  We consider the Graver basis, the universal Groebner basis, a Markov basis
and the set of the circuits of a toric ideal. Let $A, B$ be any two of these
bases such that $A\not \subset B$, we prove that there is no polynomial on the
size or on the maximal degree of the elements of $B$ which bounds the size or
the maximal degree of the elements of $A$ correspondingly.
