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