Inference procedure has parameters:
Ice fuel: 200
Timeout: 60s
Convolution: right


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(max, F:
{() -> max([s(u), z, s(u)])
() -> max([z, y, y])
(max([u, x2, _dt])) -> max([s(u), s(x2), s(_dt)])}
(max([_et, _ft, _gt]) /\ max([_et, _ft, _ht])) -> eq_nat([_gt, _ht])
)
}

properties:
{(max([a, b, _it]) /\ max([b, a, _jt])) -> eq_nat([_it, _jt])}


over-approximation: {max}
under-approximation: {}

Clause system for inference is:

{
() -> max([s(u), z, s(u)]) -> 0
() -> max([z, y, y]) -> 0
(max([a, b, _it]) /\ max([b, a, _jt])) -> eq_nat([_it, _jt]) -> 0
(max([u, x2, _dt])) -> max([s(u), s(x2), s(_dt)]) -> 0
}


Solving took 0.024571 seconds.
Proved
Model:
|_
{
max -> 
{{{
Q={q_gen_3726, q_gen_3728},
Q_f={q_gen_3726},
Delta=
{
<s, s>(q_gen_3728) -> q_gen_3728
<z, z>() -> q_gen_3728
<s, s, s>(q_gen_3726) -> q_gen_3726
<s, z, s>(q_gen_3728) -> q_gen_3726
<z, s, s>(q_gen_3728) -> q_gen_3726
<z, z, z>() -> q_gen_3726
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.004270 s (model generation: 0.004103,  model checking: 0.000167):

Model:
|_
{
max -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> max([s(u), z, s(u)]) -> 0
() -> max([z, y, y]) -> 3
(max([a, b, _it]) /\ max([b, a, _jt])) -> eq_nat([_it, _jt]) -> 1
(max([u, x2, _dt])) -> max([s(u), s(x2), s(_dt)]) -> 1
}
Sat witness: Found: (() -> max([z, y, y]), {
y -> z
})

-------------------------------------------
Step 1, which took 0.004711 s (model generation: 0.004445,  model checking: 0.000266):

Model:
|_
{
max -> 
{{{
Q={q_gen_3726},
Q_f={q_gen_3726},
Delta=
{
<z, z, z>() -> q_gen_3726
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> max([s(u), z, s(u)]) -> 3
() -> max([z, y, y]) -> 3
(max([a, b, _it]) /\ max([b, a, _jt])) -> eq_nat([_it, _jt]) -> 1
(max([u, x2, _dt])) -> max([s(u), s(x2), s(_dt)]) -> 1
}
Sat witness: Found: (() -> max([s(u), z, s(u)]), {
u -> z
})

-------------------------------------------
Step 2, which took 0.004543 s (model generation: 0.004138,  model checking: 0.000405):

Model:
|_
{
max -> 
{{{
Q={q_gen_3726, q_gen_3728},
Q_f={q_gen_3726},
Delta=
{
<z, z>() -> q_gen_3728
<s, z, s>(q_gen_3728) -> q_gen_3726
<z, z, z>() -> q_gen_3726
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> max([s(u), z, s(u)]) -> 3
() -> max([z, y, y]) -> 3
(max([a, b, _it]) /\ max([b, a, _jt])) -> eq_nat([_it, _jt]) -> 1
(max([u, x2, _dt])) -> max([s(u), s(x2), s(_dt)]) -> 4
}
Sat witness: Found: ((max([u, x2, _dt])) -> max([s(u), s(x2), s(_dt)]), {
_dt -> z  ;  u -> z  ;  x2 -> z
})

-------------------------------------------
Step 3, which took 0.005792 s (model generation: 0.004300,  model checking: 0.001492):

Model:
|_
{
max -> 
{{{
Q={q_gen_3726, q_gen_3728},
Q_f={q_gen_3726},
Delta=
{
<z, z>() -> q_gen_3728
<s, s, s>(q_gen_3726) -> q_gen_3726
<s, z, s>(q_gen_3728) -> q_gen_3726
<z, z, z>() -> q_gen_3726
}

Datatype: <nat, nat, nat>
Convolution form: right
}}}

}
--
Equality automata are defined for: {eq_nat}
_|

Teacher's answer:
New clause system:
{
() -> max([s(u), z, s(u)]) -> 3
() -> max([z, y, y]) -> 6
(max([a, b, _it]) /\ max([b, a, _jt])) -> eq_nat([_it, _jt]) -> 2
(max([u, x2, _dt])) -> max([s(u), s(x2), s(_dt)]) -> 4
}
Sat witness: Found: (() -> max([z, y, y]), {
y -> s(s(z))
})

Total time: 0.024571
Reason for stopping: Proved