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
; this definition can be further refined if we index (label) subsets of the binary relation. Despite its simplicity, an ARS is sufficient to describe important properties of rewriting systems like
normal forms,
termination, and various notions of
confluence.