In this work we will consider the calculation of Groebner-Shirshov bases of
Coxeter groups. This will be the main focus of the work. In \cite{Bokut-Shiao},
Bokut & Shiao gave the Groebner-Shirshov bases of positive definite classical
Coxeter groups $A_l, B_l, D_l$ by using the techniques of Elimination of
Leading Word.