Abstract
A Knuth–Bendix-style completion procedure for groups is presented that, instead of working with sets of string-rewriting rules, manipulates finite sets of word cycles. A characterization is given for the resulting sets of persistent word cycles, from which it follows that the completion procedure terminates successfully if and only if the reduced word problem of the finite group presentation considered is a finite set. In this case the resulting set of persistent word cycles yields a finite canonical string-rewriting system for every linear reduction ordering.
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Cremanns, R., Otto, F. A Completion Procedure for Finitely Presented Groups That Is Based on Word Cycles. Journal of Automated Reasoning 28, 235–256 (2002). https://doi.org/10.1023/A:1015741511536
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DOI: https://doi.org/10.1023/A:1015741511536