Editing Knuth–Bendix completion algorithm (section)

==Generalizations==

If Knuth–Bendix does not succeed, it will either run forever and produce successive approximations to an infinite complete system, or fail when it encounters an unorientable equation (i.e. an equation that it cannot turn into a rewrite rule). An enhanced version will not fail on unorientable equations and produces a [[ground confluent]] system, providing a [[semi-algorithm]] for the word problem.<ref>{{cite journal |last1=Bachmair |first1=Leo |last2=Dershowitz |first2=Nachum |last3=Plaisted |first3=David A. |title=Completion Without Failure |journal=Rewriting Techniques |date=1989 |pages=1–30 |doi=10.1016/B978-0-12-046371-8.50007-9 |url=http://www.cs.tau.ac.il/~nachumd/papers/unfail-paper.pdf |access-date=24 December 2021}}</ref>

The notion of [[logged rewriting]] discussed in the paper by Heyworth and Wensley listed below allows some recording or logging of the rewriting process as it proceeds. This is useful for computing identities among relations for presentations of groups.