Uncurrying for Innermost Termination and Derivational Complexity
Harald Zankl, Nao Hirokawa, and Aart MiddeldorpProceedings of the 5th International Workshop on Higher-Order Rewriting (HOR 2010), Electronic Proceedings in Theoretical Computer Science 49, pp. 46 – 57, 2011.
Abstract
First-order applicative term rewriting systems provide a natural
framework for modeling higher-order aspects. In earlier work we
introduced an uncurrying transformation which is termination
preserving and reflecting. In this paper we investigate how this
transformation behaves for innermost termination and (innermost)
derivational complexity. We prove that it reflects innermost termination
and innermost derivational complexity and that it preserves and
reflects polynomial derivational complexity. For the preservation of
innermost termination and innermost derivational complexity we give
counterexamples. Hence uncurrying may be used as a preprocessing
transformation for innermost termination proofs and establishing
polynomial upper and lower bounds on the derivational complexity.
Additionally it may be used to establish upper bounds on the innermost
derivational complexity while it neither is sound for proving innermost
non-termination nor for obtaining lower bounds on the innermost
derivational complexity.
BibTeX
@inproceedings{HZNHAM-HOR10, author = "Harald Zankl and Nao Hirokawa and Aart Middeldorp", title = "Uncurrying for Innermost Termination and Derivational Complexity", booktitle = "Proceedings of the 5th International Workshop on Higher-Order Rewriting", series = "Electronic Proceedings in Theoretical Computer Science", volume = 49, pages = "46--57", year = 2011, }