Termination of term rewriting using dependency pairs
We present techniques to prove termination and innermost termination of term rewriting systems automatically. In contrast to previous approaches, we do not compare left- and right-hand sides of rewrite rules, but introduce the notion of dependency pairs to compare left-hand sides with special subter...
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| Published in | Theoretical computer science Vol. 236; no. 1; pp. 133 - 178 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
06.04.2000
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| Subjects | |
| Online Access | Get full text |
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| Abstract | We present techniques to prove termination and innermost termination of term rewriting systems automatically. In contrast to previous approaches, we do not compare left- and right-hand sides of rewrite rules, but introduce the notion of
dependency pairs to compare left-hand sides with special subterms of the right-hand 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, well-known simplification orderings (such as the recursive path ordering, polynomial orderings, or the Knuth–Bendix ordering) can now be used to prove termination automatically. Unlike previous methods, our technique for proving
innermost termination automatically can also be applied to prove innermost termination of term rewriting systems that are not terminating. Moreover, as innermost termination implies termination for certain classes of term rewriting systems, this technique can also be used for termination proofs of such systems. |
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| AbstractList | We present techniques to prove termination and innermost termination of term rewriting systems automatically. In contrast to previous approaches, we do not compare left- and right-hand sides of rewrite rules, but introduce the notion of
dependency pairs to compare left-hand sides with special subterms of the right-hand 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, well-known simplification orderings (such as the recursive path ordering, polynomial orderings, or the Knuth–Bendix ordering) can now be used to prove termination automatically. Unlike previous methods, our technique for proving
innermost termination automatically can also be applied to prove innermost termination of term rewriting systems that are not terminating. Moreover, as innermost termination implies termination for certain classes of term rewriting systems, this technique can also be used for termination proofs of such systems. |
| Author | Giesl, Jürgen Arts, Thomas |
| Author_xml | – sequence: 1 givenname: Thomas surname: Arts fullname: Arts, Thomas email: thomas@cs.ruu.nl organization: Department of Computer Science, Utrecht University, P.O. Box 80.089, 3508 TB Utrecht, Netherlands – sequence: 2 givenname: Jürgen surname: Giesl fullname: Giesl, Jürgen email: giesl@informatik.tu-darmstadt.de organization: Department of Computer Science, Darmstadt University of Technology, Alexanderstraße 10, 64283 Darmstadt, Germany |
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| Keywords | Term rewriting Termination Verification Dependency pairs Automated theorem proving |
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| SubjectTerms | Automated theorem proving Dependency pairs Term rewriting Termination Verification |
| Title | Termination of term rewriting using dependency pairs |
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