  The word problem of a group is a very important question. The word problem in
the braid group is of particular interest for topologists, algebraists and
geometers. In previouse article we have looked at the braid group from a
topological point of view, and thus using a new computerized representation of
some elements of the fundamental group we gave a solution for its word problem.
In this paper we will give an algorithm that will make it possible to transform
the new presentation into a syntactic presentation. This will make it possible
to computerize the group operation to sets of elements of the fundamental
group, which are isomorphic to the braid group. More over we will show that it
is sufficient enough to look at the syntactic presentation in order to solve
the braid word problem, resulting with a better and faster braid word solution.
