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