# Finitely terminating rewriting system

From Groupprops

Template:Rewriting system property

*This article is about a standard (though not very rudimentary) definition in an area related to, but not strictly part of, group theory*

## Contents

## Definition

### Symbol-free definition

A rewriting system is said to be **finitely terminating** or **Noetherian** if every chain of reductions in the rewriting system terminates in finitely many steps.

Note that though this property is originally defined for a rewriting system of a monoid, it also makes sense for a rewriting system for a group.