Proving equivalence of different axiomatizations of free groups

The equivalence problem of different non-classical equational axiomatizations of free groups due to Higman and Neumann, Neumann, and others, is discussed. It is shown that such problems can be done easily using a rewrite rule based theorem prover such as RRL by generating complete rewriting systems for these axiomatizations. Some of these complete rewriting systems are obtained after introducing new function symbols which do not appear in the original non-classical axiomatizations. It is, however, suspected that these equivalence problems can be a considerable challenge for theorem provers based on other paradigms, such as natural deduction, resolution (clausal as well as non-clausal), and connection graphs.