An object "x" in "A" is called reducible if there exists some other "y" in "A" such that formula_39; otherwise it is called irreducible or a normal form. An object "y" is called a normal form of "x" if formula_40, and "y" is irreducible. If "x" has a "unique" normal form, then this is usually denoted with formula_41. In example 1 above, "c" is a normal form, and formula_42. If every object has at least one normal form, the ARS is called normalizing.