YES(?,O(n^1)) TRS: { sqr 0() -> 0(), sqr s() -> s(), terms N -> cons recip sqr N, dbl 0() -> 0(), dbl s() -> s(), add(0(), X) -> X, add(s(), Y) -> s(), first(0(), X) -> nil(), first(s(), cons Y) -> cons Y } DUP: We consider a non-duplicating system. Trs: { sqr 0() -> 0(), sqr s() -> s(), terms N -> cons recip sqr N, dbl 0() -> 0(), dbl s() -> s(), add(0(), X) -> X, add(s(), Y) -> s(), first(0(), X) -> nil(), first(s(), cons Y) -> cons Y } Natural interpretation: Strict: { sqr 0() -> 0(), sqr s() -> s(), terms N -> cons recip sqr N, dbl 0() -> 0(), dbl s() -> s(), add(0(), X) -> X, add(s(), Y) -> s(), first(0(), X) -> nil(), first(s(), cons Y) -> cons Y } Weak: {} Interpretation class: stronglylinear [first](X1, X0) = + 1*X0 + 1*X1 + 7 [add](X1, X0) = + 1*X0 + 1*X1 + 4 [dbl](X0) = + 1*X0 + 4 [s] = + 7 [0] = + 1 [terms](X0) = + 1*X0 + 6 [sqr](X0) = + 1*X0 + 1 [recip](X0) = + 1*X0 + 1 [cons](X0) = + 1*X0 + 2 [nil] = + 7 Qed