Has anyone out there written a routine that interfaces GAP and the
automatic groups software by D. Epstein, D. Holt, and S. Rees?

I think it would be very useful to have such a routine. GAP handles
finitely presented groups gracefully, so it should be a natural front end
for the automatic groups software.

I have something similar.
Prof. Joachim Neubueser suggested me to interface the stand alone
Knuth-Bendix written by the authors named above.
I have an almost completed and not satisfactorily tested
K-B written in GAP. As soon as I finish the current two papers,
I will complete and release the Knuth-Bendix for GAP.

However, the KBMAG (stands for Knuth-Bendix on Monoids and Automatic Groups),
is naturally much more powerful, and has a suitable interface to GAP.
A further important feature, that the input and output format for files
was developed by the GASP group, and conforms to the syntax of the GAP system.

In spite of the facts above, it makes sense to have a GAP implementation
of the Knuth-Bendix (for monoids and groups) as well.
(1) Some times the speed is not as important, as it is comfortable to
remain entirely within the GAP system. You might want to play with different
settings, and you might prefer the benefit of the flexible access to and
control of the algorithm, because it is written in GAP.
(2) It is on my todo list (or at least on my wish list), to profile
the GAP implementation and to write the appropriate kernel support.

Peter Prohle