Suppose that is a
well-foundedpartial order and let be the set of all finite multisets on . For multisets we define the Dershowitz–Manna ordering as follows:
whenever there exist two multisets with the following properties:
,
,
, and
dominates , that is, for all , there is some such that .
An equivalent definition was given by Huet and Oppen as follows:
if and only if
, and
for all in , if then there is some in such that and .
Huet, G.; Oppen, D. C. (1980), "Equations and rewrite rules: A survey", in Book, R. (ed.), Formal Language Theory: Perspectives and Open Problems, New York: Academic Press, pp. 349–405.