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}
)
(length, F:
{() -> length([nil, z])
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)])}
(length([_uv, _vv]) /\ length([_uv, _wv])) -> eq_nat([_vv, _wv])
)
(delete, F:
{() -> delete([x, nil, nil])
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv])
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)])}
(delete([_zv, _aw, _bw]) /\ delete([_zv, _aw, _cw])) -> eq_eltlist([_bw, _cw])
)
}

properties:
{(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw])}


over-approximation: {delete, length}
under-approximation: {leq}

Clause system for inference is:

{
() -> delete([x, nil, nil]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 0
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 0
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 0
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 0
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 0
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 0
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 0
(leq([s(nn1), z])) -> BOT -> 0
}


Solving took 0.174035 seconds.
Proved
Model:
|_
{
delete -> 
{{{
Q={q_gen_4094, q_gen_4099, q_gen_4100, q_gen_4102, q_gen_4103},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4103, q_gen_4102) -> q_gen_4102
<nil>() -> q_gen_4102
<a>() -> q_gen_4103
<b>() -> q_gen_4103
<cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4099
<cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4099
<nil, nil>() -> q_gen_4099
<a, a>() -> q_gen_4100
<a, b>() -> q_gen_4100
<b, a>() -> q_gen_4100
<b, b>() -> q_gen_4100
<a, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<a, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<a, nil, nil>() -> q_gen_4094
<b, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<b, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<b, nil, nil>() -> q_gen_4094
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4093, q_gen_4097},
Q_f={q_gen_4093},
Delta=
{
<a>() -> q_gen_4097
<b>() -> q_gen_4097
<cons, s>(q_gen_4097, q_gen_4093) -> q_gen_4093
<nil, z>() -> q_gen_4093
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<s>(q_gen_4092) -> q_gen_4092
<z>() -> q_gen_4092
<s, s>(q_gen_4090) -> q_gen_4090
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

-------------------
STEPS:
-------------------------------------------
Step 0, which took 0.004146 s (model generation: 0.003956,  model checking: 0.000190):

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

}

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

}

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

}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 0
() -> leq([z, z]) -> 3
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 1
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 1
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 1
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([z, z]), {

})

-------------------------------------------
Step 1, which took 0.005115 s (model generation: 0.004944,  model checking: 0.000171):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090},
Q_f={q_gen_4090},
Delta=
{
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 0
() -> length([nil, z]) -> 0
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 1
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 1
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 1
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> z
})

-------------------------------------------
Step 2, which took 0.006792 s (model generation: 0.006686,  model checking: 0.000106):

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

}

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

}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<z>() -> q_gen_4092
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 0
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 1
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 1
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 1
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> length([nil, z]), {

})

-------------------------------------------
Step 3, which took 0.010562 s (model generation: 0.010346,  model checking: 0.000216):

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

}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4093},
Q_f={q_gen_4093},
Delta=
{
<nil, z>() -> q_gen_4093
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<z>() -> q_gen_4092
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 1
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 1
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 1
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 1
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 1
(leq([s(nn1), z])) -> BOT -> 1
}
Sat witness: Found: (() -> delete([x, nil, nil]), {
x -> b
})

-------------------------------------------
Step 4, which took 0.011240 s (model generation: 0.010878,  model checking: 0.000362):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4094},
Q_f={q_gen_4094},
Delta=
{
<b, nil, nil>() -> q_gen_4094
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4093},
Q_f={q_gen_4093},
Delta=
{
<nil, z>() -> q_gen_4093
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<z>() -> q_gen_4092
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 1
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 1
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 1
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 1
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]), {
nn1 -> z  ;  nn2 -> z
})

-------------------------------------------
Step 5, which took 0.013039 s (model generation: 0.012738,  model checking: 0.000301):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4094},
Q_f={q_gen_4094},
Delta=
{
<b, nil, nil>() -> q_gen_4094
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4093},
Q_f={q_gen_4093},
Delta=
{
<nil, z>() -> q_gen_4093
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<z>() -> q_gen_4092
<s, s>(q_gen_4090) -> q_gen_4090
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 1
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 1
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 1
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((length([ll, _tv])) -> length([cons(x, ll), s(_tv)]), {
_tv -> z  ;  ll -> nil  ;  x -> b
})

-------------------------------------------
Step 6, which took 0.007866 s (model generation: 0.007634,  model checking: 0.000232):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4094},
Q_f={q_gen_4094},
Delta=
{
<b, nil, nil>() -> q_gen_4094
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4093, q_gen_4097},
Q_f={q_gen_4093},
Delta=
{
<b>() -> q_gen_4097
<cons, s>(q_gen_4097, q_gen_4093) -> q_gen_4093
<nil, z>() -> q_gen_4093
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<z>() -> q_gen_4092
<s, s>(q_gen_4090) -> q_gen_4090
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 1
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 1
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 4
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]), {
_yv -> nil  ;  h -> a  ;  t -> nil  ;  x -> b
})

-------------------------------------------
Step 7, which took 0.008545 s (model generation: 0.008137,  model checking: 0.000408):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4094, q_gen_4099, q_gen_4100},
Q_f={q_gen_4094},
Delta=
{
<nil, nil>() -> q_gen_4099
<a, a>() -> q_gen_4100
<b, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<b, nil, nil>() -> q_gen_4094
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4093, q_gen_4097},
Q_f={q_gen_4093},
Delta=
{
<b>() -> q_gen_4097
<cons, s>(q_gen_4097, q_gen_4093) -> q_gen_4093
<nil, z>() -> q_gen_4093
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<z>() -> q_gen_4092
<s, s>(q_gen_4090) -> q_gen_4090
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 3
() -> leq([z, z]) -> 3
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 4
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 2
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 4
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 2
(leq([s(nn1), z])) -> BOT -> 2
}
Sat witness: Found: ((delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]), {
_xv -> nil  ;  h -> b  ;  t -> nil
})

-------------------------------------------
Step 8, which took 0.008157 s (model generation: 0.007849,  model checking: 0.000308):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4094, q_gen_4099, q_gen_4100, q_gen_4102, q_gen_4103},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4102
<b>() -> q_gen_4103
<nil, nil>() -> q_gen_4099
<a, a>() -> q_gen_4100
<b, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<b, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<b, nil, nil>() -> q_gen_4094
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4093, q_gen_4097},
Q_f={q_gen_4093},
Delta=
{
<b>() -> q_gen_4097
<cons, s>(q_gen_4097, q_gen_4093) -> q_gen_4093
<nil, z>() -> q_gen_4093
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<z>() -> q_gen_4092
<s, s>(q_gen_4090) -> q_gen_4090
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 3
() -> length([nil, z]) -> 3
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 4
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 3
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 4
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 3
(leq([s(nn1), z])) -> BOT -> 3
}
Sat witness: Found: (() -> leq([z, s(nn2)]), {
nn2 -> s(z)
})

-------------------------------------------
Step 9, which took 0.010200 s (model generation: 0.008688,  model checking: 0.001512):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4094, q_gen_4099, q_gen_4100, q_gen_4102, q_gen_4103},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4102
<b>() -> q_gen_4103
<nil, nil>() -> q_gen_4099
<a, a>() -> q_gen_4100
<b, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<b, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<b, nil, nil>() -> q_gen_4094
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4093, q_gen_4097},
Q_f={q_gen_4093},
Delta=
{
<b>() -> q_gen_4097
<cons, s>(q_gen_4097, q_gen_4093) -> q_gen_4093
<nil, z>() -> q_gen_4093
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<s>(q_gen_4092) -> q_gen_4092
<z>() -> q_gen_4092
<s, s>(q_gen_4090) -> q_gen_4090
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 4
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 4
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 4
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 4
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 4
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 4
(leq([s(nn1), z])) -> BOT -> 4
}
Sat witness: Found: (() -> delete([x, nil, nil]), {
x -> a
})

-------------------------------------------
Step 10, which took 0.008480 s (model generation: 0.007950,  model checking: 0.000530):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4094, q_gen_4099, q_gen_4100, q_gen_4102, q_gen_4103},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4102
<b>() -> q_gen_4103
<nil, nil>() -> q_gen_4099
<a, a>() -> q_gen_4100
<a, nil, nil>() -> q_gen_4094
<b, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<b, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<b, nil, nil>() -> q_gen_4094
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4093, q_gen_4097},
Q_f={q_gen_4093},
Delta=
{
<b>() -> q_gen_4097
<cons, s>(q_gen_4097, q_gen_4093) -> q_gen_4093
<nil, z>() -> q_gen_4093
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<s>(q_gen_4092) -> q_gen_4092
<z>() -> q_gen_4092
<s, s>(q_gen_4090) -> q_gen_4090
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 4
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 4
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 4
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 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
}
Sat witness: Found: ((length([ll, _tv])) -> length([cons(x, ll), s(_tv)]), {
_tv -> z  ;  ll -> nil  ;  x -> a
})

-------------------------------------------
Step 11, which took 0.008964 s (model generation: 0.007784,  model checking: 0.001180):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4094, q_gen_4099, q_gen_4100, q_gen_4102, q_gen_4103},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4102
<b>() -> q_gen_4103
<nil, nil>() -> q_gen_4099
<a, a>() -> q_gen_4100
<a, nil, nil>() -> q_gen_4094
<b, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<b, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<b, nil, nil>() -> q_gen_4094
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4093, q_gen_4097},
Q_f={q_gen_4093},
Delta=
{
<a>() -> q_gen_4097
<b>() -> q_gen_4097
<cons, s>(q_gen_4097, q_gen_4093) -> q_gen_4093
<nil, z>() -> q_gen_4093
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<s>(q_gen_4092) -> q_gen_4092
<z>() -> q_gen_4092
<s, s>(q_gen_4090) -> q_gen_4090
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 4
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 4
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 7
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 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
}
Sat witness: Found: ((delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]), {
_yv -> nil  ;  h -> b  ;  t -> nil  ;  x -> a
})

-------------------------------------------
Step 12, which took 0.009051 s (model generation: 0.008340,  model checking: 0.000711):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4094, q_gen_4099, q_gen_4100, q_gen_4102, q_gen_4103},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4102
<b>() -> q_gen_4103
<nil, nil>() -> q_gen_4099
<a, a>() -> q_gen_4100
<b, b>() -> q_gen_4100
<a, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<a, nil, nil>() -> q_gen_4094
<b, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<b, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<b, nil, nil>() -> q_gen_4094
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4093, q_gen_4097},
Q_f={q_gen_4093},
Delta=
{
<a>() -> q_gen_4097
<b>() -> q_gen_4097
<cons, s>(q_gen_4097, q_gen_4093) -> q_gen_4093
<nil, z>() -> q_gen_4093
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<s>(q_gen_4092) -> q_gen_4092
<z>() -> q_gen_4092
<s, s>(q_gen_4090) -> q_gen_4090
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 6
() -> length([nil, z]) -> 4
() -> leq([z, s(nn2)]) -> 6
() -> leq([z, z]) -> 4
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 7
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 5
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 7
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 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
}
Sat witness: Found: ((delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]), {
_xv -> nil  ;  h -> a  ;  t -> nil
})

-------------------------------------------
Step 13, which took 0.009381 s (model generation: 0.008178,  model checking: 0.001203):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4094, q_gen_4099, q_gen_4100, q_gen_4102, q_gen_4103},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4102
<a>() -> q_gen_4103
<b>() -> q_gen_4103
<nil, nil>() -> q_gen_4099
<a, a>() -> q_gen_4100
<b, b>() -> q_gen_4100
<a, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<a, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<a, nil, nil>() -> q_gen_4094
<b, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<b, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<b, nil, nil>() -> q_gen_4094
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4093, q_gen_4097},
Q_f={q_gen_4093},
Delta=
{
<a>() -> q_gen_4097
<b>() -> q_gen_4097
<cons, s>(q_gen_4097, q_gen_4093) -> q_gen_4093
<nil, z>() -> q_gen_4093
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<s>(q_gen_4092) -> q_gen_4092
<z>() -> q_gen_4092
<s, s>(q_gen_4090) -> q_gen_4090
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 7
() -> length([nil, z]) -> 5
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 5
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 7
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 6
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 10
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 8
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 6
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 6
(leq([s(nn1), z])) -> BOT -> 6
}
Sat witness: Found: ((delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]), {
_yv -> nil  ;  h -> b  ;  t -> cons(a, nil)  ;  x -> a
})

-------------------------------------------
Step 14, which took 0.010613 s (model generation: 0.009528,  model checking: 0.001085):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4094, q_gen_4099, q_gen_4100, q_gen_4102, q_gen_4103},
Q_f={q_gen_4094},
Delta=
{
<nil>() -> q_gen_4102
<a>() -> q_gen_4103
<b>() -> q_gen_4103
<cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4099
<nil, nil>() -> q_gen_4099
<a, a>() -> q_gen_4100
<b, b>() -> q_gen_4100
<a, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<a, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<a, nil, nil>() -> q_gen_4094
<b, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<b, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<b, nil, nil>() -> q_gen_4094
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4093, q_gen_4097},
Q_f={q_gen_4093},
Delta=
{
<a>() -> q_gen_4097
<b>() -> q_gen_4097
<cons, s>(q_gen_4097, q_gen_4093) -> q_gen_4093
<nil, z>() -> q_gen_4093
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<s>(q_gen_4092) -> q_gen_4092
<z>() -> q_gen_4092
<s, s>(q_gen_4090) -> q_gen_4090
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 7
() -> length([nil, z]) -> 6
() -> leq([z, s(nn2)]) -> 7
() -> leq([z, z]) -> 6
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 10
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 7
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 10
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 8
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 7
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 7
(leq([s(nn1), z])) -> BOT -> 7
}
Sat witness: Found: ((delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]), {
_xv -> nil  ;  h -> b  ;  t -> cons(b, nil)
})

-------------------------------------------
Step 15, which took 0.009611 s (model generation: 0.008067,  model checking: 0.001544):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4094, q_gen_4099, q_gen_4100, q_gen_4102, q_gen_4103},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4103, q_gen_4102) -> q_gen_4102
<nil>() -> q_gen_4102
<a>() -> q_gen_4103
<b>() -> q_gen_4103
<cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4099
<nil, nil>() -> q_gen_4099
<a, a>() -> q_gen_4100
<b, b>() -> q_gen_4100
<a, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<a, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<a, nil, nil>() -> q_gen_4094
<b, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<b, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<b, nil, nil>() -> q_gen_4094
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4093, q_gen_4097},
Q_f={q_gen_4093},
Delta=
{
<a>() -> q_gen_4097
<b>() -> q_gen_4097
<cons, s>(q_gen_4097, q_gen_4093) -> q_gen_4093
<nil, z>() -> q_gen_4093
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<s>(q_gen_4092) -> q_gen_4092
<z>() -> q_gen_4092
<s, s>(q_gen_4090) -> q_gen_4090
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 8
() -> length([nil, z]) -> 7
() -> leq([z, s(nn2)]) -> 8
() -> leq([z, z]) -> 7
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 10
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 8
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 13
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 9
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 8
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 8
(leq([s(nn1), z])) -> BOT -> 8
}
Sat witness: Found: ((delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]), {
_yv -> cons(b, nil)  ;  h -> b  ;  t -> cons(b, nil)  ;  x -> a
})

-------------------------------------------
Step 16, which took 0.008815 s (model generation: 0.007849,  model checking: 0.000966):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4094, q_gen_4099, q_gen_4100, q_gen_4102, q_gen_4103},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4103, q_gen_4102) -> q_gen_4102
<nil>() -> q_gen_4102
<a>() -> q_gen_4103
<b>() -> q_gen_4103
<cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4099
<cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4099
<nil, nil>() -> q_gen_4099
<a, a>() -> q_gen_4100
<b, b>() -> q_gen_4100
<a, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<a, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<a, nil, nil>() -> q_gen_4094
<b, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<b, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<b, nil, nil>() -> q_gen_4094
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4093, q_gen_4097},
Q_f={q_gen_4093},
Delta=
{
<a>() -> q_gen_4097
<b>() -> q_gen_4097
<cons, s>(q_gen_4097, q_gen_4093) -> q_gen_4093
<nil, z>() -> q_gen_4093
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<s>(q_gen_4092) -> q_gen_4092
<z>() -> q_gen_4092
<s, s>(q_gen_4090) -> q_gen_4090
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 9
() -> length([nil, z]) -> 8
() -> leq([z, s(nn2)]) -> 9
() -> leq([z, z]) -> 8
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 13
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 9
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 13
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 10
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 9
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 9
(leq([s(nn1), z])) -> BOT -> 9
}
Sat witness: Found: ((delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]), {
_xv -> cons(b, nil)  ;  h -> a  ;  t -> cons(b, nil)
})

-------------------------------------------
Step 17, which took 0.011467 s (model generation: 0.008706,  model checking: 0.002761):

Model:
|_
{
delete -> 
{{{
Q={q_gen_4094, q_gen_4099, q_gen_4100, q_gen_4102, q_gen_4103},
Q_f={q_gen_4094},
Delta=
{
<cons>(q_gen_4103, q_gen_4102) -> q_gen_4102
<nil>() -> q_gen_4102
<a>() -> q_gen_4103
<b>() -> q_gen_4103
<cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4099
<cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4099
<nil, nil>() -> q_gen_4099
<a, a>() -> q_gen_4100
<a, b>() -> q_gen_4100
<b, b>() -> q_gen_4100
<a, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<a, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<a, nil, nil>() -> q_gen_4094
<b, cons, cons>(q_gen_4100, q_gen_4099) -> q_gen_4094
<b, cons, nil>(q_gen_4103, q_gen_4102) -> q_gen_4094
<b, nil, nil>() -> q_gen_4094
}

Datatype: <elt, eltlist, eltlist>
Convolution form: right
}}}
  ;  length -> 
{{{
Q={q_gen_4093, q_gen_4097},
Q_f={q_gen_4093},
Delta=
{
<a>() -> q_gen_4097
<b>() -> q_gen_4097
<cons, s>(q_gen_4097, q_gen_4093) -> q_gen_4093
<nil, z>() -> q_gen_4093
}

Datatype: <eltlist, nat>
Convolution form: right
}}}
  ;  leq -> 
{{{
Q={q_gen_4090, q_gen_4092},
Q_f={q_gen_4090},
Delta=
{
<s>(q_gen_4092) -> q_gen_4092
<z>() -> q_gen_4092
<s, s>(q_gen_4090) -> q_gen_4090
<z, s>(q_gen_4092) -> q_gen_4090
<z, z>() -> q_gen_4090
}

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

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

Teacher's answer:
New clause system:
{
() -> delete([x, nil, nil]) -> 10
() -> length([nil, z]) -> 9
() -> leq([z, s(nn2)]) -> 10
() -> leq([z, z]) -> 9
(delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]) -> 16
(delete([i, l, _dw]) /\ length([_dw, _ew]) /\ length([l, _fw])) -> leq([_ew, _fw]) -> 10
(delete([x, t, _yv]) /\ not eq_elt([x, h])) -> delete([x, cons(h, t), cons(h, _yv)]) -> 14
(length([ll, _tv])) -> length([cons(x, ll), s(_tv)]) -> 11
(leq([nn1, nn2])) -> leq([s(nn1), s(nn2)]) -> 10
(leq([s(nn1), s(nn2)])) -> leq([nn1, nn2]) -> 10
(leq([s(nn1), z])) -> BOT -> 10
}
Sat witness: Found: ((delete([h, t, _xv])) -> delete([h, cons(h, t), _xv]), {
_xv -> cons(a, nil)  ;  h -> b  ;  t -> cons(a, nil)
})

Total time: 0.174035
Reason for stopping: Proved