Editing Knuth–Bendix completion algorithm (section)

The '''Knuth–Bendix completion algorithm''' (named after [[Donald E. Knuth|Donald Knuth]] and Peter Bendix<ref>[http://www.win.tue.nl/~mvdbrand/courses/seminar/0809/papers/ag-genesis.pdf D. Knuth, "The Genesis of Attribute Grammars"]</ref>) is a [[semidecidable|semi-decision]]<ref name="SchwartzCantone2011">{{cite book|author1=Jacob T. Schwartz|author2=Domenico Cantone|author3=Eugenio G. Omodeo|author4=Martin Davis|title=Computational Logic and Set Theory: Applying Formalized Logic to Analysis|year=2011|publisher=Springer Science & Business Media|isbn=978-0-85729-808-9|page=200}}</ref><ref>{{Cite book | doi = 10.1007/3-540-18088-5_6| chapter = On word problems in equational theories| title = Automata, Languages and Programming| volume = 267| pages = 54| series = Lecture Notes in Computer Science| year = 1987| last1 = Hsiang | first1 = J. | last2 = Rusinowitch | first2 = M. | isbn = 978-3-540-18088-3| chapter-url = https://hal.inria.fr/inria-00075875/file/RR-0678.pdf}}, p. 55</ref> [[algorithm]] for transforming a set of [[equation]]s (over [[term (logic)|terms]]) into a [[Confluence (term rewriting)|confluent]] [[term rewriting system]].  When the algorithm succeeds, it effectively solves the [[word problem (mathematics)|word problem]] for the specified [[algebra]].

[[Buchberger's algorithm]] for computing [[Gröbner basis|Gröbner bases]] is a very similar algorithm. Although developed independently, it may also be seen as the instantiation of Knuth–Bendix algorithm in the theory of [[polynomial ring]]s.