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


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
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, _wf])) -> length([cons(x, ll), s(_wf)])}
(length([_xf, _yf]) /\ length([_xf, _zf])) -> eq_nat([_yf, _zf])
)
(append, F:
{() -> append([nil, l2, l2])
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)])}
(append([_bg, _cg, _dg]) /\ append([_bg, _cg, _eg])) -> eq_eltlist([_dg, _eg])
)
}

properties:
{(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg])}


over-approximation: {append, length}
under-approximation: {}

Clause system for inference is:

{
() -> append([nil, l2, l2]) -> 0
() -> le([z, s(nn2)]) -> 0
() -> length([nil, z]) -> 0
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 0
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 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, _wf])) -> length([cons(x, ll), s(_wf)]) -> 0
}


Solving took 0.314638 seconds.
Proved
Model:
|_
{
append -> 
{{{
Q={q_gen_1515, q_gen_1521, q_gen_1522, q_gen_1533, q_gen_1534, q_gen_1535},
Q_f={q_gen_1515},
Delta=
{
<cons>(q_gen_1534, q_gen_1533) -> q_gen_1533
<nil>() -> q_gen_1533
<a>() -> q_gen_1534
<b>() -> q_gen_1534
<cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1521
<nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1521
<nil, nil>() -> q_gen_1521
<a, a>() -> q_gen_1522
<a, b>() -> q_gen_1522
<b, a>() -> q_gen_1522
<b, b>() -> q_gen_1522
<cons, cons, cons>(q_gen_1535, q_gen_1515) -> q_gen_1515
<cons, nil, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1515
<nil, nil, nil>() -> q_gen_1515
<a, a, a>() -> q_gen_1535
<a, b, a>() -> q_gen_1535
<b, a, b>() -> q_gen_1535
<b, b, b>() -> q_gen_1535
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<s>(q_gen_1514) -> q_gen_1514
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518, q_gen_1538, q_gen_1540},
Q_f={q_gen_1512},
Delta=
{
<cons>(q_gen_1538, q_gen_1517) -> q_gen_1517
<nil>() -> q_gen_1517
<a>() -> q_gen_1538
<b>() -> q_gen_1538
<s>(q_gen_1540) -> q_gen_1540
<z>() -> q_gen_1540
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<a, s>(q_gen_1540) -> q_gen_1518
<a, z>() -> q_gen_1518
<b, s>(q_gen_1540) -> q_gen_1518
<b, z>() -> q_gen_1518
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.007326 s (model generation: 0.007073,  model checking: 0.000253):

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

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={},
Q_f={},
Delta=
{

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> le([z, s(nn2)]) -> 0
() -> length([nil, z]) -> 3
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 1
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 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, _wf])) -> length([cons(x, ll), s(_wf)]) -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 1, which took 0.007155 s (model generation: 0.006845,  model checking: 0.000310):

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

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={},
Q_f={},
Delta=
{

}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512},
Q_f={q_gen_1512},
Delta=
{
<nil, z>() -> q_gen_1512
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 0
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 1
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 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, _wf])) -> length([cons(x, ll), s(_wf)]) -> 1
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.007877 s (model generation: 0.007745,  model checking: 0.000132):

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

}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<z>() -> q_gen_1514
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512},
Q_f={q_gen_1512},
Delta=
{
<nil, z>() -> q_gen_1512
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 1
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 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, _wf])) -> length([cons(x, ll), s(_wf)]) -> 1
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> nil
})

-------------------------------------------
Step 3, which took 0.007673 s (model generation: 0.007577,  model checking: 0.000096):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515},
Q_f={q_gen_1515},
Delta=
{
<nil, nil, nil>() -> q_gen_1515
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<z>() -> q_gen_1514
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512},
Q_f={q_gen_1512},
Delta=
{
<nil, z>() -> q_gen_1512
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 1
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 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, _wf])) -> length([cons(x, ll), s(_wf)]) -> 4
}
Sat witness: Found: ((length([ll, _wf])) -> length([cons(x, ll), s(_wf)]), {
_wf -> z  ;  ll -> nil  ;  x -> b
})

-------------------------------------------
Step 4, which took 0.008184 s (model generation: 0.007950,  model checking: 0.000234):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515},
Q_f={q_gen_1515},
Delta=
{
<nil, nil, nil>() -> q_gen_1515
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<z>() -> q_gen_1514
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518},
Q_f={q_gen_1512},
Delta=
{
<nil>() -> q_gen_1517
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 1
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 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, _wf])) -> length([cons(x, ll), s(_wf)]) -> 4
}
Sat witness: Found: ((le([nn1, nn2])) -> le([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> s(z)
})

-------------------------------------------
Step 5, which took 0.007855 s (model generation: 0.007684,  model checking: 0.000171):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515},
Q_f={q_gen_1515},
Delta=
{
<nil, nil, nil>() -> q_gen_1515
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518},
Q_f={q_gen_1512},
Delta=
{
<nil>() -> q_gen_1517
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> le([z, s(nn2)]) -> 3
() -> length([nil, z]) -> 3
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 1
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 4
(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, _wf])) -> length([cons(x, ll), s(_wf)]) -> 4
}
Sat witness: Found: ((append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]), {
_ag -> nil  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 6, which took 0.009097 s (model generation: 0.008780,  model checking: 0.000317):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515, q_gen_1521, q_gen_1522},
Q_f={q_gen_1515},
Delta=
{
<nil, nil>() -> q_gen_1521
<b, b>() -> q_gen_1522
<cons, nil, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, nil, nil>() -> q_gen_1515
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518},
Q_f={q_gen_1512},
Delta=
{
<nil>() -> q_gen_1517
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 3
() -> le([z, s(nn2)]) -> 6
() -> length([nil, z]) -> 4
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 2
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 4
(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, _wf])) -> length([cons(x, ll), s(_wf)]) -> 4
}
Sat witness: Found: (() -> le([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 7, which took 0.008940 s (model generation: 0.008569,  model checking: 0.000371):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515, q_gen_1521, q_gen_1522},
Q_f={q_gen_1515},
Delta=
{
<nil, nil>() -> q_gen_1521
<b, b>() -> q_gen_1522
<cons, nil, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, nil, nil>() -> q_gen_1515
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<s>(q_gen_1514) -> q_gen_1514
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518},
Q_f={q_gen_1512},
Delta=
{
<nil>() -> q_gen_1517
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> le([z, s(nn2)]) -> 6
() -> length([nil, z]) -> 4
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 3
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 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, _wf])) -> length([cons(x, ll), s(_wf)]) -> 4
}
Sat witness: Found: (() -> append([nil, l2, l2]), {
l2 -> cons(a, cons(a, nil))
})

-------------------------------------------
Step 8, which took 0.009217 s (model generation: 0.009013,  model checking: 0.000204):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515, q_gen_1521, q_gen_1522},
Q_f={q_gen_1515},
Delta=
{
<cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1521
<nil, nil>() -> q_gen_1521
<a, a>() -> q_gen_1522
<b, b>() -> q_gen_1522
<cons, nil, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, nil, nil>() -> q_gen_1515
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<s>(q_gen_1514) -> q_gen_1514
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518},
Q_f={q_gen_1512},
Delta=
{
<nil>() -> q_gen_1517
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> le([z, s(nn2)]) -> 6
() -> length([nil, z]) -> 4
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 4
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 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, _wf])) -> length([cons(x, ll), s(_wf)]) -> 7
}
Sat witness: Found: ((length([ll, _wf])) -> length([cons(x, ll), s(_wf)]), {
_wf -> z  ;  ll -> nil  ;  x -> a
})

-------------------------------------------
Step 9, which took 0.010646 s (model generation: 0.009181,  model checking: 0.001465):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515, q_gen_1521, q_gen_1522},
Q_f={q_gen_1515},
Delta=
{
<cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1521
<nil, nil>() -> q_gen_1521
<a, a>() -> q_gen_1522
<b, b>() -> q_gen_1522
<cons, nil, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, nil, nil>() -> q_gen_1515
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<s>(q_gen_1514) -> q_gen_1514
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518},
Q_f={q_gen_1512},
Delta=
{
<nil>() -> q_gen_1517
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<a, z>() -> q_gen_1518
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 6
() -> le([z, s(nn2)]) -> 6
() -> length([nil, z]) -> 4
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 4
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 7
(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, _wf])) -> length([cons(x, ll), s(_wf)]) -> 7
}
Sat witness: Found: ((append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]), {
_ag -> cons(b, nil)  ;  h1 -> b  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 10, which took 0.011395 s (model generation: 0.010409,  model checking: 0.000986):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515, q_gen_1521, q_gen_1522, q_gen_1533, q_gen_1534, q_gen_1535},
Q_f={q_gen_1515},
Delta=
{
<nil>() -> q_gen_1533
<b>() -> q_gen_1534
<cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1521
<nil, nil>() -> q_gen_1521
<a, a>() -> q_gen_1522
<b, b>() -> q_gen_1522
<cons, cons, cons>(q_gen_1535, q_gen_1515) -> q_gen_1515
<cons, nil, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1515
<nil, nil, nil>() -> q_gen_1515
<b, b, b>() -> q_gen_1535
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<s>(q_gen_1514) -> q_gen_1514
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518},
Q_f={q_gen_1512},
Delta=
{
<nil>() -> q_gen_1517
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<a, z>() -> q_gen_1518
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> le([z, s(nn2)]) -> 7
() -> length([nil, z]) -> 5
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 5
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 7
(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, _wf])) -> length([cons(x, ll), s(_wf)]) -> 10
}
Sat witness: Found: ((length([ll, _wf])) -> length([cons(x, ll), s(_wf)]), {
_wf -> s(z)  ;  ll -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 11, which took 0.011710 s (model generation: 0.010806,  model checking: 0.000904):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515, q_gen_1521, q_gen_1522, q_gen_1533, q_gen_1534, q_gen_1535},
Q_f={q_gen_1515},
Delta=
{
<nil>() -> q_gen_1533
<b>() -> q_gen_1534
<cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1521
<nil, nil>() -> q_gen_1521
<a, a>() -> q_gen_1522
<b, b>() -> q_gen_1522
<cons, cons, cons>(q_gen_1535, q_gen_1515) -> q_gen_1515
<cons, nil, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1515
<nil, nil, nil>() -> q_gen_1515
<b, b, b>() -> q_gen_1535
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<s>(q_gen_1514) -> q_gen_1514
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518, q_gen_1538, q_gen_1540},
Q_f={q_gen_1512},
Delta=
{
<cons>(q_gen_1538, q_gen_1517) -> q_gen_1517
<nil>() -> q_gen_1517
<b>() -> q_gen_1538
<z>() -> q_gen_1540
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<a, z>() -> q_gen_1518
<b, s>(q_gen_1540) -> q_gen_1518
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 7
() -> le([z, s(nn2)]) -> 7
() -> length([nil, z]) -> 6
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 6
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 10
(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, _wf])) -> length([cons(x, ll), s(_wf)]) -> 10
}
Sat witness: Found: ((append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]), {
_ag -> cons(b, nil)  ;  h1 -> b  ;  l2 -> nil  ;  t1 -> nil
})

-------------------------------------------
Step 12, which took 0.012675 s (model generation: 0.011647,  model checking: 0.001028):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515, q_gen_1521, q_gen_1522, q_gen_1533, q_gen_1534, q_gen_1535},
Q_f={q_gen_1515},
Delta=
{
<nil>() -> q_gen_1533
<b>() -> q_gen_1534
<cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1521
<nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1521
<nil, nil>() -> q_gen_1521
<a, a>() -> q_gen_1522
<b, b>() -> q_gen_1522
<cons, cons, cons>(q_gen_1535, q_gen_1515) -> q_gen_1515
<cons, nil, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1515
<nil, nil, nil>() -> q_gen_1515
<b, b, b>() -> q_gen_1535
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<s>(q_gen_1514) -> q_gen_1514
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518, q_gen_1538, q_gen_1540},
Q_f={q_gen_1512},
Delta=
{
<cons>(q_gen_1538, q_gen_1517) -> q_gen_1517
<nil>() -> q_gen_1517
<b>() -> q_gen_1538
<z>() -> q_gen_1540
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<a, z>() -> q_gen_1518
<b, s>(q_gen_1540) -> q_gen_1518
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 8
() -> le([z, s(nn2)]) -> 8
() -> length([nil, z]) -> 7
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 7
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 10
(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, _wf])) -> length([cons(x, ll), s(_wf)]) -> 13
}
Sat witness: Found: ((length([ll, _wf])) -> length([cons(x, ll), s(_wf)]), {
_wf -> s(z)  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 13, which took 0.014588 s (model generation: 0.012347,  model checking: 0.002241):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515, q_gen_1521, q_gen_1522, q_gen_1533, q_gen_1534, q_gen_1535},
Q_f={q_gen_1515},
Delta=
{
<nil>() -> q_gen_1533
<b>() -> q_gen_1534
<cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1521
<nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1521
<nil, nil>() -> q_gen_1521
<a, a>() -> q_gen_1522
<b, b>() -> q_gen_1522
<cons, cons, cons>(q_gen_1535, q_gen_1515) -> q_gen_1515
<cons, nil, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1515
<nil, nil, nil>() -> q_gen_1515
<b, b, b>() -> q_gen_1535
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<s>(q_gen_1514) -> q_gen_1514
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518, q_gen_1538, q_gen_1540},
Q_f={q_gen_1512},
Delta=
{
<cons>(q_gen_1538, q_gen_1517) -> q_gen_1517
<nil>() -> q_gen_1517
<a>() -> q_gen_1538
<b>() -> q_gen_1538
<z>() -> q_gen_1540
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<a, z>() -> q_gen_1518
<b, s>(q_gen_1540) -> q_gen_1518
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 9
() -> le([z, s(nn2)]) -> 9
() -> length([nil, z]) -> 8
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 8
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 13
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 9
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 9
(le([s(nn1), z])) -> BOT -> 9
(le([z, z])) -> BOT -> 9
(length([ll, _wf])) -> length([cons(x, ll), s(_wf)]) -> 13
}
Sat witness: Found: ((append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]), {
_ag -> cons(b, nil)  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 14, which took 0.013887 s (model generation: 0.012609,  model checking: 0.001278):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515, q_gen_1521, q_gen_1522, q_gen_1533, q_gen_1534, q_gen_1535},
Q_f={q_gen_1515},
Delta=
{
<nil>() -> q_gen_1533
<b>() -> q_gen_1534
<cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1521
<nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1521
<nil, nil>() -> q_gen_1521
<a, a>() -> q_gen_1522
<b, b>() -> q_gen_1522
<cons, cons, cons>(q_gen_1535, q_gen_1515) -> q_gen_1515
<cons, nil, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1515
<nil, nil, nil>() -> q_gen_1515
<a, b, a>() -> q_gen_1535
<b, b, b>() -> q_gen_1535
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<s>(q_gen_1514) -> q_gen_1514
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518, q_gen_1538, q_gen_1540},
Q_f={q_gen_1512},
Delta=
{
<cons>(q_gen_1538, q_gen_1517) -> q_gen_1517
<nil>() -> q_gen_1517
<a>() -> q_gen_1538
<b>() -> q_gen_1538
<z>() -> q_gen_1540
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<a, z>() -> q_gen_1518
<b, s>(q_gen_1540) -> q_gen_1518
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 10
() -> le([z, s(nn2)]) -> 10
() -> length([nil, z]) -> 9
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 9
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 13
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 10
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 10
(le([s(nn1), z])) -> BOT -> 10
(le([z, z])) -> BOT -> 10
(length([ll, _wf])) -> length([cons(x, ll), s(_wf)]) -> 16
}
Sat witness: Found: ((length([ll, _wf])) -> length([cons(x, ll), s(_wf)]), {
_wf -> s(z)  ;  ll -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 15, which took 0.015037 s (model generation: 0.012768,  model checking: 0.002269):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515, q_gen_1521, q_gen_1522, q_gen_1533, q_gen_1534, q_gen_1535},
Q_f={q_gen_1515},
Delta=
{
<nil>() -> q_gen_1533
<b>() -> q_gen_1534
<cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1521
<nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1521
<nil, nil>() -> q_gen_1521
<a, a>() -> q_gen_1522
<b, b>() -> q_gen_1522
<cons, cons, cons>(q_gen_1535, q_gen_1515) -> q_gen_1515
<cons, nil, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1515
<nil, nil, nil>() -> q_gen_1515
<a, b, a>() -> q_gen_1535
<b, b, b>() -> q_gen_1535
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<s>(q_gen_1514) -> q_gen_1514
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518, q_gen_1538, q_gen_1540},
Q_f={q_gen_1512},
Delta=
{
<cons>(q_gen_1538, q_gen_1517) -> q_gen_1517
<nil>() -> q_gen_1517
<a>() -> q_gen_1538
<b>() -> q_gen_1538
<z>() -> q_gen_1540
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<a, s>(q_gen_1540) -> q_gen_1518
<a, z>() -> q_gen_1518
<b, s>(q_gen_1540) -> q_gen_1518
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 11
() -> le([z, s(nn2)]) -> 11
() -> length([nil, z]) -> 10
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 10
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 16
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 11
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 11
(le([s(nn1), z])) -> BOT -> 11
(le([z, z])) -> BOT -> 11
(length([ll, _wf])) -> length([cons(x, ll), s(_wf)]) -> 16
}
Sat witness: Found: ((append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]), {
_ag -> cons(a, nil)  ;  h1 -> b  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 16, which took 0.017024 s (model generation: 0.015745,  model checking: 0.001279):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515, q_gen_1521, q_gen_1522, q_gen_1533, q_gen_1534, q_gen_1535},
Q_f={q_gen_1515},
Delta=
{
<nil>() -> q_gen_1533
<a>() -> q_gen_1534
<b>() -> q_gen_1534
<cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1521
<nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1521
<nil, nil>() -> q_gen_1521
<a, a>() -> q_gen_1522
<b, b>() -> q_gen_1522
<cons, cons, cons>(q_gen_1535, q_gen_1515) -> q_gen_1515
<cons, nil, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1515
<nil, nil, nil>() -> q_gen_1515
<a, b, a>() -> q_gen_1535
<b, a, b>() -> q_gen_1535
<b, b, b>() -> q_gen_1535
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<s>(q_gen_1514) -> q_gen_1514
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518, q_gen_1538, q_gen_1540},
Q_f={q_gen_1512},
Delta=
{
<cons>(q_gen_1538, q_gen_1517) -> q_gen_1517
<nil>() -> q_gen_1517
<a>() -> q_gen_1538
<b>() -> q_gen_1538
<z>() -> q_gen_1540
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<a, s>(q_gen_1540) -> q_gen_1518
<a, z>() -> q_gen_1518
<b, s>(q_gen_1540) -> q_gen_1518
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 12
() -> le([z, s(nn2)]) -> 12
() -> length([nil, z]) -> 11
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 11
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 16
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 12
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 12
(le([s(nn1), z])) -> BOT -> 12
(le([z, z])) -> BOT -> 12
(length([ll, _wf])) -> length([cons(x, ll), s(_wf)]) -> 19
}
Sat witness: Found: ((length([ll, _wf])) -> length([cons(x, ll), s(_wf)]), {
_wf -> s(s(z))  ;  ll -> cons(a, nil)  ;  x -> b
})

-------------------------------------------
Step 17, which took 0.019166 s (model generation: 0.017627,  model checking: 0.001539):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515, q_gen_1521, q_gen_1522, q_gen_1533, q_gen_1534, q_gen_1535},
Q_f={q_gen_1515},
Delta=
{
<nil>() -> q_gen_1533
<a>() -> q_gen_1534
<b>() -> q_gen_1534
<cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1521
<nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1521
<nil, nil>() -> q_gen_1521
<a, a>() -> q_gen_1522
<b, b>() -> q_gen_1522
<cons, cons, cons>(q_gen_1535, q_gen_1515) -> q_gen_1515
<cons, nil, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1515
<nil, nil, nil>() -> q_gen_1515
<a, b, a>() -> q_gen_1535
<b, a, b>() -> q_gen_1535
<b, b, b>() -> q_gen_1535
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<s>(q_gen_1514) -> q_gen_1514
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518, q_gen_1538, q_gen_1540},
Q_f={q_gen_1512},
Delta=
{
<cons>(q_gen_1538, q_gen_1517) -> q_gen_1517
<nil>() -> q_gen_1517
<a>() -> q_gen_1538
<b>() -> q_gen_1538
<s>(q_gen_1540) -> q_gen_1540
<z>() -> q_gen_1540
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<a, s>(q_gen_1540) -> q_gen_1518
<a, z>() -> q_gen_1518
<b, s>(q_gen_1540) -> q_gen_1518
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 13
() -> le([z, s(nn2)]) -> 13
() -> length([nil, z]) -> 12
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 12
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 19
(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, z])) -> BOT -> 13
(length([ll, _wf])) -> length([cons(x, ll), s(_wf)]) -> 19
}
Sat witness: Found: ((append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]), {
_ag -> cons(a, nil)  ;  h1 -> a  ;  l2 -> cons(a, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 18, which took 0.020578 s (model generation: 0.018028,  model checking: 0.002550):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515, q_gen_1521, q_gen_1522, q_gen_1533, q_gen_1534, q_gen_1535},
Q_f={q_gen_1515},
Delta=
{
<nil>() -> q_gen_1533
<a>() -> q_gen_1534
<b>() -> q_gen_1534
<cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1521
<nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1521
<nil, nil>() -> q_gen_1521
<a, a>() -> q_gen_1522
<b, b>() -> q_gen_1522
<cons, cons, cons>(q_gen_1535, q_gen_1515) -> q_gen_1515
<cons, nil, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1515
<nil, nil, nil>() -> q_gen_1515
<a, a, a>() -> q_gen_1535
<a, b, a>() -> q_gen_1535
<b, a, b>() -> q_gen_1535
<b, b, b>() -> q_gen_1535
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<s>(q_gen_1514) -> q_gen_1514
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518, q_gen_1538, q_gen_1540},
Q_f={q_gen_1512},
Delta=
{
<cons>(q_gen_1538, q_gen_1517) -> q_gen_1517
<nil>() -> q_gen_1517
<a>() -> q_gen_1538
<b>() -> q_gen_1538
<s>(q_gen_1540) -> q_gen_1540
<z>() -> q_gen_1540
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<a, s>(q_gen_1540) -> q_gen_1518
<a, z>() -> q_gen_1518
<b, s>(q_gen_1540) -> q_gen_1518
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 14
() -> le([z, s(nn2)]) -> 14
() -> length([nil, z]) -> 13
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 13
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 22
(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, z])) -> BOT -> 14
(length([ll, _wf])) -> length([cons(x, ll), s(_wf)]) -> 20
}
Sat witness: Found: ((append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]), {
_ag -> cons(b, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(b, nil)  ;  t1 -> nil
})

-------------------------------------------
Step 19, which took 0.025733 s (model generation: 0.020725,  model checking: 0.005008):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515, q_gen_1521, q_gen_1522, q_gen_1533, q_gen_1534, q_gen_1535},
Q_f={q_gen_1515},
Delta=
{
<cons>(q_gen_1534, q_gen_1533) -> q_gen_1533
<nil>() -> q_gen_1533
<a>() -> q_gen_1534
<b>() -> q_gen_1534
<cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1521
<nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1521
<nil, nil>() -> q_gen_1521
<a, a>() -> q_gen_1522
<b, b>() -> q_gen_1522
<cons, cons, cons>(q_gen_1535, q_gen_1515) -> q_gen_1515
<cons, nil, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1515
<nil, nil, nil>() -> q_gen_1515
<a, a, a>() -> q_gen_1535
<a, b, a>() -> q_gen_1535
<b, a, b>() -> q_gen_1535
<b, b, b>() -> q_gen_1535
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<s>(q_gen_1514) -> q_gen_1514
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518, q_gen_1538, q_gen_1540},
Q_f={q_gen_1512},
Delta=
{
<cons>(q_gen_1538, q_gen_1517) -> q_gen_1517
<nil>() -> q_gen_1517
<a>() -> q_gen_1538
<b>() -> q_gen_1538
<s>(q_gen_1540) -> q_gen_1540
<z>() -> q_gen_1540
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<a, s>(q_gen_1540) -> q_gen_1518
<a, z>() -> q_gen_1518
<b, s>(q_gen_1540) -> q_gen_1518
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 15
() -> le([z, s(nn2)]) -> 15
() -> length([nil, z]) -> 14
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 14
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 25
(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, z])) -> BOT -> 15
(length([ll, _wf])) -> length([cons(x, ll), s(_wf)]) -> 21
}
Sat witness: Found: ((append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]), {
_ag -> cons(a, cons(b, nil))  ;  h1 -> a  ;  l2 -> cons(a, cons(b, nil))  ;  t1 -> nil
})

-------------------------------------------
Step 20, which took 0.029936 s (model generation: 0.024220,  model checking: 0.005716):

Model:
|_
{
append -> 
{{{
Q={q_gen_1515, q_gen_1521, q_gen_1522, q_gen_1533, q_gen_1534, q_gen_1535},
Q_f={q_gen_1515},
Delta=
{
<cons>(q_gen_1534, q_gen_1533) -> q_gen_1533
<nil>() -> q_gen_1533
<a>() -> q_gen_1534
<b>() -> q_gen_1534
<cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1521
<nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1521
<nil, nil>() -> q_gen_1521
<a, a>() -> q_gen_1522
<b, a>() -> q_gen_1522
<b, b>() -> q_gen_1522
<cons, cons, cons>(q_gen_1535, q_gen_1515) -> q_gen_1515
<cons, nil, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, cons, cons>(q_gen_1522, q_gen_1521) -> q_gen_1515
<nil, nil, cons>(q_gen_1534, q_gen_1533) -> q_gen_1515
<nil, nil, nil>() -> q_gen_1515
<a, a, a>() -> q_gen_1535
<a, b, a>() -> q_gen_1535
<b, a, b>() -> q_gen_1535
<b, b, b>() -> q_gen_1535
}

Datatype: <eltlist, eltlist, eltlist>
Convolution form: left
}}}
  ;  le -> 
{{{
Q={q_gen_1513, q_gen_1514},
Q_f={q_gen_1513},
Delta=
{
<s>(q_gen_1514) -> q_gen_1514
<z>() -> q_gen_1514
<s, s>(q_gen_1513) -> q_gen_1513
<z, s>(q_gen_1514) -> q_gen_1513
}

Datatype: <nat, nat>
Convolution form: left
}}}
  ;  length -> 
{{{
Q={q_gen_1512, q_gen_1517, q_gen_1518, q_gen_1538, q_gen_1540},
Q_f={q_gen_1512},
Delta=
{
<cons>(q_gen_1538, q_gen_1517) -> q_gen_1517
<nil>() -> q_gen_1517
<a>() -> q_gen_1538
<b>() -> q_gen_1538
<s>(q_gen_1540) -> q_gen_1540
<z>() -> q_gen_1540
<cons, s>(q_gen_1518, q_gen_1517) -> q_gen_1512
<nil, z>() -> q_gen_1512
<a, s>(q_gen_1540) -> q_gen_1518
<a, z>() -> q_gen_1518
<b, s>(q_gen_1540) -> q_gen_1518
<b, z>() -> q_gen_1518
}

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

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

Teacher's answer:
New clause system:
{
() -> append([nil, l2, l2]) -> 16
() -> le([z, s(nn2)]) -> 16
() -> length([nil, z]) -> 15
(append([l1, l2, _gg]) /\ le([z, _fg]) /\ length([_gg, _hg]) /\ length([l1, _fg])) -> le([z, _hg]) -> 15
(append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]) -> 28
(le([nn1, nn2])) -> le([s(nn1), s(nn2)]) -> 16
(le([s(nn1), s(nn2)])) -> le([nn1, nn2]) -> 16
(le([s(nn1), z])) -> BOT -> 16
(le([z, z])) -> BOT -> 16
(length([ll, _wf])) -> length([cons(x, ll), s(_wf)]) -> 22
}
Sat witness: Found: ((append([t1, l2, _ag])) -> append([cons(h1, t1), l2, cons(h1, _ag)]), {
_ag -> cons(b, cons(a, nil))  ;  h1 -> b  ;  l2 -> cons(b, cons(a, nil))  ;  t1 -> nil
})

Total time: 0.314638
Reason for stopping: Proved