MAYBE MAYBE TRS: { plus(0(), Y) -> Y, plus(s(X), Y) -> s(plus(X, Y)), min(X, 0()) -> X, min(s(X), s(Y)) -> min(X, Y), min(min(X, Y), Z()) -> min(X, plus(Y, Z())), quot(0(), s(Y)) -> 0(), quot(s(X), s(Y)) -> s(quot(min(X, Y), s(Y))) } DUP: We consider a duplicating system. Trs: { plus(0(), Y) -> Y, plus(s(X), Y) -> s(plus(X, Y)), min(X, 0()) -> X, min(s(X), s(Y)) -> min(X, Y), min(min(X, Y), Z()) -> min(X, plus(Y, Z())), quot(0(), s(Y)) -> 0(), quot(s(X), s(Y)) -> s(quot(min(X, Y), s(Y))) } Fail