YES O(n^2) 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] = [0] [X1] [1 0][X1] [0] [s]([X0]) = [0 1][X0] + [1] [X1] [1 1][X1] [1] [g]([X0]) = [0 1][X0] + [0] [X1] [1 1][X1] [1] [f]([X0]) = [0 1][X0] + [1] Qed