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