MAYBE MAYBE TRS: { p(0()) -> 0(), p(s(X)) -> X, leq(0(), Y) -> true(), leq(s(X), 0()) -> false(), leq(s(X), s(Y)) -> leq(X, Y), if(true()) -> X, if(false()) -> Y, diff(X, Y) -> if(leq(X, Y)) } DUP: We consider a duplicating system. Trs: { p(0()) -> 0(), p(s(X)) -> X, leq(0(), Y) -> true(), leq(s(X), 0()) -> false(), leq(s(X), s(Y)) -> leq(X, Y), if(true()) -> X, if(false()) -> Y, diff(X, Y) -> if(leq(X, Y)) } Fail