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