 Abstract rewriting system

In mathematical logic and theoretical computer science, an abstract rewriting system (also (abstract) reduction system or abstract rewrite system; abbreviation ARS) is a formalism that captures the quintessential notion and properties of rewriting systems.In its simplest form, an ARS is simply a set (of "objects") together with a binary relation, traditionally denoted with formula_1; this definition can be further refined if we index (label) subsets of the binary relation.