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Polynomial constraint-solving plays a prominent role in several areas of engineering and software verification. In particular, polynomial constraint solving has a long and successful history in the development of tools for proving termination of programs. Well-known and very efficient techniques, like SAT algorithms and tools, have been recently proposed(More)
Reasoning about the termination of equational programs in sophisticated equa-tional languages such as ELAN, MAUDE, OBJ, CAFEOBJ, HASKELL, and so on, requires support for advanced features such as evaluation strategies, rewriting modulo, use of extra variables in conditions, partiality, and expressive type systems (possibly including polymorphism and(More)
Context-sensitive dependency pairs (CS-DPs) are currently the most powerful method for automated termination analysis of context-sensitive rewriting. However, compared to DPs for ordinary rewriting, CS-DPs suffer from two main drawbacks: (a) CS-DPs can be collapsing. This complicates the handling of CS-DPs and makes them less powerful in practice. (b) There(More)
Context-sensitive rewriting is a simple rewriting restriction which is formalized by imposing xed restrictions on replacements. Such a restriction is given on a purely syntactic basis: it is given on the arguments of symbols of the signature and inductively extended to arbitrary positions of terms built from those symbols. The termination behavior is not(More)
Nowadays, polynomial interpretations are an essential ingredient in the development of tools for proving termination. We have recently proven that polynomial interpretations over the reals are strictly better for proving polynomial termination of rewriting than those which only use integer coefficients. Some essential aspects of their practical use, though,(More)
We present a generic scheme for the declarative debugging of functional programs modeled as term rewriting systems. We associate to our programs a semantics based on a (continuous) immediate consequence operator, T R , which models the (values/normal forms) semantics of R. Then, we develop an effective debugging methodology which is based on abstract(More)