Reduction Order
المؤلف:
Baader, F. and Nipkow, T
المصدر:
Term Rewriting and All That. Cambridge, England: Cambridge University Press, 1999.
الجزء والصفحة:
...
8-2-2022
892
Reduction Order
A strict order 
on the set of terms of a term rewriting system is called a reduction order if
1. The set of terms is well ordered with respect to 
, that is, all its nonempty subsets contain their least elements,
2. This order is compatible with functions (operations) of the system, i.e.,
and
3. For any substitution 
(cf. unification), 
.
If 
holds for every rewriting rule 
, then this term rewriting system is finitely terminating.
REFERENCES
Baader, F. and Nipkow, T. Term Rewriting and All That. Cambridge, England: Cambridge University Press, 1999.
Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 1037, 2002.
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