0 Knuth – Bendix for groups with infinitely many rules ∗

We introduce a new class of groups with solvable word problem, namely groups specified by a confluent set of short-lex-reducing Knuth– Bendix rules which form a regular language. This simultaneously generalizes short-lex-automatic groups and groups with a finite confluent set of short-lex-reducing rules. We describe a computer program which looks for such a set of rules in an arbitrary finitely presented group. Our main theorem is that our computer program finds the set of rules, if it exists, given enough time and space. (This is an optimistic description of our result—for the more pessimistic details, see the body