# Proving termination with Multiset Orderings

@inproceedings{Dershowitz1979ProvingTW, title={Proving termination with Multiset Orderings}, author={Nachum Dershowitz and Zohar Manna}, booktitle={ICALP}, year={1979} }

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

## 450 Citations

On the Formalization of Termination Techniques based on Multiset Orderings

- Computer ScienceRTA
- 2012

It is shown that checking the correct application of the techniques--where all parameters are provided--is also NP-hard, since the problem of deciding the generalized multiset ordering is NP- hard.

A general criterion for avoiding infinite unfolding during partial deduction

- Computer ScienceNew Generation Computing
- 2009

This work formulate formal and practical criteria for controlling the unfolding during the construction of SLD-trees that form the basis of a partial deduction and provides algorithms that allow to use these criteria in a constructive way.

Total termination of term rewriting

- Computer ScienceApplicable Algebra in Engineering, Communication and Computing
- 2005

It turns out that for this kind of termination the only interesting orders below ɛ0 are built from the natural numbers by lexicographic product and the multiset construction, and it is shown that both constructions are essential.

Paramodulation with non-monotonic orderings

- MathematicsProceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158)
- 1999

By a careful further analysis of the technique, this work obtains the first Knuth-Bendix completion procedure that finds a convergent TRS for a given set of equations E and a (possibly non-totalizable) reduction ordering p whenever it exists.

SAT-based termination analysis using monotonicity constraints over the integers

- Computer ScienceTheory and Practice of Logic Programming
- 2011

An algorithm for proving termination of programs abstracted to systems of monotonicity constraints in the integer domain based on the search for a special type of ranking function defined in terms of bounded differences between multisets of integer values is described.

A theory of function-induced-orders to study recursion termination

- MathematicsArXiv
- 2013

It is shown that repeated iterations of a function can induce an order amongst the elements of its domain set, and the poset is shown to look like a forest of trees, with a possible base set and a generator set.

Termination of non-simple rewrite systems

- Computer Science
- 1996

There are appendices describing the interface to code written in common lisp which implements the well-quasi general path ordering and showing its usage to prove termination of a rewrite system for insertion sort.

Total Termination of Term Rewriting

- Computer ScienceRTA
- 1993

For a wide class of term rewriting systems it is proved that total termination is a modular property, and most of the techniques are based on ordinal arithmetic.

Efficient tests for top-down termination of logical rules

- Computer ScienceJACM
- 1988

The “uniqueness” property of logical rules is introduced, which is satisfied by many of the common examples of rules and is easily recognized.

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