YES(?,O(n^2)) TRS: { +(x, +(y, z)) -> +(+(x, y), z), +(*(x, y), +(x, z)) -> *(x, +(y, z)), +(*(x, y), +(*(x, z), u)) -> +(*(x, +(y, z)), u) } DUP: We consider a non-duplicating system. Trs: { +(x, +(y, z)) -> +(+(x, y), z), +(*(x, y), +(x, z)) -> *(x, +(y, z)), +(*(x, y), +(*(x, z), u)) -> +(*(x, +(y, z)), u) } Matrix Interpretation: Interpretation class: triangular [X3] [X1] [1 0][X3] [1 0][X1] [2] [*]([X2], [X0]) = [0 0][X2] + [0 1][X0] + [1] [X3] [X1] [1 0][X3] [1 3][X1] [0] [+]([X2], [X0]) = [0 1][X2] + [0 1][X0] + [2] Qed