Church-Rosser Thue systems and formal languages

Since about 1971, much research has been done on Thue systems that have properties that ensure viable and efficient computation. The strongest of these is the Church-Rosser property, which states that two equivalent strings can each be brought to a unique canonical form by a sequence of length-reducing rules. In this paper three ways in which formal languages can be defined by Thue systems with this property are studied, and some general results about the three families of languages so determined are studied.