Finitely terminating rewriting system

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

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.

Relation with other properties

Stronger properties

• Special rewriting system
• Monadic rewriting system
• Length-reducing rewriting system
• Linear-time terminating rewriting system