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