YES O(n^4) 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] = [2] [3] [X3] [1 0 0 0][X3] [0] [X2] [0 0 0 0][X2] [0] [s]([X1]) = [0 0 1 3][X1] + [0] [X0] [0 0 0 1][X0] [1] [X7] [X3] [1 0 0 3][X7] [1 1 0 0][X3] [0] [X6] [X2] [0 0 0 0][X6] [0 0 0 0][X2] [0] [evenodd]([X5], [X1]) = [0 0 1 2][X5] + [0 0 1 0][X1] + [0] [X4] [X0] [0 0 0 0][X4] [0 0 0 1][X0] [0] [0] [0] [true] = [0] [0] [X3] [1 0 0 0][X3] [1] [X2] [0 0 0 0][X2] [0] [not]([X1]) = [0 0 0 0][X1] + [0] [X0] [0 0 0 0][X0] [0] [0] [0] [false] = [0] [0] Qed