##  [Knuth–Bendix Completion](/knuth-bendix-completion) 

  ##  [Knuth–Bendix Completion](https://puremath.quantumdictionary.io/knuth-bendix-completion-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A procedure applied to a presented rewriting system that attempts to produce a confluent (complete) term-rewriting system by orienting relations into rewrite rules under a chosen reduction ordering and adding consequences obtained from critical overlaps until no unresolved critical pairs remain or the process diverges.

 

 

 

 

 





 

 



 ##  [Knuth–Bendix Completion](https://algebra.quantumdictionary.io/knuth-bendix-completion-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An algorithmic procedure taking a set of rewrite rules (or relations) together with a well-founded reduction ordering and attempting to extend the rule set by adding consequences (resolving critical pairs) so as to produce a confluent (and terminating) rewriting system that decides word equality in the presented algebra when successful.