Termination Proofs for Term Rewriting Systems by Lexicographic Path Orderings Imply Multiply Recursive Derivation Lengths

@article{Weiermann1995TerminationPF,
  title={Termination Proofs for Term Rewriting Systems by Lexicographic Path Orderings Imply Multiply Recursive Derivation Lengths},
  author={Andreas Weiermann},
  journal={Theor. Comput. Sci.},
  year={1995},
  volume={139},
  pages={355-362}
}
It is shown that a termination proof for a term rewriting system using a lexicographic path ordering yields a multiply recursive bound on the length of derivations, measured in the depth of the starting term. This result is essentially optimal since for every multiply recursive function f a rewrite system (which reduces under the lexicographic path ordering) can be found such that its derivation length cannot be bounded by f. Let R be a (finite) rewrite system over a (finite) set ~ of function… CONTINUE READING
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