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, _ko])) -> max([s(u), s(x2), s(_ko)])}
(max([_lo, _mo, _no]) /\ max([_lo, _mo, _oo])) -> eq_nat([_no, _oo])
)
}

properties:
{(max([_po, c, _qo]) /\ max([a, _ro, _so]) /\ max([a, b, _po]) /\ max([b, c, _ro])) -> eq_nat([_qo, _so])}


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

Clause system for inference is:

{
() -> max([s(u), z, s(u)]) -> 0
() -> max([z, y, y]) -> 0
(max([_po, c, _qo]) /\ max([a, _ro, _so]) /\ max([a, b, _po]) /\ max([b, c, _ro])) -> eq_nat([_qo, _so]) -> 0
(max([u, x2, _ko])) -> max([s(u), s(x2), s(_ko)]) -> 0
}


Solving took 0.025620 seconds.
Proved
Model:
|_
{
max -> 
{{{
Q={q_gen_3025, q_gen_3027},
Q_f={q_gen_3025},
Delta=
{
<s, s>(q_gen_3027) -> q_gen_3027
<z, z>() -> q_gen_3027
<s, s, s>(q_gen_3025) -> q_gen_3025
<s, z, s>(q_gen_3027) -> q_gen_3025
<z, s, s>(q_gen_3027) -> q_gen_3025
<z, z, z>() -> q_gen_3025
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005838 s (model generation: 0.005409,  model checking: 0.000429):

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([_po, c, _qo]) /\ max([a, _ro, _so]) /\ max([a, b, _po]) /\ max([b, c, _ro])) -> eq_nat([_qo, _so]) -> 1
(max([u, x2, _ko])) -> max([s(u), s(x2), s(_ko)]) -> 1
}
Sat witness: Found: (() -> max([z, y, y]), {
y -> z
})

-------------------------------------------
Step 1, which took 0.005193 s (model generation: 0.005062,  model checking: 0.000131):

Model:
|_
{
max -> 
{{{
Q={q_gen_3025},
Q_f={q_gen_3025},
Delta=
{
<z, z, z>() -> q_gen_3025
}

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([_po, c, _qo]) /\ max([a, _ro, _so]) /\ max([a, b, _po]) /\ max([b, c, _ro])) -> eq_nat([_qo, _so]) -> 1
(max([u, x2, _ko])) -> max([s(u), s(x2), s(_ko)]) -> 1
}
Sat witness: Found: (() -> max([s(u), z, s(u)]), {
u -> z
})

-------------------------------------------
Step 2, which took 0.004876 s (model generation: 0.004503,  model checking: 0.000373):

Model:
|_
{
max -> 
{{{
Q={q_gen_3025, q_gen_3027},
Q_f={q_gen_3025},
Delta=
{
<z, z>() -> q_gen_3027
<s, z, s>(q_gen_3027) -> q_gen_3025
<z, z, z>() -> q_gen_3025
}

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([_po, c, _qo]) /\ max([a, _ro, _so]) /\ max([a, b, _po]) /\ max([b, c, _ro])) -> eq_nat([_qo, _so]) -> 1
(max([u, x2, _ko])) -> max([s(u), s(x2), s(_ko)]) -> 4
}
Sat witness: Found: ((max([u, x2, _ko])) -> max([s(u), s(x2), s(_ko)]), {
_ko -> z  ;  u -> z  ;  x2 -> z
})

-------------------------------------------
Step 3, which took 0.004620 s (model generation: 0.004391,  model checking: 0.000229):

Model:
|_
{
max -> 
{{{
Q={q_gen_3025, q_gen_3027},
Q_f={q_gen_3025},
Delta=
{
<z, z>() -> q_gen_3027
<s, s, s>(q_gen_3025) -> q_gen_3025
<s, z, s>(q_gen_3027) -> q_gen_3025
<z, z, z>() -> q_gen_3025
}

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([_po, c, _qo]) /\ max([a, _ro, _so]) /\ max([a, b, _po]) /\ max([b, c, _ro])) -> eq_nat([_qo, _so]) -> 2
(max([u, x2, _ko])) -> max([s(u), s(x2), s(_ko)]) -> 4
}
Sat witness: Found: (() -> max([z, y, y]), {
y -> s(s(z))
})

Total time: 0.025620
Reason for stopping: Proved