Solving ../../benchmarks/smtlib/true/tree_shallow_leq.smt2...

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



Learning problem is:

env: {
elt -> {a, b}  ;  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)
}
)
(max, F:
{
leq_nat(n, m) \/ max(n, m, n) <= True
max(n, m, m) <= leq_nat(n, m)
}
eq_nat(_u, _v) <= max(_s, _t, _u) /\ max(_s, _t, _v)
)
(height, F:
{
height(leaf, z) <= True
height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x)
height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x)
}
eq_nat(_ba, _ca) <= height(_aa, _ba) /\ height(_aa, _ca)
)
(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)
}
)
(height_rel, P:
{
height_rel(leaf, z) <= True
shallower(t2, nn) <= height_rel(t1, nn) /\ height_rel(node(e, t1, t2), s(nn))
height_rel(node(e, t1, t2), s(nn)) <= height_rel(t1, nn) /\ shallower(t2, nn)
height_rel(t1, nn) \/ shallower(t1, nn) <= height_rel(t2, nn) /\ height_rel(node(e, t1, t2), s(nn))
height_rel(t1, nn) \/ height_rel(node(e, t1, t2), s(nn)) <= height_rel(t2, nn) /\ shallower(t1, nn)
False <= height_rel(leaf, s(nn))
height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn))
False <= height_rel(node(e, t1, t2), z)
}
)
}

properties:
{
shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m)
}


over-approximation: {height, height_rel, max}
under-approximation: {height, height_rel}

Clause system for inference is:

{
leq_nat(n, m) \/ max(n, m, n) <= True -> 0
leq_nat(z, n2) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x) -> 0
height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x) -> 0
height_rel(node(e, t1, t2), s(nn)) <= height_rel(t1, nn) /\ shallower(t2, nn) -> 0
height_rel(t1, nn) \/ shallower(t1, nn) <= height_rel(t2, nn) /\ height_rel(node(e, t1, t2), s(nn)) -> 0
height_rel(t1, nn) \/ height_rel(node(e, t1, t2), s(nn)) <= height_rel(t2, nn) /\ shallower(t1, nn) -> 0
height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn)) -> 0
max(n, m, m) <= leq_nat(n, m) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
False <= leq_nat(s(nn1), z) -> 0
shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m) -> 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
}


Solving took 0.590314 seconds.
Yes: |_
name: None

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


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


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


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



--
Equality automata are defined for: {elt, etree, nat}
_|
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.006729 s (model generation: 0.006117,  model checking: 0.000612):

Clauses:
{
leq_nat(n, m) \/ max(n, m, n) <= True -> 0
leq_nat(z, n2) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x) -> 0
height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x) -> 0
height_rel(node(e, t1, t2), s(nn)) <= height_rel(t1, nn) /\ shallower(t2, nn) -> 0
height_rel(t1, nn) \/ shallower(t1, nn) <= height_rel(t2, nn) /\ height_rel(node(e, t1, t2), s(nn)) -> 0
height_rel(t1, nn) \/ height_rel(node(e, t1, t2), s(nn)) <= height_rel(t2, nn) /\ shallower(t1, nn) -> 0
height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn)) -> 0
max(n, m, m) <= leq_nat(n, m) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
False <= leq_nat(s(nn1), z) -> 0
shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m) -> 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
}

Accumulated learning constraints:
{

}

Current best model:
|_
name: None

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


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


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


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


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



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




Answer of teacher:

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

leq_nat(z, n2) <= True  :
Yes: {
n2 -> z
}

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

height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x)  :
No: ()

height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x)  :
No: ()

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

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

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

height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn))  :
No: ()

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

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

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

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

shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m)  :
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: ()


-------------------------------------------
Step 1, which took 0.006488 s (model generation: 0.006345,  model checking: 0.000143):

Clauses:
{
leq_nat(n, m) \/ max(n, m, n) <= True -> 0
leq_nat(z, n2) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x) -> 0
height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x) -> 0
height_rel(node(e, t1, t2), s(nn)) <= height_rel(t1, nn) /\ shallower(t2, nn) -> 0
height_rel(t1, nn) \/ shallower(t1, nn) <= height_rel(t2, nn) /\ height_rel(node(e, t1, t2), s(nn)) -> 0
height_rel(t1, nn) \/ height_rel(node(e, t1, t2), s(nn)) <= height_rel(t2, nn) /\ shallower(t1, nn) -> 0
height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn)) -> 0
max(n, m, m) <= leq_nat(n, m) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
False <= leq_nat(s(nn1), z) -> 0
shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m) -> 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
}

Accumulated learning constraints:
{
leq_nat(z, z) <= True
shallower(leaf, z) <= True
}

Current best model:
|_
name: None

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


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


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


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


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



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




Answer of teacher:

leq_nat(n, m) \/ max(n, m, n) <= True  :
Yes: {
m -> z  ;  n -> s(_vekmw_0)
}

leq_nat(z, n2) <= True  :
Yes: {
n2 -> s(_yekmw_0)
}

shallower(leaf, n) <= True  :
Yes: {
n -> s(_zekmw_0)
}

height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x)  :
No: ()

height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x)  :
No: ()

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

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

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

height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn))  :
No: ()

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

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

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

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

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

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: ()


-------------------------------------------
Step 2, which took 0.009165 s (model generation: 0.008321,  model checking: 0.000844):

Clauses:
{
leq_nat(n, m) \/ max(n, m, n) <= True -> 0
leq_nat(z, n2) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x) -> 0
height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x) -> 0
height_rel(node(e, t1, t2), s(nn)) <= height_rel(t1, nn) /\ shallower(t2, nn) -> 0
height_rel(t1, nn) \/ shallower(t1, nn) <= height_rel(t2, nn) /\ height_rel(node(e, t1, t2), s(nn)) -> 0
height_rel(t1, nn) \/ height_rel(node(e, t1, t2), s(nn)) <= height_rel(t2, nn) /\ shallower(t1, nn) -> 0
height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn)) -> 0
max(n, m, m) <= leq_nat(n, m) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
False <= leq_nat(s(nn1), z) -> 0
shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m) -> 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
}

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

Current best model:
|_
name: None

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


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


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


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



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




Answer of teacher:

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

leq_nat(z, n2) <= True  :
No: ()

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

height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x)  :
No: ()

height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x)  :
No: ()

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

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

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

height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn))  :
No: ()

max(n, m, m) <= leq_nat(n, m)  :
Yes: {
m -> z  ;  n -> s(_kfkmw_0)
}

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

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

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

}

shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m)  :
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(_pfkmw_0, _pfkmw_1, _pfkmw_2)
}

shallower(t1, m) <= shallower(node(e, t1, t2), s(m))  :
Yes: {
m -> z  ;  t1 -> node(_rfkmw_0, _rfkmw_1, _rfkmw_2)
}

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


-------------------------------------------
Step 3, which took 0.008799 s (model generation: 0.008604,  model checking: 0.000195):

Clauses:
{
leq_nat(n, m) \/ max(n, m, n) <= True -> 0
leq_nat(z, n2) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x) -> 0
height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x) -> 0
height_rel(node(e, t1, t2), s(nn)) <= height_rel(t1, nn) /\ shallower(t2, nn) -> 0
height_rel(t1, nn) \/ shallower(t1, nn) <= height_rel(t2, nn) /\ height_rel(node(e, t1, t2), s(nn)) -> 0
height_rel(t1, nn) \/ height_rel(node(e, t1, t2), s(nn)) <= height_rel(t2, nn) /\ shallower(t1, nn) -> 0
height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn)) -> 0
max(n, m, m) <= leq_nat(n, m) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
False <= leq_nat(s(nn1), z) -> 0
shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m) -> 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
}

Accumulated learning constraints:
{
leq_nat(s(z), s(z)) <= True
leq_nat(z, s(z)) <= True
leq_nat(z, z) <= True
max(s(z), 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 <= leq_nat(s(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>
{
  
}
]


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


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


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



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




Answer of teacher:

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

leq_nat(z, n2) <= True  :
No: ()

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

height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x)  :
No: ()

height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x)  :
No: ()

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

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

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

height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn))  :
No: ()

max(n, m, m) <= leq_nat(n, m)  :
Yes: {
m -> s(_ufkmw_0)  ;  n -> z
}

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

leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2))  :
Yes: {
nn1 -> s(_wfkmw_0)  ;  nn2 -> z
}

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

shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m)  :
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: {

}


-------------------------------------------
Step 4, which took 0.084641 s (model generation: 0.010393,  model checking: 0.074248):

Clauses:
{
leq_nat(n, m) \/ max(n, m, n) <= True -> 0
leq_nat(z, n2) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x) -> 0
height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x) -> 0
height_rel(node(e, t1, t2), s(nn)) <= height_rel(t1, nn) /\ shallower(t2, nn) -> 0
height_rel(t1, nn) \/ shallower(t1, nn) <= height_rel(t2, nn) /\ height_rel(node(e, t1, t2), s(nn)) -> 0
height_rel(t1, nn) \/ height_rel(node(e, t1, t2), s(nn)) <= height_rel(t2, nn) /\ shallower(t1, nn) -> 0
height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn)) -> 0
max(n, m, m) <= leq_nat(n, m) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
False <= leq_nat(s(nn1), z) -> 0
shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m) -> 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
}

Accumulated learning constraints:
{
leq_nat(s(z), s(z)) <= True
leq_nat(z, s(z)) <= True
leq_nat(z, 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 <= leq_nat(s(s(z)), s(z))
False <= leq_nat(s(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>
{
  
}
]


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


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


;
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)) <= shallower(x_0_1, x_1_0) /\ shallower(x_0_2, x_1_0)
}
]



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




Answer of teacher:

leq_nat(n, m) \/ max(n, m, n) <= True  :
Yes: {
m -> s(z)  ;  n -> s(s(_lkkmw_0))
}

leq_nat(z, n2) <= True  :
No: ()

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

height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x)  :
No: ()

height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x)  :
No: ()

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

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

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

height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn))  :
No: ()

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

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

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

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

shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m)  :
Yes: {
_da -> s(z)  ;  m -> z  ;  n -> s(s(z))  ;  t1 -> node(_zgkmw_0, leaf, node(_tmkmw_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: ()


-------------------------------------------
Step 5, which took 0.151287 s (model generation: 0.011880,  model checking: 0.139407):

Clauses:
{
leq_nat(n, m) \/ max(n, m, n) <= True -> 0
leq_nat(z, n2) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x) -> 0
height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x) -> 0
height_rel(node(e, t1, t2), s(nn)) <= height_rel(t1, nn) /\ shallower(t2, nn) -> 0
height_rel(t1, nn) \/ shallower(t1, nn) <= height_rel(t2, nn) /\ height_rel(node(e, t1, t2), s(nn)) -> 0
height_rel(t1, nn) \/ height_rel(node(e, t1, t2), s(nn)) <= height_rel(t2, nn) /\ shallower(t1, nn) -> 0
height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn)) -> 0
max(n, m, m) <= leq_nat(n, m) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
False <= leq_nat(s(nn1), z) -> 0
shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m) -> 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
}

Accumulated learning constraints:
{
leq_nat(s(z), s(z)) <= True
leq_nat(z, s(z)) <= True
leq_nat(z, z) <= True
max(s(s(z)), 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
False <= leq_nat(s(s(z)), s(z))
False <= leq_nat(s(z), 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>
{
  
}
]


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


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


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



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




Answer of teacher:

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

leq_nat(z, n2) <= True  :
No: ()

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

height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x)  :
No: ()

height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x)  :
No: ()

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

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

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

height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn))  :
No: ()

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

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

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

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

shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m)  :
Yes: {
_da -> s(z)  ;  m -> s(_zdnmw_0)  ;  n -> s(s(z))  ;  t1 -> node(_benmw_0, leaf, node(_qknmw_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: ()


-------------------------------------------
Step 6, which took 0.112132 s (model generation: 0.012627,  model checking: 0.099505):

Clauses:
{
leq_nat(n, m) \/ max(n, m, n) <= True -> 0
leq_nat(z, n2) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x) -> 0
height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x) -> 0
height_rel(node(e, t1, t2), s(nn)) <= height_rel(t1, nn) /\ shallower(t2, nn) -> 0
height_rel(t1, nn) \/ shallower(t1, nn) <= height_rel(t2, nn) /\ height_rel(node(e, t1, t2), s(nn)) -> 0
height_rel(t1, nn) \/ height_rel(node(e, t1, t2), s(nn)) <= height_rel(t2, nn) /\ shallower(t1, nn) -> 0
height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn)) -> 0
max(n, m, m) <= leq_nat(n, m) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
False <= leq_nat(s(nn1), z) -> 0
shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m) -> 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
}

Accumulated learning constraints:
{
leq_nat(s(z), s(z)) <= True
leq_nat(z, s(z)) <= True
leq_nat(z, z) <= True
max(s(s(z)), 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
False <= leq_nat(s(s(z)), s(z))
False <= leq_nat(s(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>
{
  
}
]


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


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


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



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




Answer of teacher:

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

leq_nat(z, n2) <= True  :
No: ()

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

height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x)  :
No: ()

height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x)  :
No: ()

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

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

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

height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn))  :
No: ()

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

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

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

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

shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m)  :
Yes: {
_da -> s(z)  ;  m -> s(s(z))  ;  n -> z  ;  t1 -> leaf  ;  t2 -> node(_ojqmw_0, leaf, node(_loqmw_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: ()


-------------------------------------------
Step 7, which took 0.093085 s (model generation: 0.012805,  model checking: 0.080280):

Clauses:
{
leq_nat(n, m) \/ max(n, m, n) <= True -> 0
leq_nat(z, n2) <= True -> 0
shallower(leaf, n) <= True -> 0
height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x) -> 0
height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x) -> 0
height_rel(node(e, t1, t2), s(nn)) <= height_rel(t1, nn) /\ shallower(t2, nn) -> 0
height_rel(t1, nn) \/ shallower(t1, nn) <= height_rel(t2, nn) /\ height_rel(node(e, t1, t2), s(nn)) -> 0
height_rel(t1, nn) \/ height_rel(node(e, t1, t2), s(nn)) <= height_rel(t2, nn) /\ shallower(t1, nn) -> 0
height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn)) -> 0
max(n, m, m) <= leq_nat(n, m) -> 0
leq_nat(s(nn1), s(nn2)) <= leq_nat(nn1, nn2) -> 0
leq_nat(nn1, nn2) <= leq_nat(s(nn1), s(nn2)) -> 0
False <= leq_nat(s(nn1), z) -> 0
shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m) -> 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
}

Accumulated learning constraints:
{
leq_nat(s(z), s(z)) <= True
leq_nat(z, s(z)) <= True
leq_nat(z, z) <= True
max(s(s(z)), 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
False <= leq_nat(s(s(z)), s(z))
False <= leq_nat(s(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, leaf, node(a, leaf, leaf))), s(s(z))) <= max(z, s(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>
{
  
}
]


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


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


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



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




Answer of teacher:

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

leq_nat(z, n2) <= True  :
No: ()

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

height(node(e, t1, t2), s(_z)) \/ leq_nat(_w, _x) <= height(t1, _w) /\ height(t1, _z) /\ height(t2, _x)  :
No: ()

height(node(e, t1, t2), s(_y)) <= height(t1, _w) /\ height(t2, _x) /\ height(t2, _y) /\ leq_nat(_w, _x)  :
No: ()

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

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

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

height_rel(t1, nn) \/ height_rel(t2, nn) <= height_rel(node(e, t1, t2), s(nn))  :
No: ()

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

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

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

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

shallower(node(e, t1, t2), s(_da)) <= max(n, m, _da) /\ shallower(t1, n) /\ shallower(t2, m)  :
Yes: {
_da -> s(z)  ;  m -> s(s(z))  ;  n -> s(z)  ;  t1 -> leaf  ;  t2 -> node(_lvsmw_0, leaf, node(_yitmw_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: ()


Total time: 0.590314
Learner time: 0.077092
Teacher time: 0.395234
Reasons for stopping: Yes: |_
name: None

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


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


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


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



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