In
mathematical logic and
theoretical computer science, a
rewrite system has the
(strong) normalization property or is
terminating if every term is
strongly normalizing; that is, if every sequence of rewrites eventually terminates with an
irreducible term, also called a
normal form. A rewrite system may also have the
weak normalization property, meaning that for every term, there exists at least one particular sequence of rewrites that eventually yields a normal form, i.e., an irreducible term.