  The existing algorithm to compute and verify the automata associated with an
automatic group deals only with the subclass of shortlex automatic groups. This
paper describes the extension of the algorithm to deal with automatic groups
associated with other word orders (the algorithm has now been implemented ) and
reports on the use of the algorithm for specific examples; in particular a very
natural automatic (or asynchonously automatic) structure for the
Baumslag-Solitar and related classes of groups (closely related to one
described for some of those groups by Epstein et al. is found from a wreath
product order over shortlex.
