YES O(n^4) TRS: {h(x, x) -> x, f(x, y) -> h(x, y), f(x, y) -> h(y, x)} DUP: We consider a non-duplicating system. Trs: {h(x, x) -> x, f(x, y) -> h(x, y), f(x, y) -> h(y, x)} Matrix Interpretation: Interpretation class: triangular [X7] [X3] [1 0 2 3][X7] [1 1 2 3][X3] [3] [X6] [X2] [0 1 0 0][X6] [0 1 0 0][X2] [0] [f]([X5], [X1]) = [0 0 1 0][X5] + [0 0 1 2][X1] + [2] [X4] [X0] [0 0 0 1][X4] [0 0 0 1][X0] [2] [X7] [X3] [1 0 0 3][X7] [1 0 0 1][X3] [2] [X6] [X2] [0 0 0 0][X6] [0 1 0 0][X2] [0] [h]([X5], [X1]) = [0 0 1 0][X5] + [0 0 1 0][X1] + [2] [X4] [X0] [0 0 0 0][X4] [0 0 0 1][X0] [2] Qed