>
> GAP4 has 39.5-2 Factorization (
> http://www.gap-system.org/Manuals/doc/ref/chap39.html)
>
> calling GAP from Sage is not hard...
>

Thanks for your reply -- but I am still a little puzzled:

gap has two algorithms to compute a word in generators. This one, and the 
one implemented in `word_problem` using the gap commands 
`EpimorphismFromFreeGroup` and `PreImagesRepresentative`.

The first ensures the word to be reduced by iterating through the complete 
group, while the second does not necessarily provide a reduced word.

Is there any reason for not travelling the group along the Cayley graph 
with the given set of generators, and returning a word once the element it 
found in this graph, without expanding the complete group?

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