LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ times(x, y) -> help(x, y, 0())
, help(x, y, c) -> if(lt(c, y), x, y, c)
, if(true(), x, y, c) -> plus(x, help(x, y, s(c)))
, if(false(), x, y, c) -> 0()
, lt(0(), s(x)) -> true()
, lt(s(x), 0()) -> false()
, lt(s(x), s(y)) -> lt(x, y)
, plus(x, 0()) -> x
, plus(0(), x) -> x
, plus(x, s(y)) -> s(plus(x, y))
, plus(s(x), y) -> s(plus(x, 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:
{ times(x, y) -> help(x, y, 0())
, help(x, y, c) -> if(lt(c, y), x, y, c)
, if(true(), x, y, c) -> plus(x, help(x, y, s(c)))
, if(false(), x, y, c) -> 0()
, lt(0(), s(x)) -> true()
, lt(s(x), 0()) -> false()
, lt(s(x), s(y)) -> lt(x, y)
, plus(x, 0()) -> x
, plus(0(), x) -> x
, plus(x, s(y)) -> s(plus(x, y))
, plus(s(x), y) -> s(plus(x, 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:
{ times(x, y) -> help(x, y, 0())
, help(x, y, c) -> if(lt(c, y), x, y, c)
, if(true(), x, y, c) -> plus(x, help(x, y, s(c)))
, if(false(), x, y, c) -> 0()
, lt(0(), s(x)) -> true()
, lt(s(x), 0()) -> false()
, lt(s(x), s(y)) -> lt(x, y)
, plus(x, 0()) -> x
, plus(0(), x) -> x
, plus(x, s(y)) -> s(plus(x, y))
, plus(s(x), y) -> s(plus(x, 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:
{ times(x, y) -> help(x, y, 0())
, help(x, y, c) -> if(lt(c, y), x, y, c)
, if(true(), x, y, c) -> plus(x, help(x, y, s(c)))
, if(false(), x, y, c) -> 0()
, lt(0(), s(x)) -> true()
, lt(s(x), 0()) -> false()
, lt(s(x), s(y)) -> lt(x, y)
, plus(x, 0()) -> x
, plus(0(), x) -> x
, plus(x, s(y)) -> s(plus(x, y))
, plus(s(x), y) -> s(plus(x, 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:
{ times(x, y) -> help(x, y, 0())
, help(x, y, c) -> if(lt(c, y), x, y, c)
, if(true(), x, y, c) -> plus(x, help(x, y, s(c)))
, if(false(), x, y, c) -> 0()
, lt(0(), s(x)) -> true()
, lt(s(x), 0()) -> false()
, lt(s(x), s(y)) -> lt(x, y)
, plus(x, 0()) -> x
, plus(0(), x) -> x
, plus(x, s(y)) -> s(plus(x, y))
, plus(s(x), y) -> s(plus(x, 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:
{ times(x, y) -> help(x, y, 0())
, help(x, y, c) -> if(lt(c, y), x, y, c)
, if(true(), x, y, c) -> plus(x, help(x, y, s(c)))
, if(false(), x, y, c) -> 0()
, lt(0(), s(x)) -> true()
, lt(s(x), 0()) -> false()
, lt(s(x), s(y)) -> lt(x, y)
, plus(x, 0()) -> x
, plus(0(), x) -> x
, plus(x, s(y)) -> s(plus(x, y))
, plus(s(x), y) -> s(plus(x, y))}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..