# Proving termination with multiset orderings

@article{Dershowitz1979ProvingTW, title={Proving termination with multiset orderings}, author={Nachum Dershowitz and Zohar Manna}, journal={Commun. ACM}, year={1979}, volume={22}, pages={465-476} }

A common tool for proving the termination of programs is the <italic>well-founded set</italic>, a set ordered in such a way as to admit no infinite descending sequences. The basic approach is to find a <italic>termination function</italic> that maps the values of the program variables into some well-founded set, such that the value of the termination function is repeatedly reduced throughout the computation. All too often, the termination functions required are difficult to find and are of a…

## 277 Citations

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- Computer ScienceALP
- 1994

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We present in this paper a case study of the use of the ACL2 system, describing an ACL2 formalization of multiset relations, and showing how multisets can be used to prove non-trivial termination…

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- Mathematics[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science
- 1993

It is shown that any total well-founded ordering on N/sup n/ that is preserved under vector addition must have order type omega /sup lambda / for some 1<or=k< or=n; if k<n, there are continuum many such orderings, and if k=n,there are only n-factorial lexicographic orderings.

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- 2007

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- MathematicsICALP
- 1991

A ground convergent rewrite system is one that terminates and de nes unique normal forms for all ground terms, and validity of equations is decidable for nite convergent R, since the joinability (#) relation isDecidable.

On the Completeness of Arbitrary Selection Strategies for Paramodulation

- MathematicsICALP
- 2001

It is shown that if a paramodulation-based inference system is complete with eager selection of negative equations and it is compatible with equality constraint inheritance, then it iscomplete with arbitrary selection strategies.

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