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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