YES O(n^5) TRS: { +(0(), y) -> y, +(s(x), y) -> s(+(x, y)), -(x, 0()) -> x, -(0(), y) -> 0(), -(s(x), s(y)) -> -(x, y) } DUP: We consider a non-duplicating system. Trs: { +(0(), y) -> y, +(s(x), y) -> s(+(x, y)), -(x, 0()) -> x, -(0(), y) -> 0(), -(s(x), s(y)) -> -(x, y) } Matrix Interpretation: Interpretation class: triangular [X9] [X4] [1 0 0 0 0][X9] [1 0 1 0 0][X4] [1] [X8] [X3] [0 1 0 0 0][X8] [0 0 0 0 0][X3] [0] [-]([X7], [X2]) = [0 0 1 0 0][X7] + [0 0 0 0 0][X2] + [1] [X6] [X1] [0 0 0 1 0][X6] [0 0 0 0 0][X1] [0] [X5] [X0] [0 0 0 0 1][X5] [0 0 0 0 0][X0] [0] [X4] [1 0 0 0 0][X4] [0] [X3] [0 1 0 0 0][X3] [0] [s]([X2]) = [0 0 1 0 0][X2] + [1] [X1] [0 0 0 1 0][X1] [0] [X0] [0 0 0 0 1][X0] [0] [1] [0] [0] = [0] [0] [0] [X9] [X4] [1 0 1 0 0][X9] [1 0 0 0 0][X4] [0] [X8] [X3] [0 0 0 0 0][X8] [0 1 0 0 0][X3] [0] [+]([X7], [X2]) = [0 0 1 0 0][X7] + [0 0 1 0 0][X2] + [0] [X6] [X1] [0 0 0 0 0][X6] [0 0 0 1 0][X1] [0] [X5] [X0] [0 0 0 0 0][X5] [0 0 0 0 1][X0] [0] Qed