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


Learning problem is:

env: {
nat -> {s, z}
}
definition:
{
(plus, F:
{() -> plus([n, z, n])
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)])}
(plus([_yba, _zba, _aca]) /\ plus([_yba, _zba, _bca])) -> eq_nat([_aca, _bca])
)
(le, P:
{() -> le([z, s(nn2)])
(le([nn1, nn2])) -> le([s(nn1), s(nn2)])
(le([s(nn1), s(nn2)])) -> le([nn1, nn2])
(le([s(nn1), z])) -> BOT
(le([z, z])) -> BOT}
)
}

properties:
{(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca])}


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

Clause system for inference is:

{
() -> le([z, s(nn2)]) -> 0
() -> plus([n, z, n]) -> 0
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 0
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 0
(le([s(nn1), z])) -> BOT -> 0
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 0
(le([z, z])) -> BOT -> 0
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 0
}


Solving took 0.338122 seconds.
Proved
Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591, q_gen_5604},
Q_f={q_gen_5590},
Delta=
{
<s>(q_gen_5591) -> q_gen_5591
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
<s, s>(q_gen_5604) -> q_gen_5604
<z, z>() -> q_gen_5604
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5592, q_gen_5593, q_gen_5602, q_gen_5603, q_gen_5608},
Q_f={q_gen_5589, q_gen_5592},
Delta=
{
<s>(q_gen_5602) -> q_gen_5602
<z>() -> q_gen_5602
<s, s>(q_gen_5593) -> q_gen_5593
<z, z>() -> q_gen_5593
<s, s>(q_gen_5608) -> q_gen_5608
<z, s>(q_gen_5602) -> q_gen_5608
<s, z, s>(q_gen_5593) -> q_gen_5589
<z, z, z>() -> q_gen_5589
<s, s, s>(q_gen_5592) -> q_gen_5592
<s, z, s>(q_gen_5608) -> q_gen_5592
<z, s, s>(q_gen_5593) -> q_gen_5592
<z, s, s>(q_gen_5608) -> q_gen_5592
<z, z, s>(q_gen_5602) -> q_gen_5592
<s, s, s>(q_gen_5589) -> q_gen_5603
<s, s, s>(q_gen_5603) -> q_gen_5603
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.009836 s (model generation: 0.009480,  model checking: 0.000356):

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

}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={},
Q_f={},
Delta=
{

}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 0
() -> plus([n, z, n]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 1
(le([z, z])) -> BOT -> 1
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 1
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> z
})

-------------------------------------------
Step 1, which took 0.010336 s (model generation: 0.010221,  model checking: 0.000115):

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

}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589},
Q_f={q_gen_5589},
Delta=
{
<z, z, z>() -> q_gen_5589
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> plus([n, z, n]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 1
(le([z, z])) -> BOT -> 1
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 1
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.010380 s (model generation: 0.010147,  model checking: 0.000233):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591},
Q_f={q_gen_5590},
Delta=
{
<z>() -> q_gen_5591
<z, s>(q_gen_5591) -> q_gen_5590
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589},
Q_f={q_gen_5589},
Delta=
{
<z, z, z>() -> q_gen_5589
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> plus([n, z, n]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 1
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 1
(le([s(nn1), z])) -> BOT -> 1
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 1
(le([z, z])) -> BOT -> 1
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 4
}
Sat witness: Found: ((plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]), {
_xba -> z  ;  mm -> z  ;  n -> z
})

-------------------------------------------
Step 3, which took 0.010852 s (model generation: 0.010524,  model checking: 0.000328):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591},
Q_f={q_gen_5590},
Delta=
{
<z>() -> q_gen_5591
<z, s>(q_gen_5591) -> q_gen_5590
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5593},
Q_f={q_gen_5589},
Delta=
{
<z, z>() -> q_gen_5593
<z, s, s>(q_gen_5593) -> q_gen_5589
<z, z, z>() -> q_gen_5589
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> plus([n, z, n]) -> 3
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 2
(le([s(nn1), z])) -> BOT -> 2
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 2
(le([z, z])) -> BOT -> 2
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 4
}
Sat witness: Found: ((le([nn1, nn2])) -> le([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> s(z)
})

-------------------------------------------
Step 4, which took 0.009798 s (model generation: 0.008594,  model checking: 0.001204):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591},
Q_f={q_gen_5590},
Delta=
{
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5593},
Q_f={q_gen_5589},
Delta=
{
<z, z>() -> q_gen_5593
<z, s, s>(q_gen_5593) -> q_gen_5589
<z, z, z>() -> q_gen_5589
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 3
() -> plus([n, z, n]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 3
(le([s(nn1), z])) -> BOT -> 3
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 3
(le([z, z])) -> BOT -> 3
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 4
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(s(z))
})

-------------------------------------------
Step 5, which took 0.005985 s (model generation: 0.005587,  model checking: 0.000398):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591},
Q_f={q_gen_5590},
Delta=
{
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5593},
Q_f={q_gen_5589},
Delta=
{
<s, s>(q_gen_5593) -> q_gen_5593
<z, z>() -> q_gen_5593
<s, z, s>(q_gen_5593) -> q_gen_5589
<z, s, s>(q_gen_5593) -> q_gen_5589
<z, z, z>() -> q_gen_5589
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 6
() -> plus([n, z, n]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 4
(le([s(nn1), z])) -> BOT -> 4
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 4
(le([z, z])) -> BOT -> 4
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 4
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 6, which took 0.005429 s (model generation: 0.005135,  model checking: 0.000294):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591},
Q_f={q_gen_5590},
Delta=
{
<s>(q_gen_5591) -> q_gen_5591
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5593},
Q_f={q_gen_5589},
Delta=
{
<s, s>(q_gen_5593) -> q_gen_5593
<z, z>() -> q_gen_5593
<s, z, s>(q_gen_5593) -> q_gen_5589
<z, s, s>(q_gen_5593) -> q_gen_5589
<z, z, z>() -> q_gen_5589
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 6
() -> plus([n, z, n]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 4
(le([s(nn1), z])) -> BOT -> 4
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 4
(le([z, z])) -> BOT -> 4
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 7
}
Sat witness: Found: ((plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]), {
_xba -> s(z)  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 7, which took 0.011590 s (model generation: 0.011335,  model checking: 0.000255):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591},
Q_f={q_gen_5590},
Delta=
{
<s>(q_gen_5591) -> q_gen_5591
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5593, q_gen_5602},
Q_f={q_gen_5589},
Delta=
{
<z>() -> q_gen_5602
<s, s>(q_gen_5593) -> q_gen_5593
<z, z>() -> q_gen_5593
<s, s, s>(q_gen_5589) -> q_gen_5589
<s, z, s>(q_gen_5593) -> q_gen_5589
<z, s, s>(q_gen_5593) -> q_gen_5589
<z, z, s>(q_gen_5602) -> q_gen_5589
<z, z, z>() -> q_gen_5589
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 6
() -> plus([n, z, n]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 4
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 4
(le([s(nn1), z])) -> BOT -> 4
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 7
(le([z, z])) -> BOT -> 5
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 7
}
Sat witness: Found: ((le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]), {
_cca -> s(z)  ;  m -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 8, which took 0.014460 s (model generation: 0.014192,  model checking: 0.000268):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591},
Q_f={q_gen_5590},
Delta=
{
<s>(q_gen_5591) -> q_gen_5591
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
<z, z>() -> q_gen_5590
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5593, q_gen_5602},
Q_f={q_gen_5589},
Delta=
{
<z>() -> q_gen_5602
<s, s>(q_gen_5593) -> q_gen_5593
<z, z>() -> q_gen_5593
<s, s, s>(q_gen_5589) -> q_gen_5589
<s, z, s>(q_gen_5593) -> q_gen_5589
<z, s, s>(q_gen_5593) -> q_gen_5589
<z, z, s>(q_gen_5602) -> q_gen_5589
<z, z, z>() -> q_gen_5589
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 6
() -> plus([n, z, n]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 5
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 5
(le([s(nn1), z])) -> BOT -> 5
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 7
(le([z, z])) -> BOT -> 8
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 7
}
Sat witness: Found: ((le([z, z])) -> BOT, {

})

-------------------------------------------
Step 9, which took 0.013920 s (model generation: 0.013768,  model checking: 0.000152):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591, q_gen_5605},
Q_f={q_gen_5590},
Delta=
{
<s>(q_gen_5591) -> q_gen_5591
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<s, s>(q_gen_5605) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
<z, z>() -> q_gen_5605
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5593, q_gen_5602},
Q_f={q_gen_5589},
Delta=
{
<z>() -> q_gen_5602
<s, s>(q_gen_5593) -> q_gen_5593
<z, z>() -> q_gen_5593
<s, s, s>(q_gen_5589) -> q_gen_5589
<s, z, s>(q_gen_5593) -> q_gen_5589
<z, s, s>(q_gen_5593) -> q_gen_5589
<z, z, s>(q_gen_5602) -> q_gen_5589
<z, z, z>() -> q_gen_5589
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 6
() -> plus([n, z, n]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 5
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 8
(le([s(nn1), z])) -> BOT -> 6
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 7
(le([z, z])) -> BOT -> 8
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 7
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 10, which took 0.014730 s (model generation: 0.013386,  model checking: 0.001344):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591, q_gen_5604},
Q_f={q_gen_5590},
Delta=
{
<s>(q_gen_5591) -> q_gen_5591
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
<s, s>(q_gen_5604) -> q_gen_5604
<z, z>() -> q_gen_5604
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5593, q_gen_5601, q_gen_5602},
Q_f={q_gen_5589},
Delta=
{
<z>() -> q_gen_5602
<s, s>(q_gen_5593) -> q_gen_5593
<z, z>() -> q_gen_5593
<s, s, s>(q_gen_5601) -> q_gen_5589
<s, z, s>(q_gen_5593) -> q_gen_5589
<z, s, s>(q_gen_5593) -> q_gen_5589
<z, z, z>() -> q_gen_5589
<s, s, s>(q_gen_5589) -> q_gen_5601
<z, z, s>(q_gen_5602) -> q_gen_5601
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 7
() -> plus([n, z, n]) -> 7
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 6
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 8
(le([s(nn1), z])) -> BOT -> 7
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 7
(le([z, z])) -> BOT -> 8
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 10
}
Sat witness: Found: ((plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]), {
_xba -> s(s(z))  ;  mm -> s(z)  ;  n -> s(z)
})

-------------------------------------------
Step 11, which took 0.015319 s (model generation: 0.014946,  model checking: 0.000373):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591, q_gen_5604},
Q_f={q_gen_5590},
Delta=
{
<s>(q_gen_5591) -> q_gen_5591
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
<s, s>(q_gen_5604) -> q_gen_5604
<z, z>() -> q_gen_5604
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5592, q_gen_5593, q_gen_5602, q_gen_5603},
Q_f={q_gen_5589, q_gen_5592},
Delta=
{
<z>() -> q_gen_5602
<s, s>(q_gen_5593) -> q_gen_5593
<z, s>(q_gen_5602) -> q_gen_5593
<z, z>() -> q_gen_5593
<z, z, z>() -> q_gen_5589
<s, s, s>(q_gen_5592) -> q_gen_5592
<s, z, s>(q_gen_5593) -> q_gen_5592
<z, s, s>(q_gen_5593) -> q_gen_5592
<z, z, s>(q_gen_5602) -> q_gen_5592
<s, s, s>(q_gen_5589) -> q_gen_5603
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 7
() -> plus([n, z, n]) -> 7
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 7
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 8
(le([s(nn1), z])) -> BOT -> 7
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 10
(le([z, z])) -> BOT -> 8
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 10
}
Sat witness: Found: ((le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]), {
_cca -> s(s(z))  ;  m -> s(z)  ;  n -> s(s(z))
})

-------------------------------------------
Step 12, which took 0.017204 s (model generation: 0.016147,  model checking: 0.001057):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591, q_gen_5604},
Q_f={q_gen_5590},
Delta=
{
<s>(q_gen_5591) -> q_gen_5591
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
<s, s>(q_gen_5604) -> q_gen_5604
<z, z>() -> q_gen_5604
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5592, q_gen_5593, q_gen_5602, q_gen_5603},
Q_f={q_gen_5589, q_gen_5592},
Delta=
{
<z>() -> q_gen_5602
<s, s>(q_gen_5593) -> q_gen_5593
<z, s>(q_gen_5602) -> q_gen_5593
<z, z>() -> q_gen_5593
<s, s, s>(q_gen_5592) -> q_gen_5589
<s, z, s>(q_gen_5593) -> q_gen_5589
<z, z, z>() -> q_gen_5589
<z, s, s>(q_gen_5593) -> q_gen_5592
<z, z, s>(q_gen_5602) -> q_gen_5592
<s, s, s>(q_gen_5589) -> q_gen_5603
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 8
() -> plus([n, z, n]) -> 8
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 8
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 9
(le([s(nn1), z])) -> BOT -> 8
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 10
(le([z, z])) -> BOT -> 9
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 13
}
Sat witness: Found: ((plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]), {
_xba -> s(s(z))  ;  mm -> z  ;  n -> s(s(z))
})

-------------------------------------------
Step 13, which took 0.018806 s (model generation: 0.017973,  model checking: 0.000833):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591, q_gen_5604},
Q_f={q_gen_5590},
Delta=
{
<s>(q_gen_5591) -> q_gen_5591
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
<s, s>(q_gen_5604) -> q_gen_5604
<z, z>() -> q_gen_5604
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5593, q_gen_5601, q_gen_5602, q_gen_5608},
Q_f={q_gen_5589},
Delta=
{
<z>() -> q_gen_5602
<s, s>(q_gen_5593) -> q_gen_5593
<z, z>() -> q_gen_5593
<z, s>(q_gen_5602) -> q_gen_5608
<s, s, s>(q_gen_5601) -> q_gen_5589
<s, z, s>(q_gen_5593) -> q_gen_5589
<z, s, s>(q_gen_5593) -> q_gen_5589
<z, z, z>() -> q_gen_5589
<s, s, s>(q_gen_5589) -> q_gen_5601
<s, z, s>(q_gen_5608) -> q_gen_5601
<z, s, s>(q_gen_5608) -> q_gen_5601
<z, z, s>(q_gen_5602) -> q_gen_5601
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 9
() -> plus([n, z, n]) -> 9
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 9
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 10
(le([s(nn1), z])) -> BOT -> 9
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 13
(le([z, z])) -> BOT -> 10
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 13
}
Sat witness: Found: ((le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]), {
_cca -> s(s(z))  ;  m -> s(s(z))  ;  n -> s(s(z))
})

-------------------------------------------
Step 14, which took 0.020231 s (model generation: 0.019251,  model checking: 0.000980):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591, q_gen_5604, q_gen_5605},
Q_f={q_gen_5590},
Delta=
{
<s>(q_gen_5591) -> q_gen_5591
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<s, s>(q_gen_5604) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
<s, s>(q_gen_5605) -> q_gen_5604
<z, z>() -> q_gen_5605
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5592, q_gen_5593, q_gen_5602, q_gen_5603},
Q_f={q_gen_5589, q_gen_5592},
Delta=
{
<z>() -> q_gen_5602
<s, s>(q_gen_5593) -> q_gen_5593
<z, s>(q_gen_5602) -> q_gen_5593
<z, z>() -> q_gen_5593
<s, s, s>(q_gen_5603) -> q_gen_5589
<z, z, z>() -> q_gen_5589
<s, s, s>(q_gen_5592) -> q_gen_5592
<s, z, s>(q_gen_5593) -> q_gen_5592
<z, s, s>(q_gen_5593) -> q_gen_5592
<z, z, s>(q_gen_5602) -> q_gen_5592
<s, s, s>(q_gen_5589) -> q_gen_5603
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 10
() -> plus([n, z, n]) -> 10
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 10
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 13
(le([s(nn1), z])) -> BOT -> 10
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 13
(le([z, z])) -> BOT -> 11
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 13
}
Sat witness: Found: ((le([s(nn1), s(nn2)])) -> le([nn1, nn2]), {
nn1 -> s(z)  ;  nn2 -> s(z)
})

-------------------------------------------
Step 15, which took 0.019052 s (model generation: 0.018607,  model checking: 0.000445):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591, q_gen_5604},
Q_f={q_gen_5590},
Delta=
{
<s>(q_gen_5591) -> q_gen_5591
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
<s, s>(q_gen_5604) -> q_gen_5604
<z, z>() -> q_gen_5604
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5592, q_gen_5593, q_gen_5596, q_gen_5602, q_gen_5603},
Q_f={q_gen_5589, q_gen_5592},
Delta=
{
<z>() -> q_gen_5602
<z, z>() -> q_gen_5593
<s, s>(q_gen_5593) -> q_gen_5596
<z, s>(q_gen_5602) -> q_gen_5596
<s, z, s>(q_gen_5593) -> q_gen_5589
<z, z, z>() -> q_gen_5589
<s, s, s>(q_gen_5592) -> q_gen_5592
<s, z, s>(q_gen_5596) -> q_gen_5592
<z, s, s>(q_gen_5593) -> q_gen_5592
<z, s, s>(q_gen_5596) -> q_gen_5592
<z, z, s>(q_gen_5602) -> q_gen_5592
<s, s, s>(q_gen_5589) -> q_gen_5603
<s, s, s>(q_gen_5603) -> q_gen_5603
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 10
() -> plus([n, z, n]) -> 13
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 11
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 13
(le([s(nn1), z])) -> BOT -> 11
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 13
(le([z, z])) -> BOT -> 11
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 13
}
Sat witness: Found: (() -> plus([n, z, n]), {
n -> s(s(s(z)))
})

-------------------------------------------
Step 16, which took 0.020808 s (model generation: 0.019943,  model checking: 0.000865):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591, q_gen_5604},
Q_f={q_gen_5590},
Delta=
{
<s>(q_gen_5591) -> q_gen_5591
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
<s, s>(q_gen_5604) -> q_gen_5604
<z, z>() -> q_gen_5604
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5592, q_gen_5593, q_gen_5596, q_gen_5602, q_gen_5603},
Q_f={q_gen_5589, q_gen_5592},
Delta=
{
<z>() -> q_gen_5602
<z, z>() -> q_gen_5593
<s, s>(q_gen_5593) -> q_gen_5596
<s, s>(q_gen_5596) -> q_gen_5596
<z, s>(q_gen_5602) -> q_gen_5596
<s, s, s>(q_gen_5592) -> q_gen_5589
<s, z, s>(q_gen_5593) -> q_gen_5589
<z, z, z>() -> q_gen_5589
<s, z, s>(q_gen_5596) -> q_gen_5592
<z, s, s>(q_gen_5593) -> q_gen_5592
<z, s, s>(q_gen_5596) -> q_gen_5592
<z, z, s>(q_gen_5602) -> q_gen_5592
<s, s, s>(q_gen_5589) -> q_gen_5603
<s, s, s>(q_gen_5603) -> q_gen_5603
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 11
() -> plus([n, z, n]) -> 13
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 12
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 13
(le([s(nn1), z])) -> BOT -> 12
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 13
(le([z, z])) -> BOT -> 12
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 16
}
Sat witness: Found: ((plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]), {
_xba -> s(s(z))  ;  mm -> z  ;  n -> s(z)
})

-------------------------------------------
Step 17, which took 0.023355 s (model generation: 0.022763,  model checking: 0.000592):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591, q_gen_5604},
Q_f={q_gen_5590},
Delta=
{
<s>(q_gen_5591) -> q_gen_5591
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
<s, s>(q_gen_5604) -> q_gen_5604
<z, z>() -> q_gen_5604
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5592, q_gen_5593, q_gen_5596, q_gen_5602, q_gen_5603},
Q_f={q_gen_5589, q_gen_5592},
Delta=
{
<s>(q_gen_5602) -> q_gen_5602
<z>() -> q_gen_5602
<s, s>(q_gen_5596) -> q_gen_5593
<z, z>() -> q_gen_5593
<s, s>(q_gen_5593) -> q_gen_5596
<z, s>(q_gen_5602) -> q_gen_5596
<s, z, s>(q_gen_5593) -> q_gen_5589
<z, z, z>() -> q_gen_5589
<s, s, s>(q_gen_5592) -> q_gen_5592
<s, z, s>(q_gen_5596) -> q_gen_5592
<z, s, s>(q_gen_5593) -> q_gen_5592
<z, s, s>(q_gen_5596) -> q_gen_5592
<z, z, s>(q_gen_5602) -> q_gen_5592
<s, s, s>(q_gen_5589) -> q_gen_5603
<s, s, s>(q_gen_5603) -> q_gen_5603
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 12
() -> plus([n, z, n]) -> 13
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 13
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 13
(le([s(nn1), z])) -> BOT -> 13
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 16
(le([z, z])) -> BOT -> 13
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 16
}
Sat witness: Found: ((le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]), {
_cca -> s(s(s(z)))  ;  m -> s(z)  ;  n -> s(s(s(z)))
})

-------------------------------------------
Step 18, which took 0.026587 s (model generation: 0.025453,  model checking: 0.001134):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591, q_gen_5604},
Q_f={q_gen_5590},
Delta=
{
<s>(q_gen_5591) -> q_gen_5591
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
<s, s>(q_gen_5604) -> q_gen_5604
<z, z>() -> q_gen_5604
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5592, q_gen_5593, q_gen_5602, q_gen_5603, q_gen_5608},
Q_f={q_gen_5589, q_gen_5592},
Delta=
{
<s>(q_gen_5602) -> q_gen_5602
<z>() -> q_gen_5602
<s, s>(q_gen_5593) -> q_gen_5593
<z, z>() -> q_gen_5593
<z, s>(q_gen_5602) -> q_gen_5608
<s, z, s>(q_gen_5593) -> q_gen_5589
<z, z, z>() -> q_gen_5589
<s, s, s>(q_gen_5592) -> q_gen_5592
<s, z, s>(q_gen_5608) -> q_gen_5592
<z, s, s>(q_gen_5593) -> q_gen_5592
<z, s, s>(q_gen_5608) -> q_gen_5592
<z, z, s>(q_gen_5602) -> q_gen_5592
<s, s, s>(q_gen_5589) -> q_gen_5603
<s, s, s>(q_gen_5603) -> q_gen_5603
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 13
() -> plus([n, z, n]) -> 14
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 14
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 14
(le([s(nn1), z])) -> BOT -> 14
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 16
(le([z, z])) -> BOT -> 14
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 19
}
Sat witness: Found: ((plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]), {
_xba -> s(s(z))  ;  mm -> s(z)  ;  n -> z
})

-------------------------------------------
Step 19, which took 0.028197 s (model generation: 0.026624,  model checking: 0.001573):

Model:
|_
{
le -> 
{{{
Q={q_gen_5590, q_gen_5591, q_gen_5604},
Q_f={q_gen_5590},
Delta=
{
<s>(q_gen_5591) -> q_gen_5591
<z>() -> q_gen_5591
<s, s>(q_gen_5590) -> q_gen_5590
<z, s>(q_gen_5591) -> q_gen_5590
<s, s>(q_gen_5604) -> q_gen_5604
<z, z>() -> q_gen_5604
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  plus -> 
{{{
Q={q_gen_5589, q_gen_5592, q_gen_5593, q_gen_5602, q_gen_5603, q_gen_5608},
Q_f={q_gen_5589, q_gen_5592},
Delta=
{
<s>(q_gen_5602) -> q_gen_5602
<z>() -> q_gen_5602
<s, s>(q_gen_5593) -> q_gen_5593
<z, z>() -> q_gen_5593
<s, s>(q_gen_5608) -> q_gen_5608
<z, s>(q_gen_5602) -> q_gen_5608
<s, s, s>(q_gen_5592) -> q_gen_5589
<s, z, s>(q_gen_5593) -> q_gen_5589
<z, z, z>() -> q_gen_5589
<s, z, s>(q_gen_5608) -> q_gen_5592
<z, s, s>(q_gen_5593) -> q_gen_5592
<z, s, s>(q_gen_5608) -> q_gen_5592
<z, z, s>(q_gen_5602) -> q_gen_5592
<s, s, s>(q_gen_5589) -> q_gen_5603
<s, s, s>(q_gen_5603) -> q_gen_5603
}

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

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

Teacher's answer:
New clause system:
{
() -> le([z, s(nn2)]) -> 14
() -> plus([n, z, n]) -> 15
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 15
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 15
(le([s(nn1), z])) -> BOT -> 15
(le([z, m]) /\ plus([n, m, _cca])) -> le([n, _cca]) -> 17
(le([z, z])) -> BOT -> 15
(plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]) -> 22
}
Sat witness: Found: ((plus([n, mm, _xba])) -> plus([n, s(mm), s(_xba)]), {
_xba -> s(s(s(z)))  ;  mm -> s(z)  ;  n -> s(s(z))
})

Total time: 0.338122
Reason for stopping: Proved