Finding the set of minimal cycles in Cayley graph of the group, w.r.t. the generators.

[hongyi-zhao]

I want to find the set of the minimal, indecomposable, words in generators. For this purpose, I try to utilize the Cayley graph as follows: consider the Cayley graph of the group, w.r.t. the generators. Now, the minimal cycles in the graph are exactly the minimal, indecomposable, words in generators (i.e. power product experssions).

I wonder whether I can do the above job with the help of GRAPE?

Regards,
Zhao