YES O(n^5) 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 [0] [2] [0] = [0] [0] [3] [X4] [1 0 0 2 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] [2] [X0] [0 0 0 0 1][X0] [2] [X9] [X4] [1 0 0 2 2][X9] [1 3 0 0 0][X4] [3] [X8] [X3] [0 0 0 0 1][X8] [0 0 0 0 0][X3] [0] [evenodd]([X7], [X2]) = [0 0 0 0 0][X7] + [0 0 0 0 0][X2] + [0] [X6] [X1] [0 0 0 0 2][X6] [0 0 0 0 3][X1] [0] [X5] [X0] [0 0 0 0 0][X5] [0 0 0 0 1][X0] [1] [0] [0] [true] = [0] [0] [0] [X4] [1 0 0 0 0][X4] [2] [X3] [0 0 0 0 0][X3] [0] [not]([X2]) = [0 0 0 0 0][X2] + [0] [X1] [0 0 0 0 0][X1] [0] [X0] [0 0 0 0 0][X0] [0] [0] [0] [false] = [0] [0] [0] Qed