# Commutation, Transformation, and Termination

@inproceedings{Bachmair1986CommutationTA, title={Commutation, Transformation, and Termination}, author={Leo Bachmair and Nachum Dershowitz}, booktitle={CADE}, year={1986} }

In this paper we study the use of commutation properties for proving termination of rewrite systems. Commutation properties may be used to prove termination of a combined system R∪S by proving termination of R and S separately. We present termination methods for ordinary and for equational rewrite systems. Commutation is also important for transformation techniques. We outline the application of transforms—mappings from terms to terms—to termination in general, and describe various specific…

## 141 Citations

Commutativity of Term Rewriting Systems∗

- Computer Science
- 2011

Using the concept of critical pairs between two term rewriting systems, a sufficient condition for commutativity is proposed and a new sufficient condition is offered for the Church-Rosser property of left-linearterm rewriting systems.

Proving Termination of Associative Commutative Rewriting Systems by Rewriting

- Computer ScienceCADE
- 1986

This paper proposes a special reduction ordering for proving termination of Associative Commutative rewriting systems, based on a transformation of the terms by a rewriting system with rules similar to distributivity, and shows cases where this ordering fails.

Termination Modulo Equations by Abstract Commutation with an Application to Iteration

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1997

Full-Commutation and Fair-Termination in Equational (and Combined) Term-Rewriting Systems

- Computer ScienceCADE
- 1986

This paper defines the notion of fairness in equational term-rewriting systems, where a derivation step is a composition of the equality generated by a (finite) set of equations with one step rewriting using a set of rules.

Incremental Termination Proofs and the Length of Derivations

- Computer ScienceRTA
- 1991

It is shown how an incremental termination proof for a term rewriting system T can be used to derive upper bounds on the length of derivations in T, and how these results can be applied to yield (sharp) low-degree polynomial complexity bounds.

Non-looping rewriting

- Mathematics
- 1996

In this paper we present a number of necessary conditions for the existence of loops, i.e. reductions of the form t !R c[t ]. We investigate which of the known termination preserving transformation…

Remarks on isomorphisms of simple inductive types

- MathematicsElectron. Notes Theor. Comput. Sci.
- 2003

On Lazy Commutation

- MathematicsLanguages: From Formal to Natural
- 2009

The notion of a constricting sequence is developed, which can be applied to generic path orderings used in termination proofs and combinatorial commutation properties for reordering a sequence of two kinds of steps.

Termination of Associative-Commutative Rewriting by Dependency Pairs

- MathematicsRTA
- 1998

It is shown how this criterion for termination of rewriting can be generalized to rewriting modulo associativity and commutativity, and how one can build weak AC-compatible reduction orderings which may be used in this criterion.

Isomorphisms of simple inductive types through extensional rewriting

- MathematicsMathematical Structures in Computer Science
- 2005

The notion of a faithful copy of an inductive type and a corresponding conversion relation that also preserves the good properties of the calculus are defined.

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