LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ isEmpty(cons(x, xs)) -> false()
, isEmpty(nil()) -> true()
, isZero(0()) -> true()
, isZero(s(x)) -> false()
, head(cons(x, xs)) -> x
, tail(cons(x, xs)) -> xs
, tail(nil()) -> nil()
, p(s(s(x))) -> s(p(s(x)))
, p(s(0())) -> 0()
, p(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, inc(0()) -> s(0())
, sumList(xs, y) ->
if(isEmpty(xs),
isZero(head(xs)),
y,
tail(xs),
cons(p(head(xs)), tail(xs)),
inc(y))
, if(true(), b, y, xs, ys, x) -> y
, if(false(), true(), y, xs, ys, x) -> sumList(xs, y)
, if(false(), false(), y, xs, ys, x) -> sumList(ys, x)
, sum(xs) -> sumList(xs, 0())}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ isEmpty(cons(x, xs)) -> false()
, isEmpty(nil()) -> true()
, isZero(0()) -> true()
, isZero(s(x)) -> false()
, head(cons(x, xs)) -> x
, tail(cons(x, xs)) -> xs
, tail(nil()) -> nil()
, p(s(s(x))) -> s(p(s(x)))
, p(s(0())) -> 0()
, p(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, inc(0()) -> s(0())
, sumList(xs, y) ->
if(isEmpty(xs),
isZero(head(xs)),
y,
tail(xs),
cons(p(head(xs)), tail(xs)),
inc(y))
, if(true(), b, y, xs, ys, x) -> y
, if(false(), true(), y, xs, ys, x) -> sumList(xs, y)
, if(false(), false(), y, xs, ys, x) -> sumList(ys, x)
, sum(xs) -> sumList(xs, 0())}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ isEmpty(cons(x, xs)) -> false()
, isEmpty(nil()) -> true()
, isZero(0()) -> true()
, isZero(s(x)) -> false()
, head(cons(x, xs)) -> x
, tail(cons(x, xs)) -> xs
, tail(nil()) -> nil()
, p(s(s(x))) -> s(p(s(x)))
, p(s(0())) -> 0()
, p(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, inc(0()) -> s(0())
, sumList(xs, y) ->
if(isEmpty(xs),
isZero(head(xs)),
y,
tail(xs),
cons(p(head(xs)), tail(xs)),
inc(y))
, if(true(), b, y, xs, ys, x) -> y
, if(false(), true(), y, xs, ys, x) -> sumList(xs, y)
, if(false(), false(), y, xs, ys, x) -> sumList(ys, x)
, sum(xs) -> sumList(xs, 0())}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ isEmpty(cons(x, xs)) -> false()
, isEmpty(nil()) -> true()
, isZero(0()) -> true()
, isZero(s(x)) -> false()
, head(cons(x, xs)) -> x
, tail(cons(x, xs)) -> xs
, tail(nil()) -> nil()
, p(s(s(x))) -> s(p(s(x)))
, p(s(0())) -> 0()
, p(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, inc(0()) -> s(0())
, sumList(xs, y) ->
if(isEmpty(xs),
isZero(head(xs)),
y,
tail(xs),
cons(p(head(xs)), tail(xs)),
inc(y))
, if(true(), b, y, xs, ys, x) -> y
, if(false(), true(), y, xs, ys, x) -> sumList(xs, y)
, if(false(), false(), y, xs, ys, x) -> sumList(ys, x)
, sum(xs) -> sumList(xs, 0())}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ isEmpty(cons(x, xs)) -> false()
, isEmpty(nil()) -> true()
, isZero(0()) -> true()
, isZero(s(x)) -> false()
, head(cons(x, xs)) -> x
, tail(cons(x, xs)) -> xs
, tail(nil()) -> nil()
, p(s(s(x))) -> s(p(s(x)))
, p(s(0())) -> 0()
, p(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, inc(0()) -> s(0())
, sumList(xs, y) ->
if(isEmpty(xs),
isZero(head(xs)),
y,
tail(xs),
cons(p(head(xs)), tail(xs)),
inc(y))
, if(true(), b, y, xs, ys, x) -> y
, if(false(), true(), y, xs, ys, x) -> sumList(xs, y)
, if(false(), false(), y, xs, ys, x) -> sumList(ys, x)
, sum(xs) -> sumList(xs, 0())}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ isEmpty(cons(x, xs)) -> false()
, isEmpty(nil()) -> true()
, isZero(0()) -> true()
, isZero(s(x)) -> false()
, head(cons(x, xs)) -> x
, tail(cons(x, xs)) -> xs
, tail(nil()) -> nil()
, p(s(s(x))) -> s(p(s(x)))
, p(s(0())) -> 0()
, p(0()) -> 0()
, inc(s(x)) -> s(inc(x))
, inc(0()) -> s(0())
, sumList(xs, y) ->
if(isEmpty(xs),
isZero(head(xs)),
y,
tail(xs),
cons(p(head(xs)), tail(xs)),
inc(y))
, if(true(), b, y, xs, ys, x) -> y
, if(false(), true(), y, xs, ys, x) -> sumList(xs, y)
, if(false(), false(), y, xs, ys, x) -> sumList(ys, x)
, sum(xs) -> sumList(xs, 0())}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..