Normalization property (abstract rewriting)

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.