A system in which words (expressions) of a formal language can be transformed according to a finite set of rewrite rules is called a reduction system. While reduction systems are also known as string rewriting systems or term rewriting systems, the term "reduction system" is more general. Lambda calculus is an example of a reduction system with lambda conversion rules constituting its rewrite rules. If none of the rewrite rules of a reduction system apply to expression E, then E is said to be in normal form for a reduction system.

Church-Rosser property | confluent | critical pair | finitely terminating | formal language | Knuth-Bendix completion algorithm | lambda calculus | multiway system | reduction order | string rewriting system