Leanest quasi-orderings

Authors:
Nachum Dershowitz;E. Castedo Ellerman
Affiliations:
School of Computer Science, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel;Cambridge, MA
Venue:
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Year:
2005

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Abstract

A convenient method for defining a quasi-ordering, such as those used for proving termination of rewriting, is to choose the minimum of a set of quasi-orderings satisfying some desired traits. Unfortunately, a minimum in terms of set inclusion can be non-existent even when an intuitive “minimum” exists. We suggest an alternative to set inclusion, called “leanness”, show that leanness is a partial ordering of quasi-orderings, and provide sufficient conditions for the existence of a “leanest” ordering.