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