Abstract

For a given (terminating) term rewriting system
one can often estimate its “derivational complexity” indirectly
by looking at the proof method that established termination. In this
spirit we investigate two instances of the interpretation method:
“matrix interpretations” and “context dependent interpretations”.
We introduce a subclass of matrix interpretations, denoted
as “triangular matrix interpretations”, which induce
polynomial derivational complexity and establish tight correspondence
results between a subclass of context dependent interpretations and
restricted triangular matrix interpretations.
The thus obtained new results are easy to implement and
considerably extend the analytic power of existing results.
We provide ample numerical data for assessing the viability of the method.

BibTeX

@inproceedings{GMASJW-FSTTCS08,
  author      = "Georg Moser and Andreas Schnabl and Johannes Waldmann",
  title       = "Complexity Analysis of Term Rewriting Based on Matrix and
                 Context Dependent Interpretations",
  booktitle   = "Proceedings of the 28th International Conference on
                 Foundations of Software Technology and Theoretical
                 Computer Science",
  pages       = "304--315",
  publisher   = "Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik",
  year        = 2008
}