Minimal 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

A minimal rewriting system is a complete rewriting system with the following additional properties:

• The right side of every rewrite is an irreducible word
• If $(l_{1},r_{1}),(l_{2},r_{2})\in R$ then $l_{1}$ is not a subword of $l_{2}$