Solving ../../benchmarks/smtlib/true/tree_shallow_max.smt2...

Inference procedure has parameters:
Ice fuel: 200
Timeout: Some(60.) (sec)
Teacher_type: Checks all clauses every time
Approximation method: remove every clause that can be safely removed



Learning problem is:

env: {
elt -> {a, b}  ;  etree -> {leaf, node}  ;  nat -> {s, z}
}
definition:
{
(leq_nat, P:
{
leq_nat(z, n2) <= True
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2)
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2))
False <= leq_nat(s(nn1), z)
}
)
(le_nat, P:
{
le_nat(z, s(nn2)) <= True
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2)
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2))
False <= le_nat(s(nn1), z)
False <= le_nat(z, z)
}
)
(subtree, P:
{
subtree(leaf, t) <= True
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))
False <= subtree(node(ea, ta1, ta2), leaf)
eq_elt(ea, eb) <= subtree(node(ea, ta1, ta2), node(eb, tb1, tb2))
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))
}
)
(max, F:
{
le_nat(n, m) \/ max(n, m, n) <= True
max(n, m, m) <= le_nat(n, m)
}
eq_nat(_qv, _rv) <= max(_ov, _pv, _qv) /\ max(_ov, _pv, _rv)
)
(height, F:
{
height(leaf, z) <= True
height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv)
height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv)
}
eq_nat(_xv, _yv) <= height(_wv, _xv) /\ height(_wv, _yv)
)
(shallower, P:
{
shallower(leaf, n) <= True
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))
shallower(t1, m) <= shallower(node(e, t1, t2), s(m))
False <= shallower(node(e, t1, t2), z)
}
)
(taller, P:
{
taller(leaf, z) <= True
taller(node(e, t1, t2), z) <= True
taller(node(e, t1, t2), s(m)) <= taller(t1, m)
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)
False <= taller(leaf, s(m))
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))
}
)
}

properties:
{
shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2)
}


over-approximation: {height, leq_nat, max, subtree, taller}
under-approximation: {height, leq_nat, subtree, taller}

Clause system for inference is:

{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv) -> 0
height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
False <= shallower(node(e, t1, t2), z) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}


Solving took 0.915764 seconds.
Yes: |_
name: None

height ->
[
height : <etree * nat>
{
  
}
]


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  shallower(leaf, s(x_1_0)) <= True
  shallower(leaf, z) <= True
  shallower(node(x_0_0, x_0_1, x_0_2), s(x_1_0)) <= shallower(x_0_1, x_1_0) /\ shallower(x_0_2, x_1_0)
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


;
taller ->
[
taller : <etree * nat>
{
  
}
]



--
Equality automata are defined for: {elt, etree, nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006528 s (model generation: 0.006378,  model checking: 0.000150):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv) -> 0
height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
False <= shallower(node(e, t1, t2), z) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

height ->
[
height : <etree * nat>
{
  
}
]


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


;
taller ->
[
taller : <etree * nat>
{
  
}
]



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




Answer of teacher:

le_nat(n, m) \/ max(n, m, n) <= True  :
Yes: {
m -> z  ;  n -> z
}

le_nat(z, s(nn2)) <= True  :
Yes: {

}

shallower(leaf, n) <= True  :
Yes: {
n -> z
}

height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv)  :
No: ()

height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv)  :
No: ()

max(n, m, m) <= le_nat(n, m)  :
No: ()

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

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

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

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

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

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

shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2)  :
No: ()

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
No: ()

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

False <= shallower(node(e, t1, t2), z)  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


-------------------------------------------
Step 1, which took 0.007551 s (model generation: 0.007368,  model checking: 0.000183):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv) -> 0
height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
False <= shallower(node(e, t1, t2), z) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

Accumulated learning constraints:
{
le_nat(z, s(z)) <= True
le_nat(z, z) \/ max(z, z, z) <= True
shallower(leaf, z) <= True
}

Current best model:
|_
name: None

height ->
[
height : <etree * nat>
{
  
}
]


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


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


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


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


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


;
taller ->
[
taller : <etree * nat>
{
  
}
]



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




Answer of teacher:

le_nat(n, m) \/ max(n, m, n) <= True  :
Yes: {
m -> z  ;  n -> s(_mnzmw_0)
}

le_nat(z, s(nn2)) <= True  :
No: ()

shallower(leaf, n) <= True  :
Yes: {
n -> s(_nnzmw_0)
}

height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv)  :
No: ()

height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv)  :
No: ()

max(n, m, m) <= le_nat(n, m)  :
Yes: {
m -> s(_onzmw_0)  ;  n -> z
}

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

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

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

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

}

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

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

shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2)  :
Yes: {
_zv -> z  ;  n1 -> z  ;  n2 -> z  ;  t1 -> leaf  ;  t2 -> leaf
}

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
Yes: {
m -> z  ;  t1 -> leaf  ;  t2 -> leaf
}

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

False <= shallower(node(e, t1, t2), z)  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


-------------------------------------------
Step 2, which took 0.008578 s (model generation: 0.008336,  model checking: 0.000242):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv) -> 0
height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
False <= shallower(node(e, t1, t2), z) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

Accumulated learning constraints:
{
le_nat(s(z), z) \/ max(s(z), z, s(z)) <= True
le_nat(z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
shallower(leaf, s(z)) <= True
shallower(leaf, z) <= True
shallower(node(a, leaf, leaf), s(z)) <= True
False <= le_nat(z, z)
}

Current best model:
|_
name: None

height ->
[
height : <etree * nat>
{
  
}
]


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  shallower(leaf, s(x_1_0)) <= True
  shallower(leaf, z) <= True
  shallower(node(x_0_0, x_0_1, x_0_2), s(x_1_0)) <= True
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


;
taller ->
[
taller : <etree * nat>
{
  
}
]



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




Answer of teacher:

le_nat(n, m) \/ max(n, m, n) <= True  :
Yes: {
m -> s(_cozmw_0)  ;  n -> s(_dozmw_0)
}

le_nat(z, s(nn2)) <= True  :
No: ()

shallower(leaf, n) <= True  :
No: ()

height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv)  :
No: ()

height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv)  :
No: ()

max(n, m, m) <= le_nat(n, m)  :
Yes: {
m -> z  ;  n -> s(_fozmw_0)
}

le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2)  :
Yes: {
nn1 -> z  ;  nn2 -> s(_jozmw_0)
}

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

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

}

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

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

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

shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2)  :
No: ()

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
No: ()

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
Yes: {
m -> z  ;  t1 -> leaf  ;  t2 -> node(_mozmw_0, _mozmw_1, _mozmw_2)
}

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
Yes: {
m -> z  ;  t1 -> node(_oozmw_0, _oozmw_1, _oozmw_2)
}

False <= shallower(node(e, t1, t2), z)  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


-------------------------------------------
Step 3, which took 0.012021 s (model generation: 0.011816,  model checking: 0.000205):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv) -> 0
height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
False <= shallower(node(e, t1, t2), z) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

Accumulated learning constraints:
{
le_nat(s(z), s(s(z))) <= True
le_nat(s(z), s(z)) \/ max(s(z), s(z), s(z)) <= True
le_nat(z, s(z)) <= True
max(s(z), z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
shallower(leaf, s(z)) <= True
shallower(leaf, z) <= True
shallower(node(a, leaf, leaf), s(z)) <= True
False <= le_nat(s(z), z)
False <= le_nat(z, z)
shallower(node(a, leaf, leaf), z) <= shallower(node(a, leaf, node(a, leaf, leaf)), s(z))
shallower(node(a, leaf, leaf), z) <= shallower(node(a, node(a, leaf, leaf), leaf), s(z))
}

Current best model:
|_
name: None

height ->
[
height : <etree * nat>
{
  
}
]


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  shallower(leaf, s(x_1_0)) <= True
  shallower(leaf, z) <= True
  shallower(node(x_0_0, x_0_1, x_0_2), s(x_1_0)) <= True
  shallower(node(x_0_0, x_0_1, x_0_2), z) <= True
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


;
taller ->
[
taller : <etree * nat>
{
  
}
]



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




Answer of teacher:

le_nat(n, m) \/ max(n, m, n) <= True  :
No: ()

le_nat(z, s(nn2)) <= True  :
No: ()

shallower(leaf, n) <= True  :
No: ()

height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv)  :
No: ()

height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv)  :
No: ()

max(n, m, m) <= le_nat(n, m)  :
No: ()

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

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

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

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

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

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

shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2)  :
No: ()

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
No: ()

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

False <= shallower(node(e, t1, t2), z)  :
Yes: {

}

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


-------------------------------------------
Step 4, which took 0.151839 s (model generation: 0.009657,  model checking: 0.142182):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv) -> 0
height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
False <= shallower(node(e, t1, t2), z) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

Accumulated learning constraints:
{
le_nat(s(z), s(s(z))) <= True
le_nat(z, s(z)) <= True
max(s(z), s(z), s(z)) <= True
max(s(z), z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
shallower(leaf, s(z)) <= True
shallower(leaf, z) <= True
shallower(node(a, leaf, leaf), s(z)) <= True
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
False <= le_nat(z, z)
False <= shallower(node(a, leaf, leaf), z)
False <= shallower(node(a, leaf, node(a, leaf, leaf)), s(z))
False <= shallower(node(a, node(a, leaf, leaf), leaf), s(z))
}

Current best model:
|_
name: None

height ->
[
height : <etree * nat>
{
  
}
]


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  shallower(leaf, s(x_1_0)) <= True
  shallower(leaf, z) <= True
  shallower(node(x_0_0, x_0_1, x_0_2), s(x_1_0)) <= shallower(x_0_1, x_1_0) /\ shallower(x_0_2, x_1_0)
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


;
taller ->
[
taller : <etree * nat>
{
  
}
]



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




Answer of teacher:

le_nat(n, m) \/ max(n, m, n) <= True  :
No: ()

le_nat(z, s(nn2)) <= True  :
No: ()

shallower(leaf, n) <= True  :
No: ()

height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv)  :
No: ()

height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv)  :
No: ()

max(n, m, m) <= le_nat(n, m)  :
No: ()

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

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

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

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

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

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

shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2)  :
Yes: {
_zv -> s(z)  ;  n1 -> s(s(z))  ;  n2 -> s(_zpzmw_0)  ;  t1 -> node(_aqzmw_0, leaf, node(_owzmw_0, leaf, leaf))  ;  t2 -> leaf
}

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
No: ()

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

False <= shallower(node(e, t1, t2), z)  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


-------------------------------------------
Step 5, which took 0.099266 s (model generation: 0.011438,  model checking: 0.087828):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv) -> 0
height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
False <= shallower(node(e, t1, t2), z) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

Accumulated learning constraints:
{
le_nat(s(z), s(s(z))) <= True
le_nat(z, s(z)) <= True
max(s(z), s(z), s(z)) <= True
max(s(z), z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
shallower(leaf, s(z)) <= True
shallower(leaf, z) <= True
shallower(node(a, leaf, leaf), s(z)) <= True
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
False <= le_nat(z, z)
shallower(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= max(s(s(z)), s(z), s(z)) /\ shallower(node(a, leaf, node(a, leaf, leaf)), s(s(z)))
False <= shallower(node(a, leaf, leaf), z)
False <= shallower(node(a, leaf, node(a, leaf, leaf)), s(z))
False <= shallower(node(a, node(a, leaf, leaf), leaf), s(z))
}

Current best model:
|_
name: None

height ->
[
height : <etree * nat>
{
  
}
]


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  shallower(leaf, s(x_1_0)) <= True
  shallower(leaf, z) <= True
  shallower(node(x_0_0, x_0_1, x_0_2), s(x_1_0)) <= shallower(x_0_1, x_1_0) /\ shallower(x_0_2, x_1_0)
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


;
taller ->
[
taller : <etree * nat>
{
  
}
]



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




Answer of teacher:

le_nat(n, m) \/ max(n, m, n) <= True  :
No: ()

le_nat(z, s(nn2)) <= True  :
No: ()

shallower(leaf, n) <= True  :
No: ()

height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv)  :
No: ()

height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv)  :
No: ()

max(n, m, m) <= le_nat(n, m)  :
No: ()

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

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

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

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

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

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

shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2)  :
Yes: {
_zv -> s(z)  ;  n1 -> s(s(z))  ;  n2 -> z  ;  t1 -> node(_ikdnw_0, leaf, node(_ypdnw_0, leaf, leaf))  ;  t2 -> leaf
}

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
No: ()

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

False <= shallower(node(e, t1, t2), z)  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


-------------------------------------------
Step 6, which took 0.019651 s (model generation: 0.019008,  model checking: 0.000643):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv) -> 0
height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
False <= shallower(node(e, t1, t2), z) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

Accumulated learning constraints:
{
le_nat(s(z), s(s(z))) <= True
le_nat(z, s(z)) <= True
max(s(z), s(z), s(z)) <= True
max(s(z), z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
shallower(leaf, s(z)) <= True
shallower(leaf, z) <= True
shallower(node(a, leaf, leaf), s(z)) <= True
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
False <= le_nat(z, z)
shallower(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= max(s(s(z)), s(z), s(z)) /\ shallower(node(a, leaf, node(a, leaf, leaf)), s(s(z)))
shallower(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= max(s(s(z)), z, s(z)) /\ shallower(node(a, leaf, node(a, leaf, leaf)), s(s(z)))
False <= shallower(node(a, leaf, leaf), z)
False <= shallower(node(a, leaf, node(a, leaf, leaf)), s(z))
False <= shallower(node(a, node(a, leaf, leaf), leaf), s(z))
}

Current best model:
|_
name: None

height ->
[
height : <etree * nat>
{
  
}
]


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  _r_1(leaf) <= True
  shallower(leaf, s(x_1_0)) <= True
  shallower(leaf, z) <= True
  shallower(node(x_0_0, x_0_1, x_0_2), s(x_1_0)) <= _r_1(x_0_1) /\ _r_1(x_0_2)
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


;
taller ->
[
taller : <etree * nat>
{
  
}
]



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




Answer of teacher:

le_nat(n, m) \/ max(n, m, n) <= True  :
No: ()

le_nat(z, s(nn2)) <= True  :
No: ()

shallower(leaf, n) <= True  :
No: ()

height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv)  :
No: ()

height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv)  :
No: ()

max(n, m, m) <= le_nat(n, m)  :
No: ()

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

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

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

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

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

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

shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2)  :
Yes: {
_zv -> s(_rpgnw_0)  ;  n1 -> s(_spgnw_0)  ;  n2 -> z  ;  t1 -> node(_upgnw_0, leaf, leaf)  ;  t2 -> leaf
}

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
Yes: {
m -> s(_xrgnw_0)  ;  t1 -> node(_yrgnw_0, leaf, leaf)  ;  t2 -> leaf
}

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

False <= shallower(node(e, t1, t2), z)  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


-------------------------------------------
Step 7, which took 0.021430 s (model generation: 0.020748,  model checking: 0.000682):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv) -> 0
height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
False <= shallower(node(e, t1, t2), z) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

Accumulated learning constraints:
{
le_nat(s(z), s(s(z))) <= True
le_nat(z, s(z)) <= True
max(s(z), s(z), s(z)) <= True
max(s(z), z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
shallower(leaf, s(z)) <= True
shallower(leaf, z) <= True
shallower(node(a, leaf, leaf), s(z)) <= True
shallower(node(a, node(a, leaf, leaf), leaf), s(s(z))) <= True
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
False <= le_nat(z, z)
shallower(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= max(s(s(z)), s(z), s(z)) /\ shallower(node(a, leaf, node(a, leaf, leaf)), s(s(z)))
shallower(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= max(s(s(z)), z, s(z)) /\ shallower(node(a, leaf, node(a, leaf, leaf)), s(s(z)))
False <= shallower(node(a, leaf, leaf), z)
False <= shallower(node(a, leaf, node(a, leaf, leaf)), s(z))
False <= shallower(node(a, node(a, leaf, leaf), leaf), s(z))
}

Current best model:
|_
name: None

height ->
[
height : <etree * nat>
{
  
}
]


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  _r_1(leaf, s(x_1_0)) <= True
  _r_1(leaf, z) <= True
  _r_1(node(x_0_0, x_0_1, x_0_2), s(x_1_0)) <= True
  shallower(leaf, s(x_1_0)) <= True
  shallower(leaf, z) <= True
  shallower(node(x_0_0, x_0_1, x_0_2), s(x_1_0)) <= _r_1(x_0_1, x_1_0) /\ _r_1(x_0_2, x_1_0)
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


;
taller ->
[
taller : <etree * nat>
{
  
}
]



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




Answer of teacher:

le_nat(n, m) \/ max(n, m, n) <= True  :
No: ()

le_nat(z, s(nn2)) <= True  :
No: ()

shallower(leaf, n) <= True  :
No: ()

height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv)  :
No: ()

height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv)  :
No: ()

max(n, m, m) <= le_nat(n, m)  :
No: ()

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

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

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

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

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

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

shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2)  :
No: ()

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
No: ()

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
Yes: {
m -> s(z)  ;  t1 -> leaf  ;  t2 -> node(_mygnw_0, _mygnw_1, node(_kzgnw_0, _kzgnw_1, _kzgnw_2))
}

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
Yes: {
m -> s(z)  ;  t1 -> node(_zygnw_0, _zygnw_1, node(_qzgnw_0, _qzgnw_1, _qzgnw_2))  ;  t2 -> node(_ozgnw_0, _ozgnw_1, _ozgnw_2)
}

False <= shallower(node(e, t1, t2), z)  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


-------------------------------------------
Step 8, which took 0.022734 s (model generation: 0.021855,  model checking: 0.000879):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv) -> 0
height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
False <= shallower(node(e, t1, t2), z) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

Accumulated learning constraints:
{
le_nat(s(z), s(s(z))) <= True
le_nat(z, s(z)) <= True
max(s(z), s(z), s(z)) <= True
max(s(z), z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
shallower(leaf, s(z)) <= True
shallower(leaf, z) <= True
shallower(node(a, leaf, leaf), s(z)) <= True
shallower(node(a, node(a, leaf, leaf), leaf), s(s(z))) <= True
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
False <= le_nat(z, z)
shallower(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= max(s(s(z)), s(z), s(z)) /\ shallower(node(a, leaf, node(a, leaf, leaf)), s(s(z)))
shallower(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= max(s(s(z)), z, s(z)) /\ shallower(node(a, leaf, node(a, leaf, leaf)), s(s(z)))
False <= shallower(node(a, leaf, leaf), z)
False <= shallower(node(a, leaf, node(a, leaf, leaf)), s(z))
False <= shallower(node(a, leaf, node(a, leaf, node(a, leaf, leaf))), s(s(z)))
False <= shallower(node(a, node(a, leaf, leaf), leaf), s(z))
False <= shallower(node(a, node(a, leaf, node(a, leaf, leaf)), node(a, leaf, leaf)), s(s(z)))
}

Current best model:
|_
name: None

height ->
[
height : <etree * nat>
{
  
}
]


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  _r_1(leaf) <= True
  shallower(leaf, s(x_1_0)) <= True
  shallower(leaf, z) <= True
  shallower(node(x_0_0, x_0_1, x_0_2), s(x_1_0)) <= _r_1(x_0_2) /\ shallower(x_0_1, x_1_0)
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


;
taller ->
[
taller : <etree * nat>
{
  
}
]



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




Answer of teacher:

le_nat(n, m) \/ max(n, m, n) <= True  :
No: ()

le_nat(z, s(nn2)) <= True  :
No: ()

shallower(leaf, n) <= True  :
No: ()

height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv)  :
No: ()

height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv)  :
No: ()

max(n, m, m) <= le_nat(n, m)  :
No: ()

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

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

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

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

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

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

shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2)  :
Yes: {
_zv -> s(_tchnw_0)  ;  n1 -> z  ;  n2 -> s(s(z))  ;  t1 -> leaf  ;  t2 -> node(_xchnw_0, node(_bghnw_0, leaf, leaf), leaf)
}

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
Yes: {
m -> s(s(z))  ;  t1 -> leaf  ;  t2 -> node(_vdhnw_0, node(_bghnw_0, leaf, leaf), leaf)
}

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

False <= shallower(node(e, t1, t2), z)  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


-------------------------------------------
Step 9, which took 0.140603 s (model generation: 0.031153,  model checking: 0.109450):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv) -> 0
height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
False <= shallower(node(e, t1, t2), z) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

Accumulated learning constraints:
{
le_nat(s(z), s(s(z))) <= True
le_nat(z, s(z)) <= True
max(s(z), s(z), s(z)) <= True
max(s(z), z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
shallower(leaf, s(z)) <= True
shallower(leaf, z) <= True
shallower(node(a, leaf, leaf), s(z)) <= True
shallower(node(a, node(a, leaf, leaf), leaf), s(s(z))) <= True
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
False <= le_nat(z, z)
shallower(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= max(s(s(z)), s(z), s(z)) /\ shallower(node(a, leaf, node(a, leaf, leaf)), s(s(z)))
shallower(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= max(s(s(z)), z, s(z)) /\ shallower(node(a, leaf, node(a, leaf, leaf)), s(s(z)))
shallower(node(a, leaf, node(a, node(a, leaf, leaf), leaf)), s(s(z))) <= max(z, s(s(z)), s(z))
shallower(node(a, leaf, node(a, node(a, leaf, leaf), leaf)), s(s(s(z)))) <= shallower(leaf, s(s(z)))
False <= shallower(node(a, leaf, leaf), z)
False <= shallower(node(a, leaf, node(a, leaf, leaf)), s(z))
False <= shallower(node(a, leaf, node(a, leaf, node(a, leaf, leaf))), s(s(z)))
False <= shallower(node(a, node(a, leaf, leaf), leaf), s(z))
False <= shallower(node(a, node(a, leaf, node(a, leaf, leaf)), node(a, leaf, leaf)), s(s(z)))
}

Current best model:
|_
name: None

height ->
[
height : <etree * nat>
{
  
}
]


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  shallower(leaf, s(x_1_0)) <= True
  shallower(leaf, z) <= True
  shallower(node(x_0_0, x_0_1, x_0_2), s(x_1_0)) <= shallower(x_0_1, x_1_0) /\ shallower(x_0_2, x_1_0)
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


;
taller ->
[
taller : <etree * nat>
{
  
}
]



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




Answer of teacher:

le_nat(n, m) \/ max(n, m, n) <= True  :
Yes: {
m -> z  ;  n -> s(s(_pmhnw_0))
}

le_nat(z, s(nn2)) <= True  :
No: ()

shallower(leaf, n) <= True  :
No: ()

height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv)  :
No: ()

height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv)  :
No: ()

max(n, m, m) <= le_nat(n, m)  :
Yes: {
m -> s(s(_pmhnw_0))  ;  n -> z
}

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

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

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

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

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

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

shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2)  :
Yes: {
_zv -> s(z)  ;  n1 -> s(z)  ;  n2 -> s(s(z))  ;  t1 -> leaf  ;  t2 -> node(_xhhnw_0, leaf, node(_zohnw_0, leaf, leaf))
}

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
No: ()

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

False <= shallower(node(e, t1, t2), z)  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


-------------------------------------------
Step 10, which took 0.119284 s (model generation: 0.034303,  model checking: 0.084981):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv) -> 0
height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
False <= shallower(node(e, t1, t2), z) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

Accumulated learning constraints:
{
le_nat(s(s(z)), z) \/ max(s(s(z)), z, s(s(z))) <= True
le_nat(s(z), s(s(z))) <= True
le_nat(z, s(z)) <= True
max(s(z), s(z), s(z)) <= True
max(s(z), z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
shallower(leaf, s(z)) <= True
shallower(leaf, z) <= True
shallower(node(a, leaf, leaf), s(z)) <= True
shallower(node(a, node(a, leaf, leaf), leaf), s(s(z))) <= True
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
max(z, s(s(z)), s(s(z))) <= le_nat(z, s(s(z)))
False <= le_nat(z, z)
shallower(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= max(s(s(z)), s(z), s(z)) /\ shallower(node(a, leaf, node(a, leaf, leaf)), s(s(z)))
shallower(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= max(s(s(z)), z, s(z)) /\ shallower(node(a, leaf, node(a, leaf, leaf)), s(s(z)))
False <= max(s(z), s(s(z)), s(z)) /\ shallower(node(a, leaf, node(a, leaf, leaf)), s(s(z)))
shallower(node(a, leaf, node(a, node(a, leaf, leaf), leaf)), s(s(z))) <= max(z, s(s(z)), s(z))
shallower(node(a, leaf, node(a, node(a, leaf, leaf), leaf)), s(s(s(z)))) <= shallower(leaf, s(s(z)))
False <= shallower(node(a, leaf, leaf), z)
False <= shallower(node(a, leaf, node(a, leaf, leaf)), s(z))
False <= shallower(node(a, leaf, node(a, leaf, node(a, leaf, leaf))), s(s(z)))
False <= shallower(node(a, node(a, leaf, leaf), leaf), s(z))
False <= shallower(node(a, node(a, leaf, node(a, leaf, leaf)), node(a, leaf, leaf)), s(s(z)))
}

Current best model:
|_
name: None

height ->
[
height : <etree * nat>
{
  
}
]


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  shallower(leaf, s(x_1_0)) <= True
  shallower(leaf, z) <= True
  shallower(node(x_0_0, x_0_1, x_0_2), s(x_1_0)) <= shallower(x_0_1, x_1_0) /\ shallower(x_0_2, x_1_0)
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


;
taller ->
[
taller : <etree * nat>
{
  
}
]



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




Answer of teacher:

le_nat(n, m) \/ max(n, m, n) <= True  :
Yes: {
m -> s(z)  ;  n -> s(s(_adlnw_0))
}

le_nat(z, s(nn2)) <= True  :
No: ()

shallower(leaf, n) <= True  :
No: ()

height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv)  :
No: ()

height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv)  :
No: ()

max(n, m, m) <= le_nat(n, m)  :
Yes: {
m -> s(s(_ddlnw_0))  ;  n -> s(z)
}

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

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

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

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

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

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

shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2)  :
Yes: {
_zv -> s(z)  ;  n1 -> s(s(_ujlnw_0))  ;  n2 -> s(s(z))  ;  t1 -> leaf  ;  t2 -> node(_dyknw_0, leaf, node(_wjlnw_0, leaf, leaf))
}

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
No: ()

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

False <= shallower(node(e, t1, t2), z)  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


-------------------------------------------
Step 11, which took 0.129642 s (model generation: 0.039169,  model checking: 0.090473):

Clauses:
{
le_nat(n, m) \/ max(n, m, n) <= True -> 0
le_nat(z, s(nn2)) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv) -> 0
height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv) -> 0
max(n, m, m) <= le_nat(n, m) -> 0
le_nat(s(nn1), s(nn2)) <= le_nat(nn1, nn2) -> 0
le_nat(nn1, nn2) <= le_nat(s(nn1), s(nn2)) -> 0
False <= le_nat(s(nn1), z) -> 0
False <= le_nat(z, z) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2) -> 0
shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m) -> 0
shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m)) -> 0
shallower(t1, m) <= shallower(node(e, t1, t2), s(m)) -> 0
False <= shallower(node(e, t1, t2), z) -> 0
subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2) -> 0
subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) -> 0
taller(node(e, t1, t2), s(m)) <= taller(t1, m) -> 0
taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m) -> 0
taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m)) -> 0
}

Accumulated learning constraints:
{
le_nat(s(s(z)), s(z)) \/ max(s(s(z)), s(z), s(s(z))) <= True
le_nat(s(s(z)), z) \/ max(s(s(z)), z, s(s(z))) <= True
le_nat(s(z), s(s(z))) <= True
le_nat(z, s(z)) <= True
max(s(z), s(s(z)), s(s(z))) <= True
max(s(z), s(z), s(z)) <= True
max(s(z), z, s(z)) <= True
max(z, s(z), s(z)) <= True
max(z, z, z) <= True
shallower(leaf, s(z)) <= True
shallower(leaf, z) <= True
shallower(node(a, leaf, leaf), s(z)) <= True
shallower(node(a, node(a, leaf, leaf), leaf), s(s(z))) <= True
False <= le_nat(s(z), s(z))
False <= le_nat(s(z), z)
max(z, s(s(z)), s(s(z))) <= le_nat(z, s(s(z)))
False <= le_nat(z, z)
False <= max(s(s(z)), s(s(z)), s(z)) /\ shallower(leaf, s(s(z))) /\ shallower(node(a, leaf, node(a, leaf, leaf)), s(s(z)))
shallower(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= max(s(s(z)), s(z), s(z)) /\ shallower(node(a, leaf, node(a, leaf, leaf)), s(s(z)))
shallower(node(a, node(a, leaf, node(a, leaf, leaf)), leaf), s(s(z))) <= max(s(s(z)), z, s(z)) /\ shallower(node(a, leaf, node(a, leaf, leaf)), s(s(z)))
False <= max(s(z), s(s(z)), s(z)) /\ shallower(node(a, leaf, node(a, leaf, leaf)), s(s(z)))
shallower(node(a, leaf, node(a, node(a, leaf, leaf), leaf)), s(s(z))) <= max(z, s(s(z)), s(z))
shallower(node(a, leaf, node(a, node(a, leaf, leaf), leaf)), s(s(s(z)))) <= shallower(leaf, s(s(z)))
False <= shallower(node(a, leaf, leaf), z)
False <= shallower(node(a, leaf, node(a, leaf, leaf)), s(z))
False <= shallower(node(a, leaf, node(a, leaf, node(a, leaf, leaf))), s(s(z)))
False <= shallower(node(a, node(a, leaf, leaf), leaf), s(z))
False <= shallower(node(a, node(a, leaf, node(a, leaf, leaf)), node(a, leaf, leaf)), s(s(z)))
}

Current best model:
|_
name: None

height ->
[
height : <etree * nat>
{
  
}
]


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  shallower(leaf, s(x_1_0)) <= True
  shallower(leaf, z) <= True
  shallower(node(x_0_0, x_0_1, x_0_2), s(x_1_0)) <= shallower(x_0_1, x_1_0) /\ shallower(x_0_2, x_1_0)
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


;
taller ->
[
taller : <etree * nat>
{
  
}
]



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




Answer of teacher:

le_nat(n, m) \/ max(n, m, n) <= True  :
No: ()

le_nat(z, s(nn2)) <= True  :
No: ()

shallower(leaf, n) <= True  :
No: ()

height(node(e, t1, t2), s(_vv)) \/ le_nat(_sv, _tv) <= height(t1, _sv) /\ height(t1, _vv) /\ height(t2, _tv)  :
No: ()

height(node(e, t1, t2), s(_uv)) <= height(t1, _sv) /\ height(t2, _tv) /\ height(t2, _uv) /\ le_nat(_sv, _tv)  :
No: ()

max(n, m, m) <= le_nat(n, m)  :
No: ()

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

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

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

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

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

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

shallower(node(e, t1, t2), s(_zv)) <= max(n1, n2, _zv) /\ shallower(t1, n1) /\ shallower(t2, n2)  :
Yes: {
_zv -> s(s(z))  ;  n1 -> s(s(s(z)))  ;  n2 -> z  ;  t1 -> node(_tgonw_0, leaf, node(_ylonw_0, leaf, node(_foonw_0, leaf, leaf)))  ;  t2 -> leaf
}

shallower(node(e, t1, t2), s(m)) <= shallower(t1, m) /\ shallower(t2, m)  :
No: ()

shallower(t2, m) <= shallower(t1, m) /\ shallower(node(e, t1, t2), s(m))  :
No: ()

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
No: ()

False <= shallower(node(e, t1, t2), z)  :
No: ()

subtree(node(eb, ta1, ta2), node(eb, tb1, tb2)) <= subtree(ta1, tb1) /\ subtree(ta2, tb2)  :
No: ()

subtree(ta2, tb2) <= subtree(ta1, tb1) /\ subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

subtree(ta1, tb1) <= subtree(node(eb, ta1, ta2), node(eb, tb1, tb2))  :
No: ()

taller(node(e, t1, t2), s(m)) <= taller(t1, m)  :
No: ()

taller(t1, m) \/ taller(node(e, t1, t2), s(m)) <= taller(t2, m)  :
No: ()

taller(t1, m) \/ taller(t2, m) <= taller(node(e, t1, t2), s(m))  :
No: ()


Total time: 0.915764
Learner time: 0.221229
Teacher time: 0.517898
Reasons for stopping: Yes: |_
name: None

height ->
[
height : <etree * nat>
{
  
}
]


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


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


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


;
shallower ->
[
shallower : <etree * nat>
{
  shallower(leaf, s(x_1_0)) <= True
  shallower(leaf, z) <= True
  shallower(node(x_0_0, x_0_1, x_0_2), s(x_1_0)) <= shallower(x_0_1, x_1_0) /\ shallower(x_0_2, x_1_0)
}
]


;
subtree ->
[
subtree : <etree * etree>
{
  
}
]


;
taller ->
[
taller : <etree * nat>
{
  
}
]



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