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


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(max, F:
{() -> max([s(u), z, s(u)])
() -> max([z, y, y])
(max([u, x2, _lr])) -> max([s(u), s(x2), s(_lr)])}
(max([_mr, _nr, _or]) /\ max([_mr, _nr, _pr])) -> eq_nat([_or, _pr])
)
}

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


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, _qr]) /\ max([b, a, _rr])) -> eq_nat([_qr, _rr]) -> 0
(max([u, x2, _lr])) -> max([s(u), s(x2), s(_lr)]) -> 0
}


Solving took 0.064760 seconds.
Proved
Model:
|_
{
max -> 
{{{
Q={q_gen_4819, q_gen_4821},
Q_f={q_gen_4819},
Delta=
{
<s, s>(q_gen_4821) -> q_gen_4821
<z, z>() -> q_gen_4821
<s, s, s>(q_gen_4819) -> q_gen_4819
<s, z, s>(q_gen_4821) -> q_gen_4819
<z, s, s>(q_gen_4821) -> q_gen_4819
<z, z, z>() -> q_gen_4819
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.018393 s (model generation: 0.018183,  model checking: 0.000210):

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

}

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

}
--
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, _qr]) /\ max([b, a, _rr])) -> eq_nat([_qr, _rr]) -> 1
(max([u, x2, _lr])) -> max([s(u), s(x2), s(_lr)]) -> 1
}
Sat witness: Found: (() -> max([z, y, y]), {
y -> z
})

-------------------------------------------
Step 1, which took 0.011110 s (model generation: 0.010992,  model checking: 0.000118):

Model:
|_
{
max -> 
{{{
Q={q_gen_4819},
Q_f={q_gen_4819},
Delta=
{
<z, z, z>() -> q_gen_4819
}

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

}
--
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, _qr]) /\ max([b, a, _rr])) -> eq_nat([_qr, _rr]) -> 1
(max([u, x2, _lr])) -> max([s(u), s(x2), s(_lr)]) -> 1
}
Sat witness: Found: (() -> max([s(u), z, s(u)]), {
u -> z
})

-------------------------------------------
Step 2, which took 0.012129 s (model generation: 0.011989,  model checking: 0.000140):

Model:
|_
{
max -> 
{{{
Q={q_gen_4819, q_gen_4821},
Q_f={q_gen_4819},
Delta=
{
<z, z>() -> q_gen_4821
<s, z, s>(q_gen_4821) -> q_gen_4819
<z, z, z>() -> q_gen_4819
}

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

}
--
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, _qr]) /\ max([b, a, _rr])) -> eq_nat([_qr, _rr]) -> 1
(max([u, x2, _lr])) -> max([s(u), s(x2), s(_lr)]) -> 4
}
Sat witness: Found: ((max([u, x2, _lr])) -> max([s(u), s(x2), s(_lr)]), {
_lr -> z  ;  u -> z  ;  x2 -> z
})

-------------------------------------------
Step 3, which took 0.011648 s (model generation: 0.011465,  model checking: 0.000183):

Model:
|_
{
max -> 
{{{
Q={q_gen_4819, q_gen_4821},
Q_f={q_gen_4819},
Delta=
{
<z, z>() -> q_gen_4821
<s, s, s>(q_gen_4819) -> q_gen_4819
<s, z, s>(q_gen_4821) -> q_gen_4819
<z, z, z>() -> q_gen_4819
}

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

}
--
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, _qr]) /\ max([b, a, _rr])) -> eq_nat([_qr, _rr]) -> 2
(max([u, x2, _lr])) -> max([s(u), s(x2), s(_lr)]) -> 4
}
Sat witness: Found: (() -> max([z, y, y]), {
y -> s(s(z))
})

Total time: 0.064760
Reason for stopping: Proved