YES O(n^4) 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] [1] [X7] [X3] [1 0 0 0][X7] [1 0 0 0][X3] [0] [X6] [X2] [0 0 0 0][X6] [0 0 0 0][X2] [0] [+]([X5], [X1]) = [0 0 0 0][X5] + [0 0 0 0][X1] + [0] [X4] [X0] [0 0 0 1][X4] [0 0 0 0][X0] [0] [X7] [X3] [1 0 0 1][X7] [1 0 0 0][X3] [0] [X6] [X2] [0 0 0 0][X6] [0 0 0 0][X2] [0] [*]([X5], [X1]) = [0 0 0 0][X5] + [0 0 0 0][X1] + [0] [X4] [X0] [0 0 0 1][X4] [0 0 0 1][X0] [1] Qed