 (The preference for the word "reduction" here instead of "rewriting" constitutes a departure from the uniform use of "rewriting" in the names of systems that are particularizations of ARS.Because the word "reduction" does not appear in the names of more specialized systems, in older texts reduction system is a synonym for ARS).An ARS is a set "A", whose elements are usually called objects, together with a binary relation on "A", traditionally denoted by →, and called the reduction relation, rewrite relation or just reduction.