Abstract
In this work, we first consider a goal-oriented extension of the dependency pair framework for proving termination w.r.t. a given set of initial terms. Then, we introduce a new result for proving relative termination in terms of a dependency pair problem. Both contributions put together allow us to define a simple and powerful approach to analyzing the termination of narrowing, an extension of rewriting that replaces matching with unification in order to deal with logic variables. Our approach could also be useful in other contexts where considering termination w.r.t. a given set of terms is also natural (e.g., proving the termination of functional programs).
This work has been partially supported by the Spanish Ministerio de Ciencia e Innovación under grant TIN2008-06622-C03-02, by Generalitat Valenciana under grants ACOMP/2009/017 and GV/2009/024, and by UPV (programs PAID-05-08 and PAID-06-08). The second author has been partially supported by a grant from Nagoya Industrial Science Research Institute.
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Iborra, J., Nishida, N., Vidal, G. (2010). Goal-Directed and Relative Dependency Pairs for Proving the Termination of Narrowing. In: De Schreye, D. (eds) Logic-Based Program Synthesis and Transformation. LOPSTR 2009. Lecture Notes in Computer Science, vol 6037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12592-8_5
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