Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Advanced topics in term rewriting
Advanced topics in term rewriting
Semantic foundations for generalized rewrite theories
Theoretical Computer Science
Mechanizing and Improving Dependency Pairs
Journal of Automated Reasoning
Proving Termination of Context-Sensitive Rewriting with MU-TERM
Electronic Notes in Theoretical Computer Science (ENTCS)
Proving operational termination of membership equational programs
Higher-Order and Symbolic Computation
Proceedings of the 10th international ACM SIGPLAN conference on Principles and practice of declarative programming
Usable Rules for Context-Sensitive Rewrite Systems
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Improving Context-Sensitive Dependency Pairs
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
VMTL---A Modular Termination Laboratory
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
From Outermost to Context-Sensitive Rewriting
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Automating the dependency pair method
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
Relaxing monotonicity for innermost termination
Information Processing Letters
Context-sensitive dependency pairs
Information and Computation
Context-sensitive dependency pairs
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
AProVE 1.2: automatic termination proofs in the dependency pair framework
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Proving termination properties with MU-TERM
AMAST'10 Proceedings of the 13th international conference on Algebraic methodology and software technology
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Termination of context-sensitive rewriting (CSR) is an interesting problem with several applications in the fields of term rewriting and in the analysis of programming languages like CafeOBJ, Maude, OBJ, etc. The dependency pair approach, one of the most powerful techniques for proving termination of rewriting, has been adapted to be used for proving termination of CSR. The corresponding notion of context-sensitive dependency pair (CSDP) is different from the standard one in that collapsing pairs (i.e., rules whose right-hand side is a variable) are considered. Although the implementation and practical use of CSDPs lead to a powerful framework for proving termination of CSR, handling collapsing pairs is not easy and often leads to impose heavy requirements over the base orderings which are used to achieve the proofs. A recent proposal removes collapsing pairs by transforming them into sets of new (standard) pairs. In this way, though, the role of collapsing pairs for modeling context-sensitive computations gets lost. This leads to a less intuitive and accurate description of the termination behavior of the system. In this paper, we show how to get the best of the two approaches, thus obtaining a powerful context-sensitive dependency pair framework which satisfies all practical and theoretical expectations.