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