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