YES O(n^2) 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 [X1] [1 0][X1] [0] [s]([X0]) = [0 1][X0] + [3] [2] [0] = [0] [X3] [X1] [1 0][X3] [1 1][X1] [0] [+]([X2], [X0]) = [0 1][X2] + [0 1][X0] + [0] Qed