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