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Termination of term rewriting using dependency pairs \Lambda

Summary: Termination of term rewriting using dependency
pairs \Lambda
Thomas Arts y J¨urgen Giesl z
We present techniques to prove termination and innermost termina­
tion of term rewriting systems automatically. In contrast to previous
approaches, we do not compare left­ and right­hand sides of rewrite rules,
but introduce the notion of dependency pairs to compare left­hand sides
with special subterms of the right­hand sides. This results in a technique
which allows to apply existing methods for automated termination proofs
to term rewriting systems where they failed up to now. In particular, there
are numerous term rewriting systems where a direct termination proof
with simplification orderings is not possible, but in combination with our
technique, well­known simplification orderings (such as the recursive path
ordering, polynomial orderings, or the Knuth­Bendix ordering) can now
be used to prove termination automatically.
Unlike previous methods, our technique for proving innermost termi­
nation automatically can also be applied to prove innermost termination
of term rewriting systems that are not terminating. Moreover, as inner­
most termination implies termination for certain classes of term rewriting


Source: Ábrahám, Erika - Fachgruppe Informatik, Rheinisch Westfälische Technische Hochschule Aachen (RWTH)


Collections: Computer Technologies and Information Sciences