MAYBE MAYBE TRS: { U11(tt()) -> N, plus(N, s(M)) -> U21(and(isNat())), plus(N, 0()) -> U11(isNat()), U21(tt()) -> s(plus(N, M)), U31(tt()) -> 0(), x(N, s(M)) -> U41(and(isNat())), x(N, 0()) -> U31(isNat()), U41(tt()) -> plus(x(N, M), N), and(tt()) -> X, isNat() -> tt(), isNat() -> and(isNat()), isNat() -> isNat() } DUP: We consider a duplicating system. Trs: { U11(tt()) -> N, plus(N, s(M)) -> U21(and(isNat())), plus(N, 0()) -> U11(isNat()), U21(tt()) -> s(plus(N, M)), U31(tt()) -> 0(), x(N, s(M)) -> U41(and(isNat())), x(N, 0()) -> U31(isNat()), U41(tt()) -> plus(x(N, M), N), and(tt()) -> X, isNat() -> tt(), isNat() -> and(isNat()), isNat() -> isNat() } Fail