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