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