YES Trs: { first(0(), X) -> nil(), first(s(X), cons(Y)) -> cons(Y), from(X) -> cons(X)} Comment: We consider a non-duplicating trs. BOUND: Automaton: { 0_0() -> q7, nil_1() -> q5, nil_0() -> q5, s_0(q7) -> q6, s_0(q6) -> q6, s_0(q5) -> q6, first_0(q7, q7) -> q5, first_0(q7, q6) -> q5, first_0(q7, q5) -> q5, first_0(q6, q7) -> q5, first_0(q6, q6) -> q5, first_0(q6, q5) -> q5, first_0(q5, q7) -> q5, first_0(q5, q6) -> q5, first_0(q5, q5) -> q5, from_0(q7) -> q5, from_0(q6) -> q5, from_0(q5) -> q5, cons_1(q7) -> q5, cons_1(q6) -> q5, cons_1(q5) -> q5, cons_0(q7) -> q5, cons_0(q6) -> q5, cons_0(q5) -> q5} Strict: {} Qed