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


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(leq, P:
{() -> leq([z, n2])
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)])
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2])
(leq([s(nn1), z])) -> BOT}
)
}

properties:
{(leq([m, n])) -> leq([m, s(n)])}


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

Clause system for inference is:

{
() -> leq([z, n2]) -> 0
(leq([m, n])) -> leq([m, s(n)]) -> 0
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 0
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 0
(leq([s(nn1), z])) -> BOT -> 0
}


Solving took 0.038719 seconds.
Proved
Model:
|_
{
leq -> 
{{{
Q={q_gen_348, q_gen_351},
Q_f={q_gen_348},
Delta=
{
<s>(q_gen_351) -> q_gen_351
<z>() -> q_gen_351
<s, s>(q_gen_348) -> q_gen_348
<z, s>(q_gen_351) -> q_gen_348
<z, z>() -> q_gen_348
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.007806 s (model generation: 0.007707,  model checking: 0.000099):

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

}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3
(leq([m, n])) -> leq([m, s(n)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([z, n2]), {
n2 -> z
})

-------------------------------------------
Step 1, which took 0.007304 s (model generation: 0.007212,  model checking: 0.000092):

Model:
|_
{
leq -> 
{{{
Q={q_gen_348},
Q_f={q_gen_348},
Delta=
{
<z, z>() -> q_gen_348
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3
(leq([m, n])) -> leq([m, s(n)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 2, which took 0.007145 s (model generation: 0.007072,  model checking: 0.000073):

Model:
|_
{
leq -> 
{{{
Q={q_gen_348},
Q_f={q_gen_348},
Delta=
{
<s, s>(q_gen_348) -> q_gen_348
<z, z>() -> q_gen_348
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 3
(leq([m, n])) -> leq([m, s(n)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((leq([m, n])) -> leq([m, s(n)]), {
m -> z  ;  n -> z
})

-------------------------------------------
Step 3, which took 0.008018 s (model generation: 0.007398,  model checking: 0.000620):

Model:
|_
{
leq -> 
{{{
Q={q_gen_348, q_gen_351},
Q_f={q_gen_348},
Delta=
{
<z>() -> q_gen_351
<s, s>(q_gen_348) -> q_gen_348
<z, s>(q_gen_351) -> q_gen_348
<z, z>() -> q_gen_348
}

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

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

Teacher's answer:
New clause system:
{
() -> leq([z, n2]) -> 6
(leq([m, n])) -> leq([m, s(n)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 3
(leq([s(nn1), z])) -> BOT -> 3
}
Sat witness: Found: (() -> leq([z, n2]), {
n2 -> s(s(z))
})

Total time: 0.038719
Reason for stopping: Proved