Groebner-Shirshov basis for the braid semigroup
  We found Groebner-Shirshov basis for the braid semigroup $B^+_{n+1}$. It gives a new algorithm for the solution of the word problem for the braid semigroup and so for the braid group. 
L. A. Bokut, Y. Fong, W.-F. Ke, L.-S. Shiao