LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ ge(0(), 0()) -> true()
, ge(s(x), 0()) -> ge(x, 0())
, ge(0(), s(0())) -> false()
, ge(0(), s(s(x))) -> ge(0(), s(x))
, ge(s(x), s(y)) -> ge(x, y)
, minus(0(), 0()) -> 0()
, minus(0(), s(x)) -> minus(0(), x)
, minus(s(x), 0()) -> s(minus(x, 0()))
, minus(s(x), s(y)) -> minus(x, y)
, plus(0(), 0()) -> 0()
, plus(0(), s(x)) -> s(plus(0(), x))
, plus(s(x), y) -> s(plus(x, y))
, div(x, y) -> ify(ge(y, s(0())), x, y)
, ify(false(), x, y) -> divByZeroError()
, ify(true(), x, y) -> if(ge(x, y), x, y)
, if(false(), x, y) -> 0()
, if(true(), x, y) -> s(div(minus(x, y), y))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
MPO
MAYBE
We consider the following Problem:
Strict Trs:
{ ge(0(), 0()) -> true()
, ge(s(x), 0()) -> ge(x, 0())
, ge(0(), s(0())) -> false()
, ge(0(), s(s(x))) -> ge(0(), s(x))
, ge(s(x), s(y)) -> ge(x, y)
, minus(0(), 0()) -> 0()
, minus(0(), s(x)) -> minus(0(), x)
, minus(s(x), 0()) -> s(minus(x, 0()))
, minus(s(x), s(y)) -> minus(x, y)
, plus(0(), 0()) -> 0()
, plus(0(), s(x)) -> s(plus(0(), x))
, plus(s(x), y) -> s(plus(x, y))
, div(x, y) -> ify(ge(y, s(0())), x, y)
, ify(false(), x, y) -> divByZeroError()
, ify(true(), x, y) -> if(ge(x, y), x, y)
, if(false(), x, y) -> 0()
, if(true(), x, y) -> s(div(minus(x, y), y))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ ge(0(), 0()) -> true()
, ge(s(x), 0()) -> ge(x, 0())
, ge(0(), s(0())) -> false()
, ge(0(), s(s(x))) -> ge(0(), s(x))
, ge(s(x), s(y)) -> ge(x, y)
, minus(0(), 0()) -> 0()
, minus(0(), s(x)) -> minus(0(), x)
, minus(s(x), 0()) -> s(minus(x, 0()))
, minus(s(x), s(y)) -> minus(x, y)
, plus(0(), 0()) -> 0()
, plus(0(), s(x)) -> s(plus(0(), x))
, plus(s(x), y) -> s(plus(x, y))
, div(x, y) -> ify(ge(y, s(0())), x, y)
, ify(false(), x, y) -> divByZeroError()
, ify(true(), x, y) -> if(ge(x, y), x, y)
, if(false(), x, y) -> 0()
, if(true(), x, y) -> s(div(minus(x, y), y))}
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:
{ ge(0(), 0()) -> true()
, ge(s(x), 0()) -> ge(x, 0())
, ge(0(), s(0())) -> false()
, ge(0(), s(s(x))) -> ge(0(), s(x))
, ge(s(x), s(y)) -> ge(x, y)
, minus(0(), 0()) -> 0()
, minus(0(), s(x)) -> minus(0(), x)
, minus(s(x), 0()) -> s(minus(x, 0()))
, minus(s(x), s(y)) -> minus(x, y)
, plus(0(), 0()) -> 0()
, plus(0(), s(x)) -> s(plus(0(), x))
, plus(s(x), y) -> s(plus(x, y))
, div(x, y) -> ify(ge(y, s(0())), x, y)
, ify(false(), x, y) -> divByZeroError()
, ify(true(), x, y) -> if(ge(x, y), x, y)
, if(false(), x, y) -> 0()
, if(true(), x, y) -> s(div(minus(x, y), y))}
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:
{ ge(0(), 0()) -> true()
, ge(s(x), 0()) -> ge(x, 0())
, ge(0(), s(0())) -> false()
, ge(0(), s(s(x))) -> ge(0(), s(x))
, ge(s(x), s(y)) -> ge(x, y)
, minus(0(), 0()) -> 0()
, minus(0(), s(x)) -> minus(0(), x)
, minus(s(x), 0()) -> s(minus(x, 0()))
, minus(s(x), s(y)) -> minus(x, y)
, plus(0(), 0()) -> 0()
, plus(0(), s(x)) -> s(plus(0(), x))
, plus(s(x), y) -> s(plus(x, y))
, div(x, y) -> ify(ge(y, s(0())), x, y)
, ify(false(), x, y) -> divByZeroError()
, ify(true(), x, y) -> if(ge(x, y), x, y)
, if(false(), x, y) -> 0()
, if(true(), x, y) -> s(div(minus(x, y), y))}
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:
{ ge(0(), 0()) -> true()
, ge(s(x), 0()) -> ge(x, 0())
, ge(0(), s(0())) -> false()
, ge(0(), s(s(x))) -> ge(0(), s(x))
, ge(s(x), s(y)) -> ge(x, y)
, minus(0(), 0()) -> 0()
, minus(0(), s(x)) -> minus(0(), x)
, minus(s(x), 0()) -> s(minus(x, 0()))
, minus(s(x), s(y)) -> minus(x, y)
, plus(0(), 0()) -> 0()
, plus(0(), s(x)) -> s(plus(0(), x))
, plus(s(x), y) -> s(plus(x, y))
, div(x, y) -> ify(ge(y, s(0())), x, y)
, ify(false(), x, y) -> divByZeroError()
, ify(true(), x, y) -> if(ge(x, y), x, y)
, if(false(), x, y) -> 0()
, if(true(), x, y) -> s(div(minus(x, y), y))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..