Dependency pairs for proving termination properties of conditional term rewriting systems

[EN] The notion of operational termination provides a logic-based definition of termination of computational systems as the absence of infinite inferences in the computational logic describing the operational semantics of the system. For Conditional Term Rewriting Systems we show that operational termination is characterized as the conjunction of two termination properties. One of them is traditionally called termination and corresponds to the absence of infinite sequences of rewriting steps (a horizontal dimension). The other property, that we call V-termination, concerns the absence of infinitely many attempts to launch the subsidiary processes that are required to perform a single rewriting step (a vertical dimension). We introduce appropriate notions of dependency pairs to characterize termination, V-termination, and operational termination of Conditional Term Rewriting Systems. This can be used to obtain a powerful and more expressive framework for proving termination properties of Conditional Term Rewriting Systems.Partially supported by the EU (FEDER), Spanish MINECO projects TIN 2013-45732-C4-1-P and TIN2015-69175-C4-1-R, GV project PROMETEOII/2015/013, and NSF grant CNS 13-19109. Salvador Lucas' research was partly developed during a sabbatical year at UIUCLucas Alba, S.; Meseguer, J. (2017). Dependency pairs for proving termination properties of conditional term rewriting systems. Journal of Logical and Algebraic Methods in Programming. 86(1):236-268. https://doi.org/10.1016/j.jlamp.2016.03.003S23626886