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