Abstract

We present an elementary proof of the classical result that the leftmost outermost strategy is normalizing for left-normal orthogonal rewrite systems. Our proof is local and extends to hyper-normalization and weakly orthogonal systems. Based on the new proof, we study basic normalization, i.e., we study normalization if the set of considered starting terms is restricted to basic terms. This allows us to weaken the left-normality restriction. We show that the leftmost outermost strategy is hyper-normalizing for basically left-normal orthogonal rewrite systems. This shift of focus greatly extends the applicability of the classical result, as evidenced by the experimental data provided.

BibTeX

@inproceedings{NHAMGM-RTA15,
  author    = "Nao Hirokawa and Aart Middeldorp and Georg Moser",
  title     = "Leftmost Outermost Revisited",
  booktitle = "Proceedings of the 26th International Conference on Rewriting
               Techniques and Applications (RTA 2015)",
  editor    = "Maribel Fern{\'a}ndez",
  series    = "Leibniz International Proceedings in Informatics"
  volume    = 36,
  pages     = "209--222",
  year      = 2015,
  doi       = "10.4230/LIPIcs.RTA.2015.209"
}