One of the important problems that may be formulated in an ARS is the word problem: given "x" and "y", are they equivalent under formula_48? This is a very general setting for formulating the word problem for the presentation of an algebraic structure. For instance, the word problem for groups is a particular case of an ARS word problem. Central to an "easy" solution for the word problem is the existence of unique normal forms: in this case if two objects have the same normal form, then they are equivalent under formula_34. The word problem for an ARS is undecidable in general.