  A conjecture of Gr\"obner-Shirshov basis of any Coxeter group has proposed by
L.A. Bokut and L.-S. Shiao \cite{bs01}. In this paper, we give an example to
show that the conjecture is not true in general. We list all possible
nontrivial inclusion compositions when we deal with the general cases of the
Coxeter groups. We give a Gr\"obner-Shirshov basis of a Coxeter group which is
without nontrivial inclusion compositions mentioned the above.
