Because of these equivalences, a fair bit of variation in definitions is encountered in the literature. For instance, in Bezem "et al." 2003 the Church–Rosser property and confluence are defined to be synonymous and identical to the definition of confluence presented here; Church–Rosser as defined here remains unnamed, but is given as an equivalent property; this departure from other texts is deliberate. Because of the above corollary, in a confluent ARS one may define a normal form "y" of "x" as an irreducible "y" with the property that formula_50. This definition, found in Book and Otto, is equivalent to common one given here in a confluent system, but it is more inclusive more in a non-confluent ARS.