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