Termination of term rewriting using dependency pairs
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Electronic Notes in Theoretical Computer Science (ENTCS)
Modular Termination of Basic Narrowing
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
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Logic-Based Program Synthesis and Transformation
Termination of narrowing revisited
Theoretical Computer Science
Termination of narrowing via termination of rewriting
Applicable Algebra in Engineering, Communication and Computing
An integrated framework for the diagnosis and correction of rule-based programs
Theoretical Computer Science
Goal-directed and relative dependency pairs for proving the termination of narrowing
LOPSTR'09 Proceedings of the 19th international conference on Logic-Based Program Synthesis and Transformation
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In this work, we extend the dependency pair approach for automated proofs of termination in order to prove the termination of narrowing. Our extension of the dependency pair approach generalizes the standard notion of dependency pairs by taking specifically into account the dependencies between the left-hand side of a rewrite rule and its own argument subterms. We demonstrate that the new narrowing dependency pairs exactly capture the narrowing termination behavior and provide an effective termination criterion which we prove to be sound and complete. Finally, we discuss how the problem of analyzing narrowing chains can be recast as a standard analysis problem for traditional (rewriting) chains, so that the proposed technique can be effectively mechanized by reusing the standard DP infrastructure.