YES O(n^4) 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 [X7] [X3] [1 1 0 0][X7] [1 0 0 0][X3] [0] [X6] [X2] [0 1 0 0][X6] [0 0 0 0][X2] [0] [-]([X5], [X1]) = [0 0 1 0][X5] + [0 0 0 0][X1] + [0] [X4] [X0] [0 0 0 1][X4] [0 0 0 0][X0] [0] [X3] [1 0 0 0][X3] [0] [X2] [0 1 0 0][X2] [1] [s]([X1]) = [0 0 1 0][X1] + [0] [X0] [0 0 0 1][X0] [0] [1] [1] [0] = [1] [0] [X7] [X3] [1 1 1 0][X7] [1 0 0 0][X3] [0] [X6] [X2] [0 1 0 0][X6] [0 1 0 0][X2] [0] [+]([X5], [X1]) = [0 0 0 0][X5] + [0 0 1 0][X1] + [0] [X4] [X0] [0 0 0 0][X4] [0 0 0 1][X0] [0] Qed