Recursive Path Ordering for Infinite Labelled Rewrite Systems
نویسندگان
چکیده
Semantic labelling is a transformational technique for proving termination of Term Rewriting Systems (TRSs). Only its variant with finite sets of labels was used so far in tools for automatic termination proving and variants with infinite sets of labels were considered not to be suitable for automation. We show that such automation can be achieved for semantic labelling with natural numbers, in combination with recursive path ordering (RPO). In order to do so we developed algorithms to deal with recursive path ordering for these infinite labelled systems. Using these techniques, our tool, TPA, is the only current tool that can prove termination of the SUBST system automatically.
منابع مشابه
Automation of Recursive Path Ordering for Infinite Labelled Rewrite Systems
Semantic labelling is a transformational technique for proving termination of Term Rewriting Systems (TRSs). Only its variant with finite sets of labels was used so far in tools for automatic termination proving and variants with infinite sets of labels were considered not to be suitable for automation. We show that such automation can be achieved for semantic labelling with natural numbers, in...
متن کاملA Termination Ordering for Higher Order Rewrite Systems
We present an extension of the recursive path ordering for the purpose of showing termination of higher order rewrite systems. Keeping close to the general path ordering of Dershowitz and Hoot, we demonstrate su cient properties of the termination functions for our method to apply. Thereby we describe a class of di erent orderings. Finally we compare our method to previously published extension...
متن کاملA Complex Example of a Simplifying Rewrite System
For a string rewriting system, it is known that termination by a simpliication ordering implies multiple recursive complexity. This theoretical upper bound is, however, far from having been reached by known examples of rewrite systems. All known methods used to establish termination by simpliication yield a primitive recursive bound. Furthermore, the study of the order types of simpliication or...
متن کاملA Termination Ordering for Higher Order Rewrite System
We present an extension of the recursive path ordering for the purpose of showing termination of higher order rewrite systems. Keeping close to the general path ordering of Dershowitz and Hoot, we demonstrate the necessary properties of the termination functions for our method to apply, thus describe a class of diierent orderings. We also give a counterexample to a previously published extensio...
متن کاملA Total, Ground path Ordering for Proving Termination of AC-Rewrite Systems
A new path ordering for showing termination of associative-commutative (AC) rewrite systems is deened. If the precedence relation on function symbols is total, the ordering is total on ground terms, but unlike the ordering proposed by Rubio and Nieuwenhuis, this ordering can orient the distributivity property in the proper direction. The ordering is deened in a natural way using recursive path ...
متن کامل