Abstract

We present and compare some well-founded proof orders for decreasing diagrams. These proof orders order a conversion above another conversion if the latter is obtained by filling any peak in the former by a (locally) decreasing diagram. Therefore each such proof order entails the decreasing diagrams technique for proving confluence. The proof orders differ with respect to monotonicity and complexity. Our results are developed in the setting of involutive monoids. We extend these results to obtain a decreasing diagrams technique for confluence modulo.

BibTeX

@inproceedings{BFVvO-RTA13,
  author    = "Bertram Felgenhauer and Vincent van Oostrom",
  title     = "Proof Orders for Decreasing Diagrams",
  booktitle = "Proceedings of the 24th International Conference on Rewriting
               Techniques and Applications",
  editor    = "Femke van Raamsdonk",
  series    = "Leibniz International Proceedings in Informatics",
  volume    = 21,
  pages     = "174--189",
  year      = 2013,
  doi       = "10.4230/LIPIcs.RTA.2013.174"
}