Solving ../../benchmarks/false/prefix_count.smt2...

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


Learning problem is:

env: {
elt -> {a, b}  ;  eltlist -> {cons, nil}  ;  nat -> {s, z}
}
definition:
{
(leq, P:
{() -> leq([z, s(nn2)])
() -> leq([z, z])
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)])
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2])
(leq([s(nn1), z])) -> BOT}
)
(prefix, P:
{() -> prefix([nil, y])
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)])
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys])
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT
(prefix([cons(z, zs), nil])) -> BOT}
)
(count, F:
{() -> count([x, nil, z])
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)])
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia])}
(count([_pia, _qia, _ria]) /\ count([_pia, _qia, _sia])) -> eq_nat([_ria, _sia])
)
}

properties:
{(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia])}


over-approximation: {count, prefix}
under-approximation: {leq}

Clause system for inference is:

{
() -> count([x, nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
() -> prefix([nil, y]) -> 0
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 0
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 0
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 0
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 0
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 0
(leq([s(nn1), z])) -> BOT -> 0
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 0
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 0
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 0
(prefix([cons(z, zs), nil])) -> BOT -> 0
}


Solving took 0.243719 seconds.
Disproved
-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.010600 s (model generation: 0.009812,  model checking: 0.000788):

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
() -> prefix([nil, y]) -> 3
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 1
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 1
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 1
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 1
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 1
(prefix([cons(z, zs), nil])) -> BOT -> 1
}
Sat witness: Found: (() -> prefix([nil, y]), {
y -> nil
})

-------------------------------------------
Step 1, which took 0.010199 s (model generation: 0.010110,  model checking: 0.000089):

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

}

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

}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  prefix -> 
{{{
Q={q_gen_6573},
Q_f={q_gen_6573},
Delta=
{
<nil, nil>() -> q_gen_6573
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 3
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 1
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 1
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 1
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 1
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 1
(prefix([cons(z, zs), nil])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([z, z]), {

})

-------------------------------------------
Step 2, which took 0.010622 s (model generation: 0.010494,  model checking: 0.000128):

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

}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_6574},
Q_f={q_gen_6574},
Delta=
{
<z, z>() -> q_gen_6574
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  prefix -> 
{{{
Q={q_gen_6573},
Q_f={q_gen_6573},
Delta=
{
<nil, nil>() -> q_gen_6573
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 3
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 1
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 1
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 1
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 1
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 1
(prefix([cons(z, zs), nil])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 3, which took 0.010656 s (model generation: 0.010457,  model checking: 0.000199):

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

}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_6574, q_gen_6576},
Q_f={q_gen_6574},
Delta=
{
<z>() -> q_gen_6576
<z, s>(q_gen_6576) -> q_gen_6574
<z, z>() -> q_gen_6574
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  prefix -> 
{{{
Q={q_gen_6573},
Q_f={q_gen_6573},
Delta=
{
<nil, nil>() -> q_gen_6573
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 3
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 1
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 1
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 1
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 1
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 1
(prefix([cons(z, zs), nil])) -> BOT -> 1
}
Sat witness: Found: (() -> count([x, nil, z]), {
x -> b
})

-------------------------------------------
Step 4, which took 0.016581 s (model generation: 0.010556,  model checking: 0.006025):

Model:
|_
{
count -> 
{{{
Q={q_gen_6577},
Q_f={q_gen_6577},
Delta=
{
<b, nil, z>() -> q_gen_6577
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_6574, q_gen_6576},
Q_f={q_gen_6574},
Delta=
{
<z>() -> q_gen_6576
<z, s>(q_gen_6576) -> q_gen_6574
<z, z>() -> q_gen_6574
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  prefix -> 
{{{
Q={q_gen_6573},
Q_f={q_gen_6573},
Delta=
{
<nil, nil>() -> q_gen_6573
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 3
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 1
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 1
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 4
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 2
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 2
(prefix([cons(z, zs), nil])) -> BOT -> 2
}
Sat witness: Found: ((prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]), {
y2 -> b  ;  ys -> nil  ;  zs -> nil
})

-------------------------------------------
Step 5, which took 0.011126 s (model generation: 0.010874,  model checking: 0.000252):

Model:
|_
{
count -> 
{{{
Q={q_gen_6577},
Q_f={q_gen_6577},
Delta=
{
<b, nil, z>() -> q_gen_6577
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_6574, q_gen_6576},
Q_f={q_gen_6574},
Delta=
{
<z>() -> q_gen_6576
<z, s>(q_gen_6576) -> q_gen_6574
<z, z>() -> q_gen_6574
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  prefix -> 
{{{
Q={q_gen_6573, q_gen_6579},
Q_f={q_gen_6573},
Delta=
{
<cons, cons>(q_gen_6579, q_gen_6573) -> q_gen_6573
<nil, nil>() -> q_gen_6573
<b, b>() -> q_gen_6579
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 3
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 1
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 1
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 4
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 2
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 2
(prefix([cons(z, zs), nil])) -> BOT -> 2
}
Sat witness: Found: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 6, which took 0.011491 s (model generation: 0.011116,  model checking: 0.000375):

Model:
|_
{
count -> 
{{{
Q={q_gen_6577},
Q_f={q_gen_6577},
Delta=
{
<b, nil, z>() -> q_gen_6577
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_6574, q_gen_6576},
Q_f={q_gen_6574},
Delta=
{
<z>() -> q_gen_6576
<s, s>(q_gen_6574) -> q_gen_6574
<z, s>(q_gen_6576) -> q_gen_6574
<z, z>() -> q_gen_6574
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  prefix -> 
{{{
Q={q_gen_6573, q_gen_6579},
Q_f={q_gen_6573},
Delta=
{
<cons, cons>(q_gen_6579, q_gen_6573) -> q_gen_6573
<nil, nil>() -> q_gen_6573
<b, b>() -> q_gen_6579
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 3
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 1
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 1
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 4
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 2
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 2
(prefix([cons(z, zs), nil])) -> BOT -> 2
}
Sat witness: Found: ((count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]), {
_oia -> z  ;  h1 -> a  ;  t1 -> nil  ;  x -> b
})

-------------------------------------------
Step 7, which took 0.011728 s (model generation: 0.011345,  model checking: 0.000383):

Model:
|_
{
count -> 
{{{
Q={q_gen_6577, q_gen_6582, q_gen_6583},
Q_f={q_gen_6577},
Delta=
{
<nil>() -> q_gen_6582
<a>() -> q_gen_6583
<b, cons, z>(q_gen_6583, q_gen_6582) -> q_gen_6577
<b, nil, z>() -> q_gen_6577
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_6574, q_gen_6576},
Q_f={q_gen_6574},
Delta=
{
<z>() -> q_gen_6576
<s, s>(q_gen_6574) -> q_gen_6574
<z, s>(q_gen_6576) -> q_gen_6574
<z, z>() -> q_gen_6574
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  prefix -> 
{{{
Q={q_gen_6573, q_gen_6579},
Q_f={q_gen_6573},
Delta=
{
<cons, cons>(q_gen_6579, q_gen_6573) -> q_gen_6573
<nil, nil>() -> q_gen_6573
<b, b>() -> q_gen_6579
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 3
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 1
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 4
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 4
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 2
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 2
(prefix([cons(z, zs), nil])) -> BOT -> 2
}
Sat witness: Found: ((count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]), {
_nia -> z  ;  t1 -> nil  ;  x -> b
})

-------------------------------------------
Step 8, which took 0.014288 s (model generation: 0.013852,  model checking: 0.000436):

Model:
|_
{
count -> 
{{{
Q={q_gen_6577, q_gen_6582, q_gen_6583, q_gen_6585},
Q_f={q_gen_6577},
Delta=
{
<nil>() -> q_gen_6582
<a>() -> q_gen_6583
<b>() -> q_gen_6583
<nil, z>() -> q_gen_6585
<b, cons, s>(q_gen_6583, q_gen_6585) -> q_gen_6577
<b, cons, z>(q_gen_6583, q_gen_6582) -> q_gen_6577
<b, nil, z>() -> q_gen_6577
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_6574, q_gen_6576},
Q_f={q_gen_6574},
Delta=
{
<z>() -> q_gen_6576
<s, s>(q_gen_6574) -> q_gen_6574
<z, s>(q_gen_6576) -> q_gen_6574
<z, z>() -> q_gen_6574
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  prefix -> 
{{{
Q={q_gen_6573, q_gen_6579},
Q_f={q_gen_6573},
Delta=
{
<cons, cons>(q_gen_6579, q_gen_6573) -> q_gen_6573
<nil, nil>() -> q_gen_6573
<b, b>() -> q_gen_6579
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 3
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 4
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 4
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 4
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 2
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 2
(prefix([cons(z, zs), nil])) -> BOT -> 2
}
Sat witness: Found: ((count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]), {
_tia -> s(z)  ;  _uia -> z  ;  l1 -> cons(b, nil)  ;  l2 -> cons(b, nil)  ;  x -> b
})

-------------------------------------------
Step 9, which took 0.015235 s (model generation: 0.012478,  model checking: 0.002757):

Model:
|_
{
count -> 
{{{
Q={q_gen_6577, q_gen_6582, q_gen_6583, q_gen_6585},
Q_f={q_gen_6577},
Delta=
{
<nil>() -> q_gen_6582
<a>() -> q_gen_6583
<b>() -> q_gen_6583
<nil, z>() -> q_gen_6585
<b, cons, s>(q_gen_6583, q_gen_6585) -> q_gen_6577
<b, cons, z>(q_gen_6583, q_gen_6582) -> q_gen_6577
<b, nil, z>() -> q_gen_6577
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_6574, q_gen_6576},
Q_f={q_gen_6574},
Delta=
{
<z>() -> q_gen_6576
<s, s>(q_gen_6574) -> q_gen_6574
<s, z>(q_gen_6576) -> q_gen_6574
<z, s>(q_gen_6576) -> q_gen_6574
<z, z>() -> q_gen_6574
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  prefix -> 
{{{
Q={q_gen_6573, q_gen_6579},
Q_f={q_gen_6573},
Delta=
{
<cons, cons>(q_gen_6579, q_gen_6573) -> q_gen_6573
<nil, nil>() -> q_gen_6573
<b, b>() -> q_gen_6579
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 3
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 4
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 4
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 5
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 4
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 3
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 3
(prefix([cons(z, zs), nil])) -> BOT -> 3
}
Sat witness: Found: ((leq([s(nn1), z])) -> BOT, {
nn1 -> z
})

-------------------------------------------
Step 10, which took 0.014924 s (model generation: 0.012455,  model checking: 0.002469):

Model:
|_
{
count -> 
{{{
Q={q_gen_6577, q_gen_6582, q_gen_6583, q_gen_6585, q_gen_6586, q_gen_6587},
Q_f={q_gen_6577},
Delta=
{
<nil>() -> q_gen_6582
<a>() -> q_gen_6583
<b>() -> q_gen_6586
<nil, z>() -> q_gen_6585
<b, cons, s>(q_gen_6586, q_gen_6585) -> q_gen_6577
<b, cons, z>(q_gen_6583, q_gen_6582) -> q_gen_6577
<b, nil, z>() -> q_gen_6577
<b, cons, z>(q_gen_6586, q_gen_6582) -> q_gen_6587
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_6574, q_gen_6576, q_gen_6588},
Q_f={q_gen_6574},
Delta=
{
<z>() -> q_gen_6576
<s, s>(q_gen_6574) -> q_gen_6574
<z, s>(q_gen_6576) -> q_gen_6574
<z, z>() -> q_gen_6574
<s, z>(q_gen_6576) -> q_gen_6588
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  prefix -> 
{{{
Q={q_gen_6573, q_gen_6579},
Q_f={q_gen_6573},
Delta=
{
<cons, cons>(q_gen_6579, q_gen_6573) -> q_gen_6573
<nil, nil>() -> q_gen_6573
<b, b>() -> q_gen_6579
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
() -> prefix([nil, y]) -> 6
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 4
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 4
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 3
(leq([s(nn1), z])) -> BOT -> 5
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 4
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 4
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 4
(prefix([cons(z, zs), nil])) -> BOT -> 4
}
Sat witness: Found: (() -> prefix([nil, y]), {
y -> cons(b, nil)
})

-------------------------------------------
Step 11, which took 0.013262 s (model generation: 0.012833,  model checking: 0.000429):

Model:
|_
{
count -> 
{{{
Q={q_gen_6577, q_gen_6582, q_gen_6583, q_gen_6585, q_gen_6586, q_gen_6587},
Q_f={q_gen_6577},
Delta=
{
<nil>() -> q_gen_6582
<a>() -> q_gen_6583
<b>() -> q_gen_6586
<nil, z>() -> q_gen_6585
<b, cons, s>(q_gen_6586, q_gen_6585) -> q_gen_6577
<b, cons, z>(q_gen_6583, q_gen_6582) -> q_gen_6577
<b, nil, z>() -> q_gen_6577
<b, cons, z>(q_gen_6586, q_gen_6582) -> q_gen_6587
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_6574, q_gen_6576, q_gen_6588},
Q_f={q_gen_6574},
Delta=
{
<z>() -> q_gen_6576
<s, s>(q_gen_6574) -> q_gen_6574
<z, s>(q_gen_6576) -> q_gen_6574
<z, z>() -> q_gen_6574
<s, z>(q_gen_6576) -> q_gen_6588
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  prefix -> 
{{{
Q={q_gen_6573, q_gen_6579, q_gen_6590, q_gen_6591},
Q_f={q_gen_6573},
Delta=
{
<nil>() -> q_gen_6590
<b>() -> q_gen_6591
<cons, cons>(q_gen_6579, q_gen_6573) -> q_gen_6573
<nil, cons>(q_gen_6591, q_gen_6590) -> q_gen_6573
<nil, nil>() -> q_gen_6573
<b, b>() -> q_gen_6579
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> prefix([nil, y]) -> 6
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 4
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 4
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 5
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 4
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 4
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 4
(prefix([cons(z, zs), nil])) -> BOT -> 4
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 12, which took 0.014323 s (model generation: 0.013961,  model checking: 0.000362):

Model:
|_
{
count -> 
{{{
Q={q_gen_6577, q_gen_6582, q_gen_6583, q_gen_6585, q_gen_6586, q_gen_6587},
Q_f={q_gen_6577},
Delta=
{
<nil>() -> q_gen_6582
<a>() -> q_gen_6583
<b>() -> q_gen_6586
<nil, z>() -> q_gen_6585
<b, cons, s>(q_gen_6586, q_gen_6585) -> q_gen_6577
<b, cons, z>(q_gen_6583, q_gen_6582) -> q_gen_6577
<b, nil, z>() -> q_gen_6577
<b, cons, z>(q_gen_6586, q_gen_6582) -> q_gen_6587
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_6574, q_gen_6576, q_gen_6588},
Q_f={q_gen_6574},
Delta=
{
<s>(q_gen_6576) -> q_gen_6576
<z>() -> q_gen_6576
<s, s>(q_gen_6574) -> q_gen_6574
<z, s>(q_gen_6576) -> q_gen_6574
<z, z>() -> q_gen_6574
<s, z>(q_gen_6576) -> q_gen_6588
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  prefix -> 
{{{
Q={q_gen_6573, q_gen_6579, q_gen_6590, q_gen_6591},
Q_f={q_gen_6573},
Delta=
{
<nil>() -> q_gen_6590
<b>() -> q_gen_6591
<cons, cons>(q_gen_6579, q_gen_6573) -> q_gen_6573
<nil, cons>(q_gen_6591, q_gen_6590) -> q_gen_6573
<nil, nil>() -> q_gen_6573
<b, b>() -> q_gen_6579
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> prefix([nil, y]) -> 6
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 4
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 4
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 5
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 4
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 4
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 4
(prefix([cons(z, zs), nil])) -> BOT -> 4
}
Sat witness: Found: (() -> count([x, nil, z]), {
x -> a
})

-------------------------------------------
Step 13, which took 0.017893 s (model generation: 0.013460,  model checking: 0.004433):

Model:
|_
{
count -> 
{{{
Q={q_gen_6577, q_gen_6582, q_gen_6583, q_gen_6585, q_gen_6586, q_gen_6587},
Q_f={q_gen_6577},
Delta=
{
<nil>() -> q_gen_6582
<a>() -> q_gen_6583
<b>() -> q_gen_6586
<nil, z>() -> q_gen_6585
<a, nil, z>() -> q_gen_6577
<b, cons, s>(q_gen_6586, q_gen_6585) -> q_gen_6577
<b, cons, z>(q_gen_6583, q_gen_6582) -> q_gen_6577
<b, nil, z>() -> q_gen_6577
<b, cons, z>(q_gen_6586, q_gen_6582) -> q_gen_6587
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_6574, q_gen_6576, q_gen_6588},
Q_f={q_gen_6574},
Delta=
{
<s>(q_gen_6576) -> q_gen_6576
<z>() -> q_gen_6576
<s, s>(q_gen_6574) -> q_gen_6574
<z, s>(q_gen_6576) -> q_gen_6574
<z, z>() -> q_gen_6574
<s, z>(q_gen_6576) -> q_gen_6588
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  prefix -> 
{{{
Q={q_gen_6573, q_gen_6579, q_gen_6590, q_gen_6591},
Q_f={q_gen_6573},
Delta=
{
<nil>() -> q_gen_6590
<b>() -> q_gen_6591
<cons, cons>(q_gen_6579, q_gen_6573) -> q_gen_6573
<nil, cons>(q_gen_6591, q_gen_6590) -> q_gen_6573
<nil, nil>() -> q_gen_6573
<b, b>() -> q_gen_6579
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> prefix([nil, y]) -> 6
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 4
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 4
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 5
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 7
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 5
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 5
(prefix([cons(z, zs), nil])) -> BOT -> 5
}
Sat witness: Found: ((prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]), {
y2 -> a  ;  ys -> nil  ;  zs -> nil
})

-------------------------------------------
Step 14, which took 0.015831 s (model generation: 0.014010,  model checking: 0.001821):

Model:
|_
{
count -> 
{{{
Q={q_gen_6577, q_gen_6582, q_gen_6583, q_gen_6585, q_gen_6586, q_gen_6587},
Q_f={q_gen_6577},
Delta=
{
<nil>() -> q_gen_6582
<a>() -> q_gen_6583
<b>() -> q_gen_6586
<nil, z>() -> q_gen_6585
<a, nil, z>() -> q_gen_6577
<b, cons, s>(q_gen_6586, q_gen_6585) -> q_gen_6577
<b, cons, z>(q_gen_6583, q_gen_6582) -> q_gen_6577
<b, nil, z>() -> q_gen_6577
<b, cons, z>(q_gen_6586, q_gen_6582) -> q_gen_6587
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_6574, q_gen_6576, q_gen_6588},
Q_f={q_gen_6574},
Delta=
{
<s>(q_gen_6576) -> q_gen_6576
<z>() -> q_gen_6576
<s, s>(q_gen_6574) -> q_gen_6574
<z, s>(q_gen_6576) -> q_gen_6574
<z, z>() -> q_gen_6574
<s, z>(q_gen_6576) -> q_gen_6588
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  prefix -> 
{{{
Q={q_gen_6573, q_gen_6579, q_gen_6590, q_gen_6591},
Q_f={q_gen_6573},
Delta=
{
<nil>() -> q_gen_6590
<b>() -> q_gen_6591
<cons, cons>(q_gen_6579, q_gen_6573) -> q_gen_6573
<nil, cons>(q_gen_6591, q_gen_6590) -> q_gen_6573
<nil, nil>() -> q_gen_6573
<a, a>() -> q_gen_6579
<b, b>() -> q_gen_6579
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> prefix([nil, y]) -> 6
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 4
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 4
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 7
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 5
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 5
(prefix([cons(z, zs), nil])) -> BOT -> 5
}
Sat witness: Found: ((count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]), {
_oia -> z  ;  h1 -> b  ;  t1 -> nil  ;  x -> a
})

-------------------------------------------
Step 15, which took 0.015946 s (model generation: 0.014443,  model checking: 0.001503):

Model:
|_
{
count -> 
{{{
Q={q_gen_6577, q_gen_6582, q_gen_6583, q_gen_6585, q_gen_6586, q_gen_6587},
Q_f={q_gen_6577},
Delta=
{
<nil>() -> q_gen_6582
<a>() -> q_gen_6583
<b>() -> q_gen_6586
<nil, z>() -> q_gen_6585
<a, cons, z>(q_gen_6586, q_gen_6582) -> q_gen_6577
<a, nil, z>() -> q_gen_6577
<b, cons, s>(q_gen_6586, q_gen_6585) -> q_gen_6577
<b, cons, z>(q_gen_6583, q_gen_6582) -> q_gen_6577
<b, nil, z>() -> q_gen_6577
<b, cons, z>(q_gen_6586, q_gen_6582) -> q_gen_6587
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_6574, q_gen_6576, q_gen_6588},
Q_f={q_gen_6574},
Delta=
{
<s>(q_gen_6576) -> q_gen_6576
<z>() -> q_gen_6576
<s, s>(q_gen_6574) -> q_gen_6574
<z, s>(q_gen_6576) -> q_gen_6574
<z, z>() -> q_gen_6574
<s, z>(q_gen_6576) -> q_gen_6588
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  prefix -> 
{{{
Q={q_gen_6573, q_gen_6579, q_gen_6590, q_gen_6591},
Q_f={q_gen_6573},
Delta=
{
<nil>() -> q_gen_6590
<b>() -> q_gen_6591
<cons, cons>(q_gen_6579, q_gen_6573) -> q_gen_6573
<nil, cons>(q_gen_6591, q_gen_6590) -> q_gen_6573
<nil, nil>() -> q_gen_6573
<a, a>() -> q_gen_6579
<b, b>() -> q_gen_6579
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> prefix([nil, y]) -> 6
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 4
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 7
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 7
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 5
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 5
(prefix([cons(z, zs), nil])) -> BOT -> 5
}
Sat witness: Found: ((count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]), {
_nia -> z  ;  t1 -> nil  ;  x -> a
})

-------------------------------------------
Step 16, which took 0.015030 s (model generation: 0.014591,  model checking: 0.000439):

Model:
|_
{
count -> 
{{{
Q={q_gen_6577, q_gen_6582, q_gen_6583, q_gen_6585, q_gen_6586, q_gen_6587},
Q_f={q_gen_6577},
Delta=
{
<nil>() -> q_gen_6582
<a>() -> q_gen_6583
<b>() -> q_gen_6586
<nil, z>() -> q_gen_6585
<a, cons, s>(q_gen_6583, q_gen_6585) -> q_gen_6577
<a, cons, z>(q_gen_6586, q_gen_6582) -> q_gen_6577
<a, nil, z>() -> q_gen_6577
<b, cons, s>(q_gen_6586, q_gen_6585) -> q_gen_6577
<b, cons, z>(q_gen_6583, q_gen_6582) -> q_gen_6577
<b, nil, z>() -> q_gen_6577
<b, cons, z>(q_gen_6586, q_gen_6582) -> q_gen_6587
}

Datatype: <elt, eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_6574, q_gen_6576, q_gen_6588},
Q_f={q_gen_6574},
Delta=
{
<s>(q_gen_6576) -> q_gen_6576
<z>() -> q_gen_6576
<s, s>(q_gen_6574) -> q_gen_6574
<z, s>(q_gen_6576) -> q_gen_6574
<z, z>() -> q_gen_6574
<s, z>(q_gen_6576) -> q_gen_6588
}

Datatype: <nat, nat>
Convolution form: right
}}}
  ;  prefix -> 
{{{
Q={q_gen_6573, q_gen_6579, q_gen_6590, q_gen_6591},
Q_f={q_gen_6573},
Delta=
{
<nil>() -> q_gen_6590
<b>() -> q_gen_6591
<cons, cons>(q_gen_6579, q_gen_6573) -> q_gen_6573
<nil, cons>(q_gen_6591, q_gen_6590) -> q_gen_6573
<nil, nil>() -> q_gen_6573
<a, a>() -> q_gen_6579
<b, b>() -> q_gen_6579
}

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

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

Teacher's answer:
New clause system:
{
() -> count([x, nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
() -> prefix([nil, y]) -> 6
(count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]) -> 7
(count([x, t1, _nia])) -> count([x, cons(x, t1), s(_nia)]) -> 7
(count([x, t1, _oia]) /\ not eq_elt([h1, x])) -> count([x, cons(h1, t1), _oia]) -> 7
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 5
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 5
(leq([s(nn1), z])) -> BOT -> 5
(prefix([zs, ys])) -> prefix([cons(y2, zs), cons(y2, ys)]) -> 7
(prefix([cons(y2, zs), cons(y2, ys)])) -> prefix([zs, ys]) -> 5
(prefix([cons(z, zs), cons(y2, ys)]) /\ not eq_elt([z, y2])) -> BOT -> 5
(prefix([cons(z, zs), nil])) -> BOT -> 5
}
Sat witness: Found: ((count([x, l1, _uia]) /\ count([x, l2, _tia]) /\ prefix([l1, l2])) -> leq([_tia, _uia]), {
_tia -> s(z)  ;  _uia -> z  ;  l1 -> nil  ;  l2 -> cons(b, nil)  ;  x -> b
})

Total time: 0.243719
Reason for stopping: Disproved