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


Learning problem is:

env: {
nat -> {s, z}  ;  natlist -> {cons, nil}
}
definition:
{
(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}
)
(length, F:
{() -> length([nil, z])
(length([ll, _tr])) -> length([cons(x, ll), s(_tr)])}
(length([_ur, _vr]) /\ length([_ur, _wr])) -> eq_nat([_vr, _wr])
)
(fcons, F:
{() -> fcons([x, l, cons(x, l)])}
(fcons([_xr, _yr, _as]) /\ fcons([_xr, _yr, _zr])) -> eq_natlist([_zr, _as])
)
}

properties:
{(fcons([x, l, _cs]) /\ length([_cs, _ds]) /\ length([l, _bs])) -> le([_bs, _ds])}


over-approximation: {fcons, length}
under-approximation: {le}

Clause system for inference is:

{
() -> fcons([x, l, cons(x, l)]) -> 0
() -> le([z, s(nn2)]) -> 0
() -> length([nil, z]) -> 0
(fcons([x, l, _cs]) /\ length([_cs, _ds]) /\ length([l, _bs])) -> le([_bs, _ds]) -> 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, z])) -> BOT -> 0
(length([ll, _tr])) -> length([cons(x, ll), s(_tr)]) -> 0
}


Solving took 60.000033 seconds.
DontKnow. Stopped because: timeout
Working model:
|_
{
fcons -> 
{{{
Q={q_gen_3511, q_gen_3512, q_gen_3513, q_gen_3519, q_gen_3520, q_gen_3521, q_gen_3522, q_gen_3523, q_gen_3526, q_gen_3527, q_gen_3528, q_gen_3529, q_gen_3530, q_gen_3531, q_gen_3532, q_gen_3533, q_gen_3534, q_gen_3535, q_gen_3536, q_gen_3537, q_gen_3538},
Q_f={},
Delta=
{
<nil>() -> q_gen_3512
<z>() -> q_gen_3513
<s>(q_gen_3513) -> q_gen_3528
<s>(q_gen_3528) -> q_gen_3531
<nil, cons>(q_gen_3513, q_gen_3512) -> q_gen_3521
<z, z>() -> q_gen_3522
<z, s>(q_gen_3513) -> q_gen_3523
<z, nil>() -> q_gen_3527
<s, nil>(q_gen_3513) -> q_gen_3530
<s, s>(q_gen_3535) -> q_gen_3534
<s, z>(q_gen_3513) -> q_gen_3535
<cons, cons>(q_gen_3522, q_gen_3521) -> q_gen_3538
<z, nil, cons>(q_gen_3513, q_gen_3512) -> q_gen_3511
<s, cons, cons>(q_gen_3523, q_gen_3520) -> q_gen_3519
<z, cons, cons>(q_gen_3522, q_gen_3521) -> q_gen_3520
<s, nil, cons>(q_gen_3528, q_gen_3527) -> q_gen_3526
<s, nil, cons>(q_gen_3531, q_gen_3530) -> q_gen_3529
<s, cons, cons>(q_gen_3534, q_gen_3533) -> q_gen_3532
<z, nil, cons>(q_gen_3531, q_gen_3512) -> q_gen_3533
<s, cons, cons>(q_gen_3523, q_gen_3537) -> q_gen_3536
<z, cons, cons>(q_gen_3522, q_gen_3538) -> q_gen_3537
}

Datatype: <nat, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_3509, q_gen_3510, q_gen_3516, q_gen_3517, q_gen_3518},
Q_f={},
Delta=
{
<z>() -> q_gen_3510
<s>(q_gen_3510) -> q_gen_3518
<z, s>(q_gen_3510) -> q_gen_3509
<s, s>(q_gen_3509) -> q_gen_3516
<z, s>(q_gen_3518) -> q_gen_3517
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_3508, q_gen_3514, q_gen_3515, q_gen_3524, q_gen_3525},
Q_f={},
Delta=
{
<z>() -> q_gen_3515
<s>(q_gen_3515) -> q_gen_3525
<nil, z>() -> q_gen_3508
<cons, s>(q_gen_3515, q_gen_3508) -> q_gen_3514
<cons, s>(q_gen_3525, q_gen_3508) -> q_gen_3524
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.005497 s (model generation: 0.005120,  model checking: 0.000377):

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 0
() -> le([z, s(nn2)]) -> 0
() -> length([nil, z]) -> 3
(fcons([x, l, _cs]) /\ length([_cs, _ds]) /\ length([l, _bs])) -> le([_bs, _ds]) -> 1
(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, z])) -> BOT -> 1
(length([ll, _tr])) -> length([cons(x, ll), s(_tr)]) -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 1, which took 0.004749 s (model generation: 0.004592,  model checking: 0.000157):

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

}

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

}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_3508},
Q_f={q_gen_3508},
Delta=
{
<nil, z>() -> q_gen_3508
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 0
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(fcons([x, l, _cs]) /\ length([_cs, _ds]) /\ length([l, _bs])) -> le([_bs, _ds]) -> 1
(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, z])) -> BOT -> 1
(length([ll, _tr])) -> length([cons(x, ll), s(_tr)]) -> 1
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.005051 s (model generation: 0.004735,  model checking: 0.000316):

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

}

Datatype: <nat, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_3509, q_gen_3510},
Q_f={q_gen_3509},
Delta=
{
<z>() -> q_gen_3510
<z, s>(q_gen_3510) -> q_gen_3509
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_3508},
Q_f={q_gen_3508},
Delta=
{
<nil, z>() -> q_gen_3508
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 3
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(fcons([x, l, _cs]) /\ length([_cs, _ds]) /\ length([l, _bs])) -> le([_bs, _ds]) -> 1
(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, z])) -> BOT -> 1
(length([ll, _tr])) -> length([cons(x, ll), s(_tr)]) -> 1
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> nil  ;  x -> z
})

-------------------------------------------
Step 3, which took 0.005839 s (model generation: 0.004516,  model checking: 0.001323):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_3511, q_gen_3512, q_gen_3513},
Q_f={q_gen_3511},
Delta=
{
<nil>() -> q_gen_3512
<z>() -> q_gen_3513
<z, nil, cons>(q_gen_3513, q_gen_3512) -> q_gen_3511
}

Datatype: <nat, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_3509, q_gen_3510},
Q_f={q_gen_3509},
Delta=
{
<z>() -> q_gen_3510
<z, s>(q_gen_3510) -> q_gen_3509
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_3508},
Q_f={q_gen_3508},
Delta=
{
<nil, z>() -> q_gen_3508
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 3
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(fcons([x, l, _cs]) /\ length([_cs, _ds]) /\ length([l, _bs])) -> le([_bs, _ds]) -> 1
(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, z])) -> BOT -> 1
(length([ll, _tr])) -> length([cons(x, ll), s(_tr)]) -> 4
}
Sat witness: Found: ((length([ll, _tr])) -> length([cons(x, ll), s(_tr)]), {
_tr -> z  ;  ll -> nil  ;  x -> z
})

-------------------------------------------
Step 4, which took 0.004420 s (model generation: 0.004323,  model checking: 0.000097):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_3511, q_gen_3512, q_gen_3513},
Q_f={q_gen_3511},
Delta=
{
<nil>() -> q_gen_3512
<z>() -> q_gen_3513
<z, nil, cons>(q_gen_3513, q_gen_3512) -> q_gen_3511
}

Datatype: <nat, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_3509, q_gen_3510},
Q_f={q_gen_3509},
Delta=
{
<z>() -> q_gen_3510
<z, s>(q_gen_3510) -> q_gen_3509
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_3508, q_gen_3515},
Q_f={q_gen_3508},
Delta=
{
<z>() -> q_gen_3515
<cons, s>(q_gen_3515, q_gen_3508) -> q_gen_3508
<nil, z>() -> q_gen_3508
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 3
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(fcons([x, l, _cs]) /\ length([_cs, _ds]) /\ length([l, _bs])) -> le([_bs, _ds]) -> 1
(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, z])) -> BOT -> 2
(length([ll, _tr])) -> length([cons(x, ll), s(_tr)]) -> 4
}
Sat witness: Found: ((le([nn1, nn2])) -> le([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> s(z)
})

-------------------------------------------
Step 5, which took 0.004739 s (model generation: 0.004478,  model checking: 0.000261):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_3511, q_gen_3512, q_gen_3513},
Q_f={q_gen_3511},
Delta=
{
<nil>() -> q_gen_3512
<z>() -> q_gen_3513
<z, nil, cons>(q_gen_3513, q_gen_3512) -> q_gen_3511
}

Datatype: <nat, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_3509, q_gen_3510},
Q_f={q_gen_3509},
Delta=
{
<z>() -> q_gen_3510
<s, s>(q_gen_3509) -> q_gen_3509
<z, s>(q_gen_3510) -> q_gen_3509
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_3508, q_gen_3515},
Q_f={q_gen_3508},
Delta=
{
<z>() -> q_gen_3515
<cons, s>(q_gen_3515, q_gen_3508) -> q_gen_3508
<nil, z>() -> q_gen_3508
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 3
() -> le([z, s(nn2)]) -> 6
() -> length([nil, z]) -> 4
(fcons([x, l, _cs]) /\ length([_cs, _ds]) /\ length([l, _bs])) -> le([_bs, _ds]) -> 2
(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, z])) -> BOT -> 3
(length([ll, _tr])) -> length([cons(x, ll), s(_tr)]) -> 4
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 6, which took 0.008365 s (model generation: 0.006874,  model checking: 0.001491):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_3511, q_gen_3512, q_gen_3513},
Q_f={q_gen_3511},
Delta=
{
<nil>() -> q_gen_3512
<z>() -> q_gen_3513
<z, nil, cons>(q_gen_3513, q_gen_3512) -> q_gen_3511
}

Datatype: <nat, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_3509, q_gen_3510},
Q_f={q_gen_3509},
Delta=
{
<s>(q_gen_3510) -> q_gen_3510
<z>() -> q_gen_3510
<s, s>(q_gen_3509) -> q_gen_3509
<z, s>(q_gen_3510) -> q_gen_3509
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_3508, q_gen_3515},
Q_f={q_gen_3508},
Delta=
{
<z>() -> q_gen_3515
<cons, s>(q_gen_3515, q_gen_3508) -> q_gen_3508
<nil, z>() -> q_gen_3508
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 6
() -> le([z, s(nn2)]) -> 6
() -> length([nil, z]) -> 4
(fcons([x, l, _cs]) /\ length([_cs, _ds]) /\ length([l, _bs])) -> le([_bs, _ds]) -> 3
(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, z])) -> BOT -> 4
(length([ll, _tr])) -> length([cons(x, ll), s(_tr)]) -> 4
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(z, cons(z, nil))  ;  x -> s(z)
})

-------------------------------------------
Step 7, which took 0.010566 s (model generation: 0.009804,  model checking: 0.000762):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_3511, q_gen_3512, q_gen_3513, q_gen_3521, q_gen_3522},
Q_f={q_gen_3511},
Delta=
{
<nil>() -> q_gen_3512
<z>() -> q_gen_3513
<nil, cons>(q_gen_3513, q_gen_3512) -> q_gen_3521
<z, s>(q_gen_3513) -> q_gen_3522
<z, z>() -> q_gen_3522
<s, cons, cons>(q_gen_3522, q_gen_3511) -> q_gen_3511
<z, cons, cons>(q_gen_3522, q_gen_3521) -> q_gen_3511
<z, nil, cons>(q_gen_3513, q_gen_3512) -> q_gen_3511
}

Datatype: <nat, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_3509, q_gen_3510},
Q_f={q_gen_3509},
Delta=
{
<s>(q_gen_3510) -> q_gen_3510
<z>() -> q_gen_3510
<s, s>(q_gen_3509) -> q_gen_3509
<z, s>(q_gen_3510) -> q_gen_3509
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_3508, q_gen_3515},
Q_f={q_gen_3508},
Delta=
{
<z>() -> q_gen_3515
<cons, s>(q_gen_3515, q_gen_3508) -> q_gen_3508
<nil, z>() -> q_gen_3508
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 6
() -> le([z, s(nn2)]) -> 6
() -> length([nil, z]) -> 4
(fcons([x, l, _cs]) /\ length([_cs, _ds]) /\ length([l, _bs])) -> le([_bs, _ds]) -> 4
(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, z])) -> BOT -> 4
(length([ll, _tr])) -> length([cons(x, ll), s(_tr)]) -> 7
}
Sat witness: Found: ((length([ll, _tr])) -> length([cons(x, ll), s(_tr)]), {
_tr -> z  ;  ll -> nil  ;  x -> s(z)
})

-------------------------------------------
Step 8, which took 0.008777 s (model generation: 0.004773,  model checking: 0.004004):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_3511, q_gen_3512, q_gen_3513, q_gen_3521, q_gen_3522},
Q_f={q_gen_3511},
Delta=
{
<nil>() -> q_gen_3512
<z>() -> q_gen_3513
<nil, cons>(q_gen_3513, q_gen_3512) -> q_gen_3521
<z, s>(q_gen_3513) -> q_gen_3522
<z, z>() -> q_gen_3522
<s, cons, cons>(q_gen_3522, q_gen_3511) -> q_gen_3511
<z, cons, cons>(q_gen_3522, q_gen_3521) -> q_gen_3511
<z, nil, cons>(q_gen_3513, q_gen_3512) -> q_gen_3511
}

Datatype: <nat, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_3509, q_gen_3510},
Q_f={q_gen_3509},
Delta=
{
<s>(q_gen_3510) -> q_gen_3510
<z>() -> q_gen_3510
<s, s>(q_gen_3509) -> q_gen_3509
<z, s>(q_gen_3510) -> q_gen_3509
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_3508, q_gen_3515},
Q_f={q_gen_3508},
Delta=
{
<s>(q_gen_3515) -> q_gen_3515
<z>() -> q_gen_3515
<cons, s>(q_gen_3515, q_gen_3508) -> q_gen_3508
<nil, z>() -> q_gen_3508
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 9
() -> le([z, s(nn2)]) -> 7
() -> length([nil, z]) -> 5
(fcons([x, l, _cs]) /\ length([_cs, _ds]) /\ length([l, _bs])) -> le([_bs, _ds]) -> 5
(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, z])) -> BOT -> 5
(length([ll, _tr])) -> length([cons(x, ll), s(_tr)]) -> 7
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> nil  ;  x -> s(z)
})

-------------------------------------------
Step 9, which took 0.016332 s (model generation: 0.012833,  model checking: 0.003499):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_3511, q_gen_3512, q_gen_3513, q_gen_3521, q_gen_3522, q_gen_3527},
Q_f={q_gen_3511},
Delta=
{
<nil>() -> q_gen_3512
<s>(q_gen_3513) -> q_gen_3513
<z>() -> q_gen_3513
<nil, cons>(q_gen_3513, q_gen_3512) -> q_gen_3521
<z, s>(q_gen_3513) -> q_gen_3522
<z, z>() -> q_gen_3522
<z, nil>() -> q_gen_3527
<s, cons, cons>(q_gen_3522, q_gen_3511) -> q_gen_3511
<s, nil, cons>(q_gen_3513, q_gen_3527) -> q_gen_3511
<z, cons, cons>(q_gen_3522, q_gen_3521) -> q_gen_3511
<z, nil, cons>(q_gen_3513, q_gen_3512) -> q_gen_3511
}

Datatype: <nat, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_3509, q_gen_3510},
Q_f={q_gen_3509},
Delta=
{
<s>(q_gen_3510) -> q_gen_3510
<z>() -> q_gen_3510
<s, s>(q_gen_3509) -> q_gen_3509
<z, s>(q_gen_3510) -> q_gen_3509
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_3508, q_gen_3515},
Q_f={q_gen_3508},
Delta=
{
<s>(q_gen_3515) -> q_gen_3515
<z>() -> q_gen_3515
<cons, s>(q_gen_3515, q_gen_3508) -> q_gen_3508
<nil, z>() -> q_gen_3508
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 12
() -> le([z, s(nn2)]) -> 8
() -> length([nil, z]) -> 6
(fcons([x, l, _cs]) /\ length([_cs, _ds]) /\ length([l, _bs])) -> le([_bs, _ds]) -> 6
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 6
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 6
(le([s(nn1), z])) -> BOT -> 6
(le([z, z])) -> BOT -> 6
(length([ll, _tr])) -> length([cons(x, ll), s(_tr)]) -> 8
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> nil  ;  x -> s(s(z))
})

-------------------------------------------
Step 10, which took 0.016725 s (model generation: 0.013494,  model checking: 0.003231):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_3511, q_gen_3512, q_gen_3513, q_gen_3521, q_gen_3522, q_gen_3527},
Q_f={q_gen_3511},
Delta=
{
<nil>() -> q_gen_3512
<s>(q_gen_3513) -> q_gen_3513
<z>() -> q_gen_3513
<nil, cons>(q_gen_3513, q_gen_3512) -> q_gen_3521
<z, s>(q_gen_3513) -> q_gen_3522
<z, z>() -> q_gen_3522
<s, nil>(q_gen_3513) -> q_gen_3527
<z, nil>() -> q_gen_3527
<s, cons, cons>(q_gen_3522, q_gen_3511) -> q_gen_3511
<s, nil, cons>(q_gen_3513, q_gen_3527) -> q_gen_3511
<z, cons, cons>(q_gen_3522, q_gen_3521) -> q_gen_3511
<z, nil, cons>(q_gen_3513, q_gen_3512) -> q_gen_3511
}

Datatype: <nat, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_3509, q_gen_3510},
Q_f={q_gen_3509},
Delta=
{
<s>(q_gen_3510) -> q_gen_3510
<z>() -> q_gen_3510
<s, s>(q_gen_3509) -> q_gen_3509
<z, s>(q_gen_3510) -> q_gen_3509
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_3508, q_gen_3515},
Q_f={q_gen_3508},
Delta=
{
<s>(q_gen_3515) -> q_gen_3515
<z>() -> q_gen_3515
<cons, s>(q_gen_3515, q_gen_3508) -> q_gen_3508
<nil, z>() -> q_gen_3508
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 15
() -> le([z, s(nn2)]) -> 9
() -> length([nil, z]) -> 7
(fcons([x, l, _cs]) /\ length([_cs, _ds]) /\ length([l, _bs])) -> le([_bs, _ds]) -> 7
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 7
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 7
(le([s(nn1), z])) -> BOT -> 7
(le([z, z])) -> BOT -> 7
(length([ll, _tr])) -> length([cons(x, ll), s(_tr)]) -> 9
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(s(s(z)), nil)  ;  x -> s(z)
})

-------------------------------------------
Step 11, which took 0.013332 s (model generation: 0.012239,  model checking: 0.001093):

Model:
|_
{
fcons -> 
{{{
Q={q_gen_3511, q_gen_3512, q_gen_3513, q_gen_3521, q_gen_3522, q_gen_3527},
Q_f={q_gen_3511},
Delta=
{
<nil>() -> q_gen_3512
<s>(q_gen_3513) -> q_gen_3513
<z>() -> q_gen_3513
<nil, cons>(q_gen_3513, q_gen_3512) -> q_gen_3521
<s, s>(q_gen_3522) -> q_gen_3522
<s, z>(q_gen_3513) -> q_gen_3522
<z, s>(q_gen_3513) -> q_gen_3522
<z, z>() -> q_gen_3522
<s, nil>(q_gen_3513) -> q_gen_3527
<z, nil>() -> q_gen_3527
<s, cons, cons>(q_gen_3522, q_gen_3511) -> q_gen_3511
<s, nil, cons>(q_gen_3513, q_gen_3527) -> q_gen_3511
<z, cons, cons>(q_gen_3522, q_gen_3521) -> q_gen_3511
<z, nil, cons>(q_gen_3513, q_gen_3512) -> q_gen_3511
}

Datatype: <nat, natlist, natlist>
Convolution form: right
}}}
  ;  le -> 
{{{
Q={q_gen_3509, q_gen_3510},
Q_f={q_gen_3509},
Delta=
{
<s>(q_gen_3510) -> q_gen_3510
<z>() -> q_gen_3510
<s, s>(q_gen_3509) -> q_gen_3509
<z, s>(q_gen_3510) -> q_gen_3509
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_3508, q_gen_3515},
Q_f={q_gen_3508},
Delta=
{
<s>(q_gen_3515) -> q_gen_3515
<z>() -> q_gen_3515
<cons, s>(q_gen_3515, q_gen_3508) -> q_gen_3508
<nil, z>() -> q_gen_3508
}

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

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

Teacher's answer:
New clause system:
{
() -> fcons([x, l, cons(x, l)]) -> 18
() -> le([z, s(nn2)]) -> 10
() -> length([nil, z]) -> 8
(fcons([x, l, _cs]) /\ length([_cs, _ds]) /\ length([l, _bs])) -> le([_bs, _ds]) -> 8
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 8
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 8
(le([s(nn1), z])) -> BOT -> 8
(le([z, z])) -> BOT -> 8
(length([ll, _tr])) -> length([cons(x, ll), s(_tr)]) -> 10
}
Sat witness: Found: (() -> fcons([x, l, cons(x, l)]), {
l -> cons(z, cons(z, cons(z, nil)))  ;  x -> s(z)
})

Total time: 60.000033
Reason for stopping: DontKnow. Stopped because: timeout