YES O(n) TRS: { first(0(), X) -> nil(), first(s(X), cons(Y)) -> cons(Y), from(X) -> cons(X) } DUP: We consider a non-duplicating system. Trs: { first(0(), X) -> nil(), first(s(X), cons(Y)) -> cons(Y), from(X) -> cons(X) } BOUND: Automaton: { from_0(8) -> 6, from_0(7) -> 6, from_0(6) -> 6, s_0(8) -> 8, s_0(7) -> 8, s_0(6) -> 8, cons_1(8) -> 6, cons_1(7) -> 6, cons_1(6) -> 6, cons_0(8) -> 6, cons_0(7) -> 6, cons_0(6) -> 6, 0_0() -> 7, first_0(8, 8) -> 6, first_0(8, 7) -> 6, first_0(8, 6) -> 6, first_0(7, 8) -> 6, first_0(7, 7) -> 6, first_0(7, 6) -> 6, first_0(6, 8) -> 6, first_0(6, 7) -> 6, first_0(6, 6) -> 6, nil_1() -> 6, nil_0() -> 6 } Strict: {} Qed