We immediately get some very useful connections with other areas of algebra. For example, the alphabet {"a", "b"} with the rules { "ab" → ε, "ba" → ε }, where ε is the empty string, is a presentation of the free group on one generator. If instead the rules are just { "ab" → ε }, then we obtain a presentation of the bicyclic monoid. Thus semi-Thue systems constitute a natural framework for solving the word problem for monoids and groups. In fact, every monoid has a presentation of the form formula_66, i.e. it may always be presented by a semi-Thue system, possibly over an infinite alphabet.