Group with a finite complete rewriting system

Definition
A finitely generated group is termed a group with a finite complete rewriting system if it has a complete rewriting system (i.e., a rewriting system that is both finitely terminating and confluent) with respect to a finite generating set such that the rewriting system is finite in size, i.e., it makes use of only finitely many rewriting rules.

Note that it is possible for a group to have a finite complete rewriting system with respect to one finite generating set but not have any finite complete rewriting system with respect to a different finite generating set. We use the term group with a finite complete rewriting system if there exists at least one finite generating set for which a finite complete rewriting system exists.