YES(?,O(n^2)) 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 [X3] [X1] [1 1][X3] [1 3][X1] [0] [+]([X2], [X0]) = [0 1][X2] + [0 1][X0] + [0] [X1] [1 0][X1] [2] [s]([X0]) = [0 1][X0] + [2] [0] [0] = [2] [X1] [1 2][X1] [3] [odd]([X0]) = [0 1][X0] + [2] [2] [true] = [0] [X1] [1 0][X1] [2] [not]([X0]) = [0 0][X0] + [0] [2] [false] = [0] Qed