An efficient strategy for word-cycle completion in finitely presented groups

We present an efficient strategy for the application of the inference rules of a completion procedure for finitely presented groups. This procedure has been proposed by Cremanns and Otto and uses a combinatorial structure called word-cycle. Our strategy is complete in the sense that a set of persistent word-cycles can be used to solve the reduced word problem of the finitely presented group given as input. This procedure has been implemented in order to experiment with various examples of groups.