YES O(n^5) 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] = [0] [0] [0] [X4] [1 0 0 0 0][X4] [0] [X3] [0 0 0 0 0][X3] [0] [s]([X2]) = [0 0 0 0 0][X2] + [0] [X1] [0 0 0 0 0][X1] [0] [X0] [0 0 0 0 1][X0] [1] [X4] [1 0 0 0 1][X4] [1] [X3] [0 0 0 0 0][X3] [0] [g]([X2]) = [0 0 0 0 0][X2] + [0] [X1] [0 0 0 0 0][X1] [0] [X0] [0 0 0 0 1][X0] [0] [X4] [1 0 0 0 1][X4] [1] [X3] [0 0 0 0 0][X3] [0] [f]([X2]) = [0 0 0 0 0][X2] + [0] [X1] [0 0 0 0 0][X1] [0] [X0] [0 0 0 0 1][X0] [1] Qed