Related papers: Confluence by Critical Pair Analysis Revisited (Ex…
Logically Constrained Term Rewriting Systems (LCTRSs) provide a general framework for term rewriting with constraints. We discuss a simple dependency pair approach to prove termination of LCTRSs. We see that existing techniques transfer to…
Convergent rewriting systems on algebraic structures give methods to solve decision problems, to prove coherence results, and to compute homological invariants. These methods are based on higher-dimensional extensions of the critical…
Conditional term rewriting is an intuitive yet complex extension of term rewriting. In order to benefit from the simpler framework of unconditional rewriting, transformations have been defined to eliminate the conditions of conditional term…
Previous results on proving confluence for Constraint Handling Rules are extended in two ways in order to allow a larger and more realistic class of CHR programs to be considered confluent. Firstly, we introduce the relaxed notion of…
Confluence of a nondeterministic program ensures a functional input-output relation, freeing the programmer from considering the actual scheduling strategy, and allowing optimized and perhaps parallel implementations. The more general…
Dependency pairs are a key concept at the core of modern automated termination provers for first-order term rewriting systems. In this paper, we introduce an extension of this technique for a large class of dependently-typed higher-order…
Refinement types are a well-studied manner of performing in-depth analysis on functional programs. The dependency pair method is a very powerful method used to prove termination of rewrite systems; however its extension to higher order…
We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…
In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…
Rewriting systems on words are very useful in the study of monoids. In good cases, they give finite presentations of the monoids, allowing their manipulation by a computer. Even better, when the presentation is confluent and terminating,…
For the lambda-calculus with surjective pairing and terminal type, Curien and Di Cosmo were inspired by Knuth-Bendix completion, and introduced a confluent rewriting system that (1) extends the naive rewriting system, and (2) is stable…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
We study the derivational complexity of rewrite systems whose termination is provable in the dependency pair framework using the processors for reduction pairs, dependency graphs, or the subterm criterion. We show that the derivational…
We present crest, a tool for automatically proving (non-)confluence and termination of logically constrained rewrite systems. We compare crest to other tools for logically constrained rewriting. Extensive experiments demonstrate the promise…
We revisit completion modulo equational theories for left-linear term rewrite systems where unification modulo the theory is avoided and the normal rewrite relation can be used in order to decide validity questions. To that end, we give a…
Dependency pairs are one of the most powerful techniques for proving termination of term rewrite systems (TRSs), and they are used in almost all tools for termination analysis of TRSs. Problem #106 of the RTA List of Open Problems asks for…
This paper presents a formalization of decreasing diagrams in the theorem prover Isabelle. It discusses mechanical proofs showing that any locally decreasing abstract rewrite system is confluent. The valley and the conversion version of…
We present an Isabelle/HOL formalization of a characterization of confluence for quasi-reductive strongly deterministic conditional term rewrite systems, due to Avenhaus and Lor\'ia-S\'aenz.
Dependency pairs constitute a series of very effective techniques for the termination analysis of term rewriting systems. In this paper, we adapt the static dependency pair framework to logically constrained simply-typed term rewriting…
The notion of normal forms is ubiquitous in various equivalent transformations. Confluence (CR), one of the central properties of term rewriting systems (TRSs), concerns uniqueness of normal forms. Yet another such property, which is weaker…