YES O(n^3) TRS: { +(0(), y) -> y, +(s(x), 0()) -> s(x), +(s(x), s(y)) -> s(+(s(x), +(y, 0()))) } DUP: We consider a non-duplicating system. Trs: { +(0(), y) -> y, +(s(x), 0()) -> s(x), +(s(x), s(y)) -> s(+(s(x), +(y, 0()))) } Matrix Interpretation: Interpretation class: triangular [X2] [1 0 0][X2] [0] [s]([X1]) = [0 0 1][X1] + [1] [X0] [0 0 1][X0] [1] [1] [0] = [0] [0] [X5] [X2] [1 0 0][X5] [1 1 1][X2] [0] [+]([X4], [X1]) = [0 0 1][X4] + [0 1 0][X1] + [0] [X3] [X0] [0 0 1][X3] [0 0 1][X0] [0] Qed