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, _pu])) -> max([s(u), s(x2), s(_pu)])}
(max([_qu, _ru, _su]) /\ max([_qu, _ru, _tu])) -> eq_nat([_su, _tu])
)
}

properties:
{(max([_uu, c, _vu]) /\ max([a, _wu, _xu]) /\ max([a, b, _uu]) /\ max([b, c, _wu])) -> eq_nat([_vu, _xu])}


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

Clause system for inference is:

{
() -> max([s(u), z, s(u)]) -> 0
() -> max([z, y, y]) -> 0
(max([_uu, c, _vu]) /\ max([a, _wu, _xu]) /\ max([a, b, _uu]) /\ max([b, c, _wu])) -> eq_nat([_vu, _xu]) -> 0
(max([u, x2, _pu])) -> max([s(u), s(x2), s(_pu)]) -> 0
}


Solving took 0.047754 seconds.
Proved
Model:
|_
{
max -> 
{{{
Q={q_gen_5520, q_gen_5522},
Q_f={q_gen_5520},
Delta=
{
<s, s>(q_gen_5522) -> q_gen_5522
<z, z>() -> q_gen_5522
<s, s, s>(q_gen_5520) -> q_gen_5520
<s, z, s>(q_gen_5522) -> q_gen_5520
<z, s, s>(q_gen_5522) -> q_gen_5520
<z, z, z>() -> q_gen_5520
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.009760 s (model generation: 0.009615,  model checking: 0.000145):

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([_uu, c, _vu]) /\ max([a, _wu, _xu]) /\ max([a, b, _uu]) /\ max([b, c, _wu])) -> eq_nat([_vu, _xu]) -> 1
(max([u, x2, _pu])) -> max([s(u), s(x2), s(_pu)]) -> 1
}
Sat witness: Found: (() -> max([z, y, y]), {
y -> z
})

-------------------------------------------
Step 1, which took 0.008785 s (model generation: 0.008685,  model checking: 0.000100):

Model:
|_
{
max -> 
{{{
Q={q_gen_5520},
Q_f={q_gen_5520},
Delta=
{
<z, z, z>() -> q_gen_5520
}

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([_uu, c, _vu]) /\ max([a, _wu, _xu]) /\ max([a, b, _uu]) /\ max([b, c, _wu])) -> eq_nat([_vu, _xu]) -> 1
(max([u, x2, _pu])) -> max([s(u), s(x2), s(_pu)]) -> 1
}
Sat witness: Found: (() -> max([s(u), z, s(u)]), {
u -> z
})

-------------------------------------------
Step 2, which took 0.009834 s (model generation: 0.009585,  model checking: 0.000249):

Model:
|_
{
max -> 
{{{
Q={q_gen_5520, q_gen_5522},
Q_f={q_gen_5520},
Delta=
{
<z, z>() -> q_gen_5522
<s, z, s>(q_gen_5522) -> q_gen_5520
<z, z, z>() -> q_gen_5520
}

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([_uu, c, _vu]) /\ max([a, _wu, _xu]) /\ max([a, b, _uu]) /\ max([b, c, _wu])) -> eq_nat([_vu, _xu]) -> 1
(max([u, x2, _pu])) -> max([s(u), s(x2), s(_pu)]) -> 4
}
Sat witness: Found: ((max([u, x2, _pu])) -> max([s(u), s(x2), s(_pu)]), {
_pu -> z  ;  u -> z  ;  x2 -> z
})

-------------------------------------------
Step 3, which took 0.009409 s (model generation: 0.009155,  model checking: 0.000254):

Model:
|_
{
max -> 
{{{
Q={q_gen_5520, q_gen_5522},
Q_f={q_gen_5520},
Delta=
{
<z, z>() -> q_gen_5522
<s, s, s>(q_gen_5520) -> q_gen_5520
<s, z, s>(q_gen_5522) -> q_gen_5520
<z, z, z>() -> q_gen_5520
}

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([_uu, c, _vu]) /\ max([a, _wu, _xu]) /\ max([a, b, _uu]) /\ max([b, c, _wu])) -> eq_nat([_vu, _xu]) -> 2
(max([u, x2, _pu])) -> max([s(u), s(x2), s(_pu)]) -> 4
}
Sat witness: Found: (() -> max([z, y, y]), {
y -> s(s(z))
})

Total time: 0.047754
Reason for stopping: Proved