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