YES O(n^3) TRS: { U12(tt(), M, N) -> s(plus(activate(N), activate(M))), activate(X) -> X, U11(tt(), M, N) -> U12(tt(), activate(M), activate(N)), plus(N, s(M)) -> U11(tt(), M, N), plus(N, 0()) -> N } DUP: We consider a non-duplicating system. Trs: { U12(tt(), M, N) -> s(plus(activate(N), activate(M))), activate(X) -> X, U11(tt(), M, N) -> U12(tt(), activate(M), activate(N)), plus(N, s(M)) -> U11(tt(), M, N), plus(N, 0()) -> N } Matrix Interpretation: Interpretation class: triangular [1] [0] = [0] [1] [X5] [X2] [1 0 0][X5] [1 0 3][X2] [0] [plus]([X4], [X1]) = [0 1 0][X4] + [0 0 0][X1] + [0] [X3] [X0] [0 0 1][X3] [0 0 1][X0] [0] [X2] [1 0 0][X2] [0] [s]([X1]) = [0 0 0][X1] + [0] [X0] [0 0 1][X0] [3] [X8] [X5] [X2] [1 3 0][X8] [1 0 3][X5] [1 0 0][X2] [0] [U11]([X7], [X4], [X1]) = [0 0 0][X7] + [0 0 0][X4] + [0 0 0][X1] + [0] [X6] [X3] [X0] [0 0 0][X6] [0 0 1][X3] [0 0 1][X0] [3] [X2] [1 0 0][X2] [1] [activate]([X1]) = [0 1 0][X1] + [0] [X0] [0 0 1][X0] [0] [1] [tt] = [2] [0] [X8] [X5] [X2] [1 0 0][X8] [1 0 3][X5] [1 0 0][X2] [2] [U12]([X7], [X4], [X1]) = [0 0 0][X7] + [0 0 0][X4] + [0 0 0][X1] + [0] [X6] [X3] [X0] [0 0 0][X6] [0 0 1][X3] [0 0 1][X0] [3] Qed