YES O(n^5) 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) } Matrix Interpretation: Interpretation class: triangular [X4] [1 0 0 0 0][X4] [1] [X3] [0 0 0 0 0][X3] [0] [from]([X2]) = [0 0 0 0 0][X2] + [0] [X1] [0 0 0 0 0][X1] [0] [X0] [0 0 0 0 0][X0] [0] [X4] [1 0 0 0 0][X4] [1] [X3] [0 0 0 0 0][X3] [0] [s]([X2]) = [0 0 0 0 0][X2] + [0] [X1] [0 0 0 0 0][X1] [1] [X0] [0 0 0 0 0][X0] [0] [X4] [1 0 0 0 0][X4] [0] [X3] [0 0 0 0 0][X3] [0] [cons]([X2]) = [0 0 0 0 0][X2] + [0] [X1] [0 0 0 0 0][X1] [0] [X0] [0 0 0 0 0][X0] [0] [0] [0] [0] = [0] [1] [1] [X9] [X4] [1 0 0 1 1][X9] [1 0 0 0 0][X4] [0] [X8] [X3] [0 0 0 0 0][X8] [0 0 0 0 0][X3] [0] [first]([X7], [X2]) = [0 0 0 0 0][X7] + [0 0 0 0 0][X2] + [0] [X6] [X1] [0 0 0 0 0][X6] [0 0 0 0 0][X1] [0] [X5] [X0] [0 0 0 0 0][X5] [0 0 0 0 0][X0] [0] [0] [0] [nil] = [0] [0] [0] Qed