil)  ;  _ila -> s(z)  ;  _jla -> s(z)  ;  _kla -> s(_wblq_0)  ;  _lla -> z  ;  e -> a  ;  l -> econs(b, enil)
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
Yes: {
_vka -> econs(_qhlq_0, _qhlq_1)  ;  h -> b  ;  t -> econs(a, _shlq_1)
}

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 14, which took 0.165934 s (model generation: 0.164804,  model checking: 0.001130):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, enil), s(z)) /\ delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= count_elt(b, econs(a, econs(a, enil)), s(z)) /\ delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil)) /\ length_elt(econs(a, econs(a, enil)), s(z))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_2(b) <= True
  _r_3(a) <= True
  _r_4(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_2(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_2(b) <= True
  _r_3(a) <= True
  _r_4(econs(x_0_0, x_0_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_2(x_1_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_2(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= True
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(_smlq_0, enil)  ;  _ila -> s(z)  ;  _jla -> s(s(z))  ;  _kla -> s(_vmlq_0)  ;  _lla -> z  ;  e -> b  ;  l -> econs(b, econs(_dulq_0, enil))
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
Yes: {
_cla -> s(_fqlq_0)  ;  h1 -> b  ;  t1 -> econs(a, _hqlq_1)  ;  x -> a
}

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 15, which took 0.194619 s (model generation: 0.192647,  model checking: 0.001972):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, enil), s(z)) /\ delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= count_elt(b, econs(a, econs(a, enil)), s(z)) /\ delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil)) /\ length_elt(econs(a, econs(a, enil)), s(z))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, econs(a, enil)), s(z)) /\ length_elt(econs(b, econs(a, enil)), s(s(z))) /\ minus(s(s(z)), s(z), z)
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_2(a) <= True
  _r_3(b) <= True
  _r_4(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_1_0)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_1_0) /\ _r_4(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0) /\ length_elt(x_1_1, x_2_0)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_2(x_1_0)
  count_elt(b, enil, z) <= True
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_2(a) <= True
  _r_3(b) <= True
  _r_4(econs(x_0_0, x_0_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_2(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_2(x_1_0)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= True
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(_xwlq_0, enil)  ;  _ila -> s(z)  ;  _jla -> s(z)  ;  _kla -> z  ;  _lla -> s(s(_gjmq_0))  ;  e -> a  ;  l -> econs(b, enil)
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
Yes: {
_bla -> z  ;  t1 -> econs(a, _tcmq_1)  ;  x -> b
}

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 16, which took 0.343684 s (model generation: 0.342372,  model checking: 0.001312):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, enil), s(z)) /\ delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= count_elt(b, econs(a, econs(a, enil)), s(z)) /\ delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil)) /\ length_elt(econs(a, econs(a, enil)), s(z))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), econs(a, enil)) /\ minus(s(z), z, s(s(z)))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= length_elt(econs(b, econs(a, enil)), s(s(z))) /\ minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_3(b) <= True
  _r_4(a) <= True
  _r_5(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= True
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_5(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_4(x_1_0)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(b) <= True
  _r_4(a) <= True
  _r_5(econs(x_0_0, x_0_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_3(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_5(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_4(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_5(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  _r_1(enil, z) <= True
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= _r_1(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_2(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_2(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= True
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(b, enil)  ;  _ila -> s(z)  ;  _jla -> s(z)  ;  _kla -> s(_rkmq_0)  ;  _lla -> z  ;  e -> a  ;  l -> econs(b, enil)
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
Yes: {
_mka -> s(z)  ;  ll -> econs(_jumq_0, enil)
}

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 17, which took 0.417175 s (model generation: 0.415732,  model checking: 0.001443):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, econs(a, enil)), s(s(z))) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, enil), s(z))
False <= count_elt(b, econs(a, econs(a, enil)), s(z)) /\ delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil)) /\ length_elt(econs(a, econs(a, enil)), s(z))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), econs(a, enil)) /\ minus(s(z), z, s(s(z)))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= length_elt(econs(b, econs(a, enil)), s(s(z))) /\ minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_3(a) <= True
  _r_4(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_5(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_4(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_5(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(a) <= True
  _r_4(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_4(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_5(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_5(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_4(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  _r_2(z) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_2(x_0_0)
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(_nbnq_0, enil)  ;  _ila -> s(z)  ;  _jla -> s(s(z))  ;  _kla -> z  ;  _lla -> s(s(_qinq_0))  ;  e -> b  ;  l -> econs(a, econs(_rinq_0, enil))
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
Yes: {
_qka -> z  ;  u -> s(z)  ;  x2 -> s(_ohnq_0)
}


-------------------------------------------
Step 18, which took 0.401406 s (model generation: 0.399968,  model checking: 0.001438):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, econs(a, enil)), s(s(z))) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(s(z)), z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, enil), s(z))
False <= count_elt(b, econs(a, econs(a, enil)), s(z)) /\ delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil)) /\ length_elt(econs(a, econs(a, enil)), s(z))
False <= count_elt(b, econs(a, econs(a, enil)), z) /\ delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil)) /\ minus(s(s(z)), z, s(s(z)))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), econs(a, enil)) /\ minus(s(z), z, s(s(z)))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= length_elt(econs(b, econs(a, enil)), s(s(z))) /\ minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_3(a) <= True
  _r_4(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_5(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_4(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_5(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(a) <= True
  _r_4(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_5(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_5(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_4(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  _r_2(z) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_1(x_1_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_2(x_0_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_2(x_2_0)
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
Yes: {
u -> s(_bxnq_0)
}

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(_vjnq_0, enil)  ;  _ila -> s(z)  ;  _jla -> s(s(z))  ;  _kla -> s(s(_cxnq_0))  ;  _lla -> z  ;  e -> a  ;  l -> econs(a, econs(_nxnq_0, enil))
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 19, which took 0.416996 s (model generation: 0.412610,  model checking: 0.004386):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, econs(a, enil)), s(s(z))) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(s(z)), z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(s(z)), z, s(s(z))) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, econs(a, enil)), s(s(z))) /\ delete_all_elt(a, econs(a, econs(a, enil)), econs(a, enil))
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, enil), s(z))
False <= count_elt(b, econs(a, econs(a, enil)), s(z)) /\ delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil)) /\ length_elt(econs(a, econs(a, enil)), s(z))
False <= count_elt(b, econs(a, econs(a, enil)), z) /\ delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), econs(a, enil)) /\ minus(s(z), z, s(s(z)))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= length_elt(econs(b, econs(a, enil)), s(s(z))) /\ minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_2(a) <= True
  _r_3(b) <= True
  _r_4(enil) <= True
  _r_5(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_1_0)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_5(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_5(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_2(x_1_0) /\ _r_4(x_1_1)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_2(a) <= True
  _r_3(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_3(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_2_0) /\ _r_5(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_2(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_2(x_1_0)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_5(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  _r_2(a) <= True
  _r_4(enil) <= True
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= _r_2(x_0_0) /\ length_elt(x_0_1, x_1_0)
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= _r_4(x_0_1) /\ length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= True
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(_eqoq_0, enil)  ;  _ila -> s(z)  ;  _jla -> s(s(z))  ;  _kla -> s(_hqoq_0)  ;  _lla -> z  ;  e -> b  ;  l -> econs(a, econs(a, enil))
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
Yes: {
_cla -> z  ;  h1 -> a  ;  t1 -> econs(a, enil)  ;  x -> b
}

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
Yes: {
_mka -> s(z)  ;  ll -> econs(a, enil)  ;  x -> b
}

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 20, which took 0.763069 s (model generation: 0.760795,  model checking: 0.002274):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(a, enil)), z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, econs(a, enil)), s(s(z))) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, econs(a, enil)), s(s(z))) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(s(z)), z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(s(z)), z, s(s(z))) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, econs(a, enil)), s(s(z))) /\ delete_all_elt(a, econs(a, econs(a, enil)), econs(a, enil))
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, enil), s(z))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), econs(a, enil)) /\ minus(s(z), z, s(s(z)))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_3(a) <= True
  _r_4(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_5(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_4(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_5(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(a) <= True
  _r_4(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= True
  _r_6(enil) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_4(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_2_0) /\ _r_5(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_6(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_4(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(z) <= True
  _r_2(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_2(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_2(x_1_0)
  minus(s(x_0_0), z, s(x_2_0)) <= True
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(b, enil)  ;  _ila -> s(z)  ;  _jla -> s(z)  ;  _kla -> z  ;  _lla -> s(s(_yaqq_0))  ;  e -> a  ;  l -> econs(b, enil)
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
Yes: {
_wka -> enil  ;  h -> a  ;  t -> econs(b, _lypq_1)  ;  x -> b
}

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 21, which took 1.315429 s (model generation: 1.313655,  model checking: 0.001774):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(a, enil)), z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, econs(b, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, econs(a, enil)), s(s(z))) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, econs(a, enil)), s(s(z))) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(s(z)), z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(s(z)), z, s(s(z))) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, econs(a, enil)), s(s(z))) /\ delete_all_elt(a, econs(a, econs(a, enil)), econs(a, enil))
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, enil), s(z))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
False <= minus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_4(a) <= True
  _r_5(b) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_0)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_6(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_5(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_5(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_6(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_4(x_1_0)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_2(econs(x_0_0, x_0_1), enil) <= _r_5(x_0_0)
  _r_2(enil, enil) <= True
  _r_4(a) <= True
  _r_5(b) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_2(x_1_1, x_2_1) /\ _r_6(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_5(x_1_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_4(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_2(x_1_1, x_2_1) /\ _r_4(x_1_0)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_5(x_1_0) /\ _r_6(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_5(x_1_0)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0), s(x_1_0)) <= True
  _r_1(z, z) <= True
  _r_3(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_3(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_1(x_0_0, x_1_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0, x_2_0)
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> enil  ;  _ila -> z  ;  _jla -> s(s(z))  ;  _kla -> s(_xfqq_0)  ;  _lla -> s(_yfqq_0)  ;  e -> b  ;  l -> econs(b, econs(_trqq_0, enil))
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
Yes: {
_vka -> econs(_mkqq_0, econs(_orqq_0, _orqq_1))  ;  h -> a  ;  t -> econs(b, _okqq_1)
}

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
Yes: {
_wka -> econs(_lnqq_0, enil)  ;  h -> a  ;  t -> econs(a, enil)  ;  x -> b
}

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
Yes: {
_qka -> z  ;  u -> z  ;  x2 -> s(_mqqq_0)
}


-------------------------------------------
Step 22, which took 1.025196 s (model generation: 1.021782,  model checking: 0.003414):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(a, enil)), z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, econs(a, enil)), econs(a, econs(a, enil))) <= True
delete_all_elt(b, econs(a, econs(b, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, econs(a, enil)), s(s(z))) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, econs(a, enil)), s(s(z))) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(s(z)), z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(s(z)), z, s(s(z))) <= True
minus(s(z), s(s(z)), z) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, econs(a, enil)), s(s(z))) /\ delete_all_elt(a, econs(a, econs(a, enil)), econs(a, enil))
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, enil), s(z))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, econs(a, enil))) <= delete_all_elt(a, econs(b, enil), econs(a, econs(a, enil)))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, econs(a, enil)), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
False <= minus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_3(a) <= True
  _r_4(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_5(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_4(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_5(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(a) <= True
  _r_4(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= True
  _r_6(econs(x_0_0, x_0_1)) <= _r_4(x_0_0)
  _r_6(enil) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_4(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_2_0) /\ _r_5(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_6(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_5(x_2_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_4(x_1_0) /\ _r_6(x_1_1)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  _r_2(z) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_1(x_1_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_2(x_0_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_2(x_2_0)
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(_jzqq_0, econs(_trrq_0, enil))  ;  _ila -> s(s(z))  ;  _jla -> s(z)  ;  _kla -> s(s(_rqrq_0))  ;  _lla -> z  ;  e -> b  ;  l -> econs(b, enil)
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 23, which took 1.299622 s (model generation: 1.295993,  model checking: 0.003629):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(a, enil)), z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, econs(a, enil)), econs(a, econs(a, enil))) <= True
delete_all_elt(b, econs(a, econs(b, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, econs(a, enil)), s(s(z))) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, econs(a, enil)), s(s(z))) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(s(z)), z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(s(z)), z, s(s(z))) <= True
minus(s(z), s(s(z)), z) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, econs(a, enil)), s(s(z))) /\ delete_all_elt(a, econs(a, econs(a, enil)), econs(a, enil))
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, enil), s(z))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), s(s(z))) /\ delete_all_elt(b, econs(b, enil), econs(a, econs(a, enil)))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, econs(a, enil))) <= delete_all_elt(a, econs(b, enil), econs(a, econs(a, enil)))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, econs(a, enil)), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
False <= minus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_3(b) <= True
  _r_4(a) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_0)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_6(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_6(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_4(x_1_0)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(b) <= True
  _r_4(a) <= True
  _r_5(econs(x_0_0, x_0_1)) <= _r_3(x_0_0)
  _r_5(enil) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_3(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_2_0) /\ _r_6(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_4(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_6(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_6(x_2_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  _r_2(z) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_1(x_1_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_2(x_0_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_2(x_2_0)
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(b, enil)  ;  _ila -> s(z)  ;  _jla -> s(s(z))  ;  _kla -> s(s(_hvsq_0))  ;  _lla -> z  ;  e -> a  ;  l -> econs(b, econs(_uvsq_0, enil))
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 24, which took 1.253069 s (model generation: 1.247295,  model checking: 0.005774):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(a, enil)), z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, econs(a, enil)), econs(a, econs(a, enil))) <= True
delete_all_elt(b, econs(a, econs(b, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, econs(a, enil)), s(s(z))) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, econs(a, enil)), s(s(z))) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(s(z)), z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(s(z)), z, s(s(z))) <= True
minus(s(z), s(s(z)), z) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, econs(a, enil)), s(s(z))) /\ delete_all_elt(a, econs(a, econs(a, enil)), econs(a, enil))
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, econs(a, enil)), s(s(z))) /\ delete_all_elt(a, econs(b, econs(a, enil)), econs(b, enil))
False <= count_elt(a, econs(b, enil), s(z))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), s(s(z))) /\ delete_all_elt(b, econs(b, enil), econs(a, econs(a, enil)))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, econs(a, enil))) <= delete_all_elt(a, econs(b, enil), econs(a, econs(a, enil)))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, econs(a, enil)), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
False <= minus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_3(a) <= True
  _r_4(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_5(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_4(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_5(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(a) <= True
  _r_4(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= True
  _r_6(econs(x_0_0, x_0_1)) <= _r_4(x_0_0)
  _r_6(enil) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_4(x_2_0) /\ _r_5(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_4(x_2_0) /\ _r_6(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_5(x_2_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_6(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_4(x_1_0) /\ _r_6(x_1_1)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  _r_2(z) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_1(x_1_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_2(x_0_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_2(x_2_0)
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> enil  ;  _ila -> z  ;  _jla -> s(s(z))  ;  _kla -> s(_cysq_0)  ;  _lla -> s(_dysq_0)  ;  e -> a  ;  l -> econs(a, econs(_teuq_0, enil))
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
Yes: {
_wka -> enil  ;  h -> b  ;  t -> econs(a, _dutq_1)  ;  x -> a
}

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 25, which took 3.711973 s (model generation: 3.708831,  model checking: 0.003142):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(a, enil)), z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, econs(a, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, econs(a, enil)), econs(a, econs(a, enil))) <= True
delete_all_elt(b, econs(a, econs(b, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, econs(a, enil)), s(s(z))) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, econs(a, enil)), s(s(z))) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(s(z)), z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(s(z)), z, s(s(z))) <= True
minus(s(z), s(s(z)), z) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, econs(a, enil)), s(s(z))) /\ delete_all_elt(a, econs(a, econs(a, enil)), econs(a, enil))
False <= count_elt(a, econs(a, econs(a, enil)), s(z)) /\ delete_all_elt(a, econs(a, econs(a, enil)), enil)
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, econs(a, enil)), s(s(z)))
False <= count_elt(a, econs(b, enil), s(z))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), s(s(z))) /\ delete_all_elt(b, econs(b, enil), econs(a, econs(a, enil)))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, econs(a, enil))) <= delete_all_elt(a, econs(b, enil), econs(a, econs(a, enil)))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, econs(a, enil)), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
False <= minus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_1(z) <= True
  _r_3(b) <= True
  _r_4(a) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_2_0) /\ _r_4(x_1_0)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_2_0) /\ _r_6(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_2_0) /\ _r_3(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_6(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_4(x_1_0)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(b) <= True
  _r_4(a) <= True
  _r_5(econs(x_0_0, x_0_1)) <= _r_3(x_0_0)
  _r_5(enil) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_6(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_6(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_6(x_2_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(z) <= True
  _r_2(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_2(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_2(x_1_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_2_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_2(x_0_0)
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(_mpuq_0, econs(_ffvq_0, enil))  ;  _ila -> s(s(z))  ;  _jla -> s(s(z))  ;  _kla -> s(s(_tevq_0))  ;  _lla -> z  ;  e -> b  ;  l -> econs(_spuq_0, econs(_hfvq_0, enil))
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
Yes: {
_bla -> s(z)  ;  t1 -> econs(_isuq_0, econs(_dfvq_0, _dfvq_1))  ;  x -> a
}

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
No: ()

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
Yes: {
_vka -> enil  ;  h -> a  ;  t -> econs(a, enil)
}

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 26, which took 7.643618 s (model generation: 7.639228,  model checking: 0.004390):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(a, enil)), z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(a, enil)), enil) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, econs(a, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, econs(a, enil)), econs(a, econs(a, enil))) <= True
delete_all_elt(b, econs(a, econs(b, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, econs(a, enil)), s(s(z))) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, econs(a, enil)), s(s(z))) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(s(z)), z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(s(z)), z, s(s(z))) <= True
minus(s(z), s(s(z)), z) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, econs(a, enil)), s(s(z))) /\ delete_all_elt(a, econs(a, econs(a, enil)), econs(a, enil))
False <= count_elt(a, econs(a, econs(a, enil)), s(z))
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, econs(a, enil)), s(s(z)))
False <= count_elt(a, econs(b, enil), s(z))
False <= count_elt(b, econs(a, econs(a, enil)), s(s(z)))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, enil), s(s(z))) /\ delete_all_elt(b, econs(b, enil), econs(a, econs(a, enil)))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, econs(a, enil))) <= delete_all_elt(a, econs(b, enil), econs(a, econs(a, enil)))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, econs(a, enil)), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
False <= minus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_1(z) <= True
  _r_3(b) <= True
  _r_4(a) <= True
  _r_5(econs(x_0_0, x_0_1)) <= _r_3(x_0_0)
  _r_5(enil) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_2_0) /\ _r_3(x_1_0) /\ _r_6(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_2_0) /\ _r_6(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_4(x_1_0)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(b) <= True
  _r_4(a) <= True
  _r_5(econs(x_0_0, x_0_1)) <= _r_3(x_0_0)
  _r_5(enil) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_6(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_4(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_6(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_6(x_2_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(z) <= True
  _r_2(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_2(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_2(x_1_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_2_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_2(x_0_0)
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(_movq_0, enil)  ;  _ila -> s(z)  ;  _jla -> s(s(z))  ;  _kla -> s(s(_dlwq_0))  ;  _lla -> z  ;  e -> b  ;  l -> econs(b, econs(_emwq_0, enil))
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
Yes: {
_bla -> s(_jtvq_0)  ;  t1 -> econs(a, enil)  ;  x -> a
}

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
Yes: {
_cla -> s(s(_alwq_0))  ;  h1 -> a  ;  t1 -> econs(b, _wyvq_1)  ;  x -> b
}

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 27, which took 3.357358 s (model generation: 3.353600,  model checking: 0.003758):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, econs(a, enil)), s(s(z))) <= True
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(a, enil)), z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(a, enil)), enil) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, econs(a, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, econs(a, enil)), econs(a, econs(a, enil))) <= True
delete_all_elt(b, econs(a, econs(b, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, econs(a, enil)), s(s(z))) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, econs(a, enil)), s(s(z))) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(s(z)), z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(s(z)), z, s(s(z))) <= True
minus(s(z), s(s(z)), z) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, econs(a, enil)), s(z))
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, econs(a, enil)), s(s(z)))
False <= count_elt(a, econs(b, enil), s(z))
False <= count_elt(b, econs(a, econs(a, enil)), s(s(z)))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, econs(a, enil)), s(s(z)))
count_elt(b, econs(a, econs(b, enil)), s(s(z))) <= count_elt(b, econs(b, enil), s(s(z)))
False <= count_elt(b, econs(b, enil), s(s(z))) /\ delete_all_elt(b, econs(b, enil), econs(a, econs(a, enil)))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, econs(a, enil))) <= delete_all_elt(a, econs(b, enil), econs(a, econs(a, enil)))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, econs(a, enil)), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
False <= minus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_2(z) <= True
  _r_3(b) <= True
  _r_4(a) <= True
  _r_5(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_2_0) /\ _r_3(x_1_0) /\ _r_5(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_0) /\ length_elt(x_1_1, x_2_0)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_2_0) /\ _r_3(x_1_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_2_0) /\ _r_5(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_4(x_1_0)
  count_elt(b, enil, z) <= True
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(b) <= True
  _r_4(a) <= True
  _r_5(econs(x_0_0, x_0_1)) <= True
  _r_6(econs(x_0_0, x_0_1)) <= _r_3(x_0_0)
  _r_6(enil) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_3(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_2_0) /\ _r_5(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_4(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_6(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_5(x_2_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0) /\ _r_6(x_1_1)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  _r_2(z) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_1(x_1_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_2(x_0_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_2(x_2_0)
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(_muwq_0, econs(_nsxq_0, enil))  ;  _ila -> s(s(z))  ;  _jla -> s(z)  ;  _kla -> s(z)  ;  _lla -> z  ;  e -> b  ;  l -> econs(b, enil)
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
Yes: {
_bla -> s(z)  ;  t1 -> econs(_ucxq_0, econs(_csxq_0, _csxq_1))  ;  x -> b
}

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
Yes: {
_cla -> s(s(z))  ;  h1 -> b  ;  t1 -> econs(a, econs(_zsxq_0, enil))  ;  x -> a
}

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 28, which took 14.932672 s (model generation: 14.921422,  model checking: 0.011250):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, econs(a, enil)), s(s(z))) <= True
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, econs(a, enil))), s(s(z))) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(a, enil)), z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(a, enil)), enil) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, econs(a, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, econs(a, enil)), econs(a, econs(a, enil))) <= True
delete_all_elt(b, econs(a, econs(b, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, econs(a, enil)), s(s(z))) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, econs(a, enil)), s(s(z))) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(s(z)), z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(s(z)), z, s(s(z))) <= True
minus(s(z), s(s(z)), z) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, econs(a, enil)), s(z))
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, econs(a, enil)), s(s(z)))
False <= count_elt(a, econs(b, enil), s(z))
False <= count_elt(b, econs(a, econs(a, enil)), s(s(z)))
count_elt(b, econs(b, econs(a, econs(a, enil))), s(s(z))) <= count_elt(b, econs(a, econs(a, enil)), s(z))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, econs(a, enil)), s(s(z)))
count_elt(b, econs(a, econs(b, enil)), s(s(z))) <= count_elt(b, econs(b, enil), s(s(z)))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, econs(a, enil))) <= delete_all_elt(a, econs(b, enil), econs(a, econs(a, enil)))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, econs(a, enil)), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, econs(a, enil)))
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
False <= minus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_1(z) <= True
  _r_2(s(x_0_0)) <= True
  _r_3(b) <= True
  _r_4(a) <= True
  _r_5(econs(x_0_0, x_0_1)) <= _r_3(x_0_0)
  _r_5(econs(x_0_0, x_0_1)) <= _r_6(x_0_1)
  _r_5(enil) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_2_0) /\ _r_3(x_1_0) /\ _r_6(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_2_0) /\ _r_4(x_1_0)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_2_0) /\ _r_5(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_2_0) /\ _r_6(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_2_0) /\ _r_5(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0) /\ _r_5(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_4(x_1_0)
  count_elt(b, enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(b) <= True
  _r_4(a) <= True
  _r_5(econs(x_0_0, x_0_1)) <= _r_3(x_0_0)
  _r_5(econs(x_0_0, x_0_1)) <= _r_6(x_0_1)
  _r_5(enil) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_3(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_2_0) /\ _r_6(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_4(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_6(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_6(x_2_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(z) <= True
  _r_2(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_2(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_2(x_1_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_2_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_2(x_0_0)
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> enil  ;  _ila -> z  ;  _jla -> s(s(z))  ;  _kla -> s(s(_xzzq_0))  ;  _lla -> s(_kxxq_0)  ;  e -> a  ;  l -> econs(a, econs(_pcar_0, enil))
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
Yes: {
_bla -> s(s(_rcar_0))  ;  t1 -> econs(a, enil)  ;  x -> b
}

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
Yes: {
_cla -> s(s(_ybar_0))  ;  h1 -> a  ;  t1 -> econs(a, enil)  ;  x -> b
}

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 29, which took 10.921231 s (model generation: 10.909530,  model checking: 0.011701):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, econs(a, enil)), s(s(z))) <= True
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, econs(a, enil))), s(s(z))) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(a, enil)), z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(a, enil)), enil) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, econs(a, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, econs(a, enil)), econs(a, econs(a, enil))) <= True
delete_all_elt(b, econs(a, econs(b, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, econs(a, enil)), s(s(z))) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, econs(a, enil)), s(s(z))) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(s(z)), z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(s(z)), z, s(s(z))) <= True
minus(s(z), s(s(z)), z) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, econs(a, enil)), s(z))
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, econs(a, enil)), s(s(z)))
False <= count_elt(a, econs(b, enil), s(z))
False <= count_elt(b, econs(a, econs(a, enil)), s(s(z)))
count_elt(b, econs(b, econs(a, econs(a, enil))), s(s(z))) <= count_elt(b, econs(a, econs(a, enil)), s(z))
False <= count_elt(b, econs(a, enil), s(s(z)))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, econs(a, enil)), s(s(z)))
count_elt(b, econs(a, econs(b, enil)), s(s(z))) <= count_elt(b, econs(b, enil), s(s(z)))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, econs(a, enil))) <= delete_all_elt(a, econs(b, enil), econs(a, econs(a, enil)))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, econs(a, enil)), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, econs(a, enil)))
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(s(z)), s(s(z)), s(z))
False <= minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
False <= minus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_1(s(x_0_0)) <= True
  _r_2(s(x_0_0)) <= _r_1(x_0_0)
  _r_2(z) <= True
  _r_3(b) <= True
  _r_4(a) <= True
  _r_5(econs(x_0_0, x_0_1)) <= _r_3(x_0_0)
  _r_5(econs(x_0_0, x_0_1)) <= _r_6(x_0_1)
  _r_5(enil) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_2_0) /\ _r_4(x_1_0)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_2_0) /\ _r_5(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_2_0) /\ _r_3(x_1_0) /\ _r_6(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_2_0) /\ _r_6(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0) /\ _r_5(x_1_1) /\ length_elt(x_1_1, x_2_0)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_4(x_1_0)
  count_elt(b, enil, z) <= True
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(econs(x_0_0, x_0_1), z) <= True
  length_elt(enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(b) <= True
  _r_4(a) <= True
  _r_5(econs(x_0_0, x_0_1)) <= _r_3(x_0_0)
  _r_5(econs(x_0_0, x_0_1)) <= _r_6(x_0_1)
  _r_5(enil) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_3(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_2_0) /\ _r_6(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_4(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_6(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_6(x_1_1) /\ _r_6(x_2_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(econs(x_0_0, x_0_1), z) <= True
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= True
  _r_2(s(x_0_0)) <= _r_1(x_0_0)
  _r_2(z) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0) /\ _r_2(x_1_0)
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ _r_2(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_1(x_1_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_2(x_0_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_0_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_2(x_2_0)
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(b, enil)  ;  _ila -> s(z)  ;  _jla -> z  ;  _kla -> z  ;  _lla -> z  ;  e -> a  ;  l -> econs(b, econs(_lzcr_0, _lzcr_1))
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
No: ()

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
Yes: {
_cla -> s(s(z))  ;  h1 -> b  ;  t1 -> econs(a, enil)  ;  x -> a
}

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


-------------------------------------------
Step 30, which took 9.408819 s (model generation: 9.395734,  model checking: 0.013085):

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, econs(a, enil)), s(s(z))) <= True
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, econs(a, enil))), s(s(z))) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(a, enil)), z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(a, enil)), enil) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, econs(a, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, econs(a, enil)), econs(a, econs(a, enil))) <= True
delete_all_elt(b, econs(a, econs(b, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, econs(a, enil)), s(s(z))) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, econs(a, enil)), s(s(z))) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(s(z)), z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(s(z)), z, s(s(z))) <= True
minus(s(z), s(s(z)), z) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, econs(a, enil)), s(z))
False <= count_elt(a, econs(a, enil), s(s(z)))
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, econs(a, enil)), s(s(z)))
False <= count_elt(a, econs(b, econs(a, enil)), z) /\ length_elt(econs(b, econs(a, enil)), z)
False <= count_elt(a, econs(b, enil), s(z))
False <= count_elt(b, econs(a, econs(a, enil)), s(s(z)))
count_elt(b, econs(b, econs(a, econs(a, enil))), s(s(z))) <= count_elt(b, econs(a, econs(a, enil)), s(z))
False <= count_elt(b, econs(a, enil), s(s(z)))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, econs(a, enil)), s(s(z)))
count_elt(b, econs(a, econs(b, enil)), s(s(z))) <= count_elt(b, econs(b, enil), s(s(z)))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, econs(a, enil))) <= delete_all_elt(a, econs(b, enil), econs(a, econs(a, enil)))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, econs(a, enil)), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, econs(a, enil)))
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(s(z)), s(s(z)), s(z))
False <= minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
False <= minus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_1(s(x_0_0)) <= _r_2(x_0_0)
  _r_1(z) <= True
  _r_2(s(x_0_0)) <= True
  _r_3(a) <= True
  _r_4(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= _r_4(x_0_0)
  _r_5(econs(x_0_0, x_0_1)) <= _r_6(x_0_1)
  _r_5(enil) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_2_0) /\ _r_4(x_1_0) /\ _r_6(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_2_0) /\ _r_4(x_1_0) /\ _r_5(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0) /\ length_elt(x_1_1, x_2_0)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_4(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_2_0) /\ _r_6(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_2_0) /\ _r_5(x_1_1) /\ length_elt(x_1_1, x_2_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(b, enil, z) <= True
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(a) <= True
  _r_4(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= _r_4(x_0_0)
  _r_5(econs(x_0_0, x_0_1)) <= _r_6(x_0_1)
  _r_5(enil) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_4(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_2_0) /\ _r_6(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_6(x_2_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_6(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= _r_2(x_0_0)
  _r_1(z) <= True
  _r_2(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0) /\ _r_2(x_1_0)
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ _r_2(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_2(x_1_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_2_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_2(x_0_0)
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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




Answer of teacher:

count_elt(x, enil, z) <= True  :
No: ()

delete_all_elt(x, enil, enil) <= True  :
No: ()

length_elt(enil, z) <= True  :
No: ()

minus(s(u), z, s(u)) <= True  :
No: ()

minus(z, y, z) <= True  :
No: ()

eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla)  :
Yes: {
_hla -> econs(b, enil)  ;  _ila -> s(z)  ;  _jla -> s(s(z))  ;  _kla -> z  ;  _lla -> s(s(_rwfr_0))  ;  e -> a  ;  l -> econs(b, econs(_fyfr_0, enil))
}

count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla)  :
Yes: {
_bla -> z  ;  t1 -> econs(b, _hher_1)  ;  x -> a
}

eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla)  :
Yes: {
_cla -> s(s(z))  ;  h1 -> a  ;  t1 -> econs(b, econs(b, _dbgr_1))  ;  x -> b
}

delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka)  :
No: ()

eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka)  :
No: ()

length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka)  :
No: ()

minus(s(u), s(x2), _qka) <= minus(u, x2, _qka)  :
No: ()


Total time: 59.442734
Learner time: 58.343608
Teacher time: 0.082098
Reasons for stopping: Maybe:  timeout during learnerLast solver state:

Clauses:
{
count_elt(x, enil, z) <= True -> 0
delete_all_elt(x, enil, enil) <= True -> 0
length_elt(enil, z) <= True -> 0
minus(s(u), z, s(u)) <= True -> 0
minus(z, y, z) <= True -> 0
eq_nat(_ila, _lla) <= count_elt(e, l, _kla) /\ delete_all_elt(e, l, _hla) /\ length_elt(_hla, _ila) /\ length_elt(l, _jla) /\ minus(_jla, _kla, _lla) -> 0
count_elt(x, econs(x, t1), s(_bla)) <= count_elt(x, t1, _bla) -> 0
eq_elt(h1, x) \/ count_elt(x, econs(h1, t1), _cla) <= count_elt(x, t1, _cla) -> 0
delete_all_elt(h, econs(h, t), _vka) <= delete_all_elt(h, t, _vka) -> 0
eq_elt(x, h) \/ delete_all_elt(x, econs(h, t), econs(h, _wka)) <= delete_all_elt(x, t, _wka) -> 0
length_elt(econs(x, ll), s(_mka)) <= length_elt(ll, _mka) -> 0
minus(s(u), s(x2), _qka) <= minus(u, x2, _qka) -> 0
}

Accumulated learning constraints:
{
count_elt(a, econs(a, econs(a, enil)), s(s(z))) <= True
count_elt(a, econs(a, econs(b, enil)), s(z)) <= True
count_elt(a, econs(a, enil), s(z)) <= True
count_elt(a, econs(b, econs(a, econs(a, enil))), s(s(z))) <= True
count_elt(a, econs(b, econs(a, enil)), s(z)) <= True
count_elt(a, econs(b, enil), z) <= True
count_elt(a, enil, z) <= True
count_elt(b, econs(a, econs(a, enil)), z) <= True
count_elt(b, econs(a, econs(b, enil)), s(z)) <= True
count_elt(b, econs(a, enil), z) <= True
count_elt(b, econs(b, econs(a, enil)), s(z)) <= True
count_elt(b, econs(b, enil), s(z)) <= True
count_elt(b, enil, z) <= True
delete_all_elt(a, econs(a, econs(a, enil)), enil) <= True
delete_all_elt(a, econs(a, econs(b, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(a, enil), enil) <= True
delete_all_elt(a, econs(b, econs(a, enil)), econs(b, enil)) <= True
delete_all_elt(a, econs(b, enil), econs(b, enil)) <= True
delete_all_elt(a, enil, enil) <= True
delete_all_elt(b, econs(a, econs(a, enil)), econs(a, econs(a, enil))) <= True
delete_all_elt(b, econs(a, econs(b, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(a, enil), econs(a, enil)) <= True
delete_all_elt(b, econs(b, econs(a, enil)), econs(a, enil)) <= True
delete_all_elt(b, econs(b, enil), enil) <= True
delete_all_elt(b, enil, enil) <= True
length_elt(econs(a, econs(a, enil)), s(s(z))) <= True
length_elt(econs(a, enil), s(z)) <= True
length_elt(econs(b, econs(a, enil)), s(s(z))) <= True
length_elt(econs(b, enil), s(z)) <= True
length_elt(enil, z) <= True
minus(s(s(s(z))), s(s(z)), s(z)) <= True
minus(s(s(z)), s(s(z)), z) <= True
minus(s(s(z)), s(z), s(z)) <= True
minus(s(s(z)), z, s(s(z))) <= True
minus(s(z), s(s(z)), z) <= True
minus(s(z), s(z), z) <= True
minus(s(z), z, s(z)) <= True
minus(z, s(z), z) <= True
minus(z, z, z) <= True
False <= count_elt(a, econs(a, econs(a, enil)), s(z))
False <= count_elt(a, econs(a, enil), s(s(z)))
False <= count_elt(a, econs(a, enil), z)
False <= count_elt(a, econs(b, econs(a, enil)), s(s(z)))
False <= count_elt(a, econs(b, econs(a, enil)), z)
False <= count_elt(a, econs(b, enil), s(z))
False <= count_elt(b, econs(a, econs(a, enil)), s(s(z)))
count_elt(b, econs(b, econs(a, econs(a, enil))), s(s(z))) <= count_elt(b, econs(a, econs(a, enil)), s(z))
False <= count_elt(b, econs(a, enil), s(s(z)))
False <= count_elt(b, econs(a, enil), s(z))
False <= count_elt(b, econs(b, econs(a, enil)), s(s(z)))
count_elt(b, econs(a, econs(b, econs(b, enil))), s(s(z))) <= count_elt(b, econs(b, econs(b, enil)), s(s(z)))
count_elt(b, econs(a, econs(b, enil)), s(s(z))) <= count_elt(b, econs(b, enil), s(s(z)))
False <= count_elt(b, econs(b, enil), z)
False <= delete_all_elt(a, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(a, enil))
False <= delete_all_elt(a, econs(a, enil), econs(b, enil))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, econs(a, enil))) <= delete_all_elt(a, econs(b, enil), econs(a, econs(a, enil)))
delete_all_elt(a, econs(a, econs(b, enil)), econs(a, enil)) <= delete_all_elt(a, econs(b, enil), econs(a, enil))
False <= delete_all_elt(a, econs(b, enil), enil)
False <= delete_all_elt(b, econs(a, econs(a, enil)), econs(a, enil))
False <= delete_all_elt(b, econs(a, enil), enil)
False <= delete_all_elt(b, econs(b, econs(a, enil)), enil)
False <= delete_all_elt(b, econs(b, enil), econs(a, econs(a, enil)))
False <= delete_all_elt(b, econs(b, enil), econs(a, enil))
False <= length_elt(econs(a, enil), s(s(z)))
False <= minus(s(s(z)), s(s(z)), s(z))
False <= minus(s(s(z)), s(z), z)
False <= minus(s(z), s(z), s(z))
False <= minus(s(z), z, s(s(z)))
}

Current best model:
|_
name: None

count_elt ->
[
count_elt : <elt * elist * nat>
{
  _r_1(s(x_0_0)) <= _r_2(x_0_0)
  _r_1(z) <= True
  _r_2(s(x_0_0)) <= True
  _r_3(a) <= True
  _r_4(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= _r_4(x_0_0)
  _r_5(econs(x_0_0, x_0_1)) <= _r_6(x_0_1)
  _r_5(enil) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_2_0) /\ _r_4(x_1_0) /\ _r_6(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_2_0) /\ _r_4(x_1_0) /\ _r_5(x_1_1)
  count_elt(a, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_3(x_1_0) /\ length_elt(x_1_1, x_2_0)
  count_elt(a, econs(x_1_0, x_1_1), z) <= _r_4(x_1_0)
  count_elt(a, enil, z) <= True
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_1(x_2_0) /\ _r_6(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_2(x_2_0) /\ _r_5(x_1_1) /\ length_elt(x_1_1, x_2_0)
  count_elt(b, econs(x_1_0, x_1_1), s(x_2_0)) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  count_elt(b, econs(x_1_0, x_1_1), z) <= _r_3(x_1_0)
  count_elt(b, enil, z) <= True
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
delete_all_elt ->
[
delete_all_elt : <elt * elist * elist>
{
  _r_3(a) <= True
  _r_4(b) <= True
  _r_5(econs(x_0_0, x_0_1)) <= _r_4(x_0_0)
  _r_5(econs(x_0_0, x_0_1)) <= _r_6(x_0_1)
  _r_5(enil) <= True
  _r_6(econs(x_0_0, x_0_1)) <= True
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_4(x_2_0)
  delete_all_elt(a, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_2_0) /\ _r_6(x_1_1)
  delete_all_elt(a, econs(x_1_0, x_1_1), enil) <= _r_3(x_1_0)
  delete_all_elt(a, enil, enil) <= True
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_3(x_1_0) /\ _r_6(x_2_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), econs(x_2_0, x_2_1)) <= _r_4(x_1_0) /\ _r_6(x_1_1)
  delete_all_elt(b, econs(x_1_0, x_1_1), enil) <= _r_4(x_1_0) /\ _r_5(x_1_1)
  delete_all_elt(b, enil, enil) <= True
}
]


;
length_elt ->
[
length_elt : <elist * nat>
{
  length_elt(econs(x_0_0, x_0_1), s(x_1_0)) <= length_elt(x_0_1, x_1_0)
  length_elt(enil, z) <= True
}
]


;
minus ->
[
minus : <nat * nat * nat>
{
  _r_1(s(x_0_0)) <= _r_2(x_0_0)
  _r_1(z) <= True
  _r_2(s(x_0_0)) <= True
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_0_0) /\ _r_2(x_1_0)
  minus(s(x_0_0), s(x_1_0), s(x_2_0)) <= _r_1(x_1_0) /\ _r_2(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_1(x_0_0)
  minus(s(x_0_0), s(x_1_0), z) <= _r_2(x_1_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_1(x_2_0)
  minus(s(x_0_0), z, s(x_2_0)) <= _r_2(x_0_0)
  minus(z, s(x_1_0), z) <= True
  minus(z, z, z) <= True
}
]



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