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.
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- 7.Serebrenik, A., Schreye, D.D.: On termination of meta-programs. Theory and Practice of Logic Programming. To appear, available at http://arxiv.org/abs/cs.PL/0110035