Groebner-Shirshov basis for the braid group in the Artin-Garside   generators
  In this paper, we give a Groebner-Shirshov basis of the braid group $B_{n+1}$ in the Artin--Garside generators. As results, we obtain a new algorithm for getting the Garside normal form, and a new proof that the braid semigroup $B^+{n+1}$ is the subsemigroup in $B_{n+1}$. 
L. A. Bokut