MAYBE MAYBE TRS: { zeros() -> cons(0()), length(cons(N)) -> U11(and(isNatList())), length(nil()) -> 0(), U11(tt()) -> s(length(L)), U21(tt()) -> nil(), U31(tt()) -> cons(N), and(tt()) -> X, isNat() -> tt(), isNat() -> isNat(), isNat() -> isNatList(), isNatList() -> tt(), isNatList() -> and(isNat()), isNatIList() -> tt(), isNatIList() -> and(isNat()), isNatIList() -> isNatList(), take(0(), IL) -> U21(isNatIList()), take(s(M), cons(N)) -> U31(and(isNatIList())) } DUP: We consider a duplicating system. Trs: { zeros() -> cons(0()), length(cons(N)) -> U11(and(isNatList())), length(nil()) -> 0(), U11(tt()) -> s(length(L)), U21(tt()) -> nil(), U31(tt()) -> cons(N), and(tt()) -> X, isNat() -> tt(), isNat() -> isNat(), isNat() -> isNatList(), isNatList() -> tt(), isNatList() -> and(isNat()), isNatIList() -> tt(), isNatIList() -> and(isNat()), isNatIList() -> isNatList(), take(0(), IL) -> U21(isNatIList()), take(s(M), cons(N)) -> U31(and(isNatIList())) } Fail