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infChecker: A Tool for Checking Infeasibility

Given a CTRS R and terms s and t, we say that the reachability condition s = t isfeasible if there is a substitution sigma instantiating the variables in s and t such that the reachability test sigma(s) ->*R sigma(t) succeeds; otherwise, we call it infeasible. Given a sequence of reachability conditions (s1 = t1),…,(sn = tn), where n > 0, we say that the sequence is R-feasible if there is a substitution such that all the reachability tests sigma(si) ->*R sigma(ti) are satised.In [5, 6] we presented an approach to deal with infeasibility using a semantic criterion. In this paper we present infChecker, a new tool for checking infeasibility conditions of CTRSs based on this approach. We succesfully participated in the 2019 Confuence Competition in the INF (infeasibility) category, being the most powerful tool for checking both infeasibility and feasibility.

The 2D Dependency Pair Framework for conditional rewrite systems (Trabajo ya publicado)

Different termination properties of conditional term rewriting systems have been recently described emphasizing the bidimensional nature of the termination behavior of conditional rewriting. The absence of infinite sequences of rewriting steps (termination in the usual sense), provides the horizontal dimension. The absence of infinitely many attempts to launch the subsidiary processes that are required to check the rule’s condition and perform a single rewriting step has been called V-termination and provides the vertical dimension. We have characterized these properties by means of appropriate notions of dependency pairs and dependency chains. In this paper we introduce a 2D Dependency Pair Framework for automatically proving and disproving all these termination properties. Our implementation of the framework as part of the termination tool MU-TERM and the benchmarks obtained so far suggest that the 2D Dependency Pair Framework is currently the most powerful technique for proving operational termination of conditional term rewriting systems.