# Dershowitz–Manna ordering

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In mathematics, the **Dershowitz–Manna ordering** is a well-founded ordering on multisets named after Nachum Dershowitz and Zohar Manna. It is often used in context of termination of programs or term rewriting systems.

Suppose that is a partial 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:

An equivalent definition was given by Huet and Oppen as follows:

## References

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}}. (Also in *Proceedings of the International Colloquium on Automata, Languages and Programming*, Graz, Lecture Notes in Computer Science 71, Springer-Verlag, pp. 188–202 [July 1979].)

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