YES O(n^3) TRS: { not(false()) -> true(), not(true()) -> false(), evenodd(x, 0()) -> not(evenodd(x, s(0()))), evenodd(s(x), s(0())) -> evenodd(x, 0()), evenodd(0(), s(0())) -> false() } DUP: We consider a non-duplicating system. Trs: { not(false()) -> true(), not(true()) -> false(), evenodd(x, 0()) -> not(evenodd(x, s(0()))), evenodd(s(x), s(0())) -> evenodd(x, 0()), evenodd(0(), s(0())) -> false() } Matrix Interpretation: Interpretation class: triangular [2] [0] = [3] [2] [X2] [1 0 0][X2] [2] [s]([X1]) = [0 0 0][X1] + [0] [X0] [0 0 1][X0] [2] [X5] [X2] [1 0 2][X5] [1 3 1][X2] [3] [evenodd]([X4], [X1]) = [0 0 0][X4] + [0 0 0][X1] + [1] [X3] [X0] [0 0 1][X3] [0 0 1][X0] [0] [0] [true] = [1] [0] [X2] [1 2 0][X2] [0] [not]([X1]) = [0 0 0][X1] + [1] [X0] [0 0 0][X0] [1] [1] [false] = [0] [0] Qed