2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162420We 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.Group TheoryCombinatoricstext