Abstract
It is known that if there exists a Grobner-Shirshov basis for a group G, then we say that one of the decision problem, namely the word problem, is solvable for G as well. Therefore, as the main target of this paper, we will present a (non-commutative) Grobner-Shirshov basis for the braid group associated with the congruence classes of complex reflection group G(12) which will give us normal forms of the elements of G(12) and so will obtain a new algorithm to solve the word problem over it.