# Orderings for term-rewriting systems

@article{Dershowitz1979OrderingsFT, title={Orderings for term-rewriting systems}, author={Nachum Dershowitz}, journal={20th Annual Symposium on Foundations of Computer Science (sfcs 1979)}, year={1979}, pages={123-131} }

Methods of proving that a term-rewriting system terminates are presented. They are based on the notion of "simplification orderings", orderings in which any term that is homeomorphically embeddable in another is smaller than the other. A particularly useful class of simplification orderings, the "recursive path orderings", is defined. Several examples of the use of such orderings in termination proofs are given.

#### 545 Citations

A Path Ordering for Proving Termination of Term Rewriting Systems

- Mathematics, Computer Science
- TAPSOFT, Vol.1
- 1985

A new partial ordering scheme for proving uniform termination of term rewriting systems is presented and it is shown that the ordering is a well-founded simplification ordering and also a strict extension of the recursive path ordering scheme of Dershowitz. Expand

Termination of Rewriting

- Mathematics, Computer Science
- J. Symb. Comput.
- 1987

Methods for proving that systems of rewrite rules are terminating programs are described, including polynomial interpretations and path orderings, which are used in termination proofs of various kinds of orderings on terms. Expand

Simplification orderings: Putting them to the test

- Mathematics, Computer Science
- Journal of Automated Reasoning
- 2004

A collection of well-known simplification orderings will be briefly presented including path orderings and decomposition orderings to describe a detailed empirical study of their time complexities with respect to comparable pairs of terms. Expand

The Termination Hierarchy for Term Rewriting

- Mathematics, Computer Science
- Applicable Algebra in Engineering, Communication and Computing
- 2001

Abstract. A number of properties of term rewriting systems related to termination are discussed. It is examined how these properties are affected by modifications in the definitions like weakening… Expand

Termination of Order-sorted Rewriting

- Computer Science
- ALP
- 1992

The goal is to perform termination proofs of programs for executable specification languages like OBJ3, and an extension of Lexicographic Path Ordering is proposed, that gives a termination proof for order-sorted rewrite systems, that would not terminate in the unsorted case. Expand

Termination of Term Rewriting by Interpretation

- Computer Science, Mathematics
- CTRS
- 1992

A transformation on term rewriting systems eliminating distributive rules is introduced and a new termination proof of SUBST from [10] is given. Expand

Natural Termination

- Computer Science
- Theor. Comput. Sci.
- 1995

Two techniques are examined for showing termination of rewrite systems when simpli cation ordering are insu cient, both of which allow the use of natural interpretations under which rules rewrite terms to terms of the same value. Expand

Simplification Orderings: Histrory of Results

- Mathematics, Computer Science
- Fundam. Informaticae
- 1995

An overview on different aspects of termination proof techniques for unconditional term rewriting systems using simplification orderings and a formalism that allows clear representations of orderings is introduced. Expand

Multiset Path Orderings and Their Application to Termination of Term Rewriting Systems

- Mathematics
- 2013

In this expository paper, a comprehensive study of multiset orderings, nested multiset orderings and multiset path orderings is presented. In particular, it is illustrated how multiset path orderings… Expand

A Termination Ordering for Higher Order Rewrite System

- Computer Science
- RTA
- 1995

We present an extension of the recursive path ordering for the purpose of showing termination of higher order rewrite systems. Keeping close to the general path ordering of Dershowitz and Hoot, we… Expand

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