FYI: cross-posted at 
http://math.stackexchange.com/questions/1310423/free-group-in-gap

> On 5 Jun 2015, at 10:05, fahime babaee <f.alibab...@gmail.com> wrote:
> 
>  Let F be a free group on two generator, I need the following program in
> GAP
> Suppose that w \in [F,F] and let x be its first letter. then x^{-1} must
> also occur in w, so w=xux^{-1}v for some u and v  in F, and hence
> w=(xux^{-1})(uv) and it is sufficent to express uv as product of
> commutators. Since length of uv is two less than than w
> this process terminates. By this algorithm I can express w as a product of
> commutators.
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