On Transfinite Knuth-Bendix Orders

  • Laura Kovács
  • Georg Moser
  • Andrei Voronkov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6803)


In this paper we discuss the recently introduced transfinite Knuth-Bendix orders. We prove that any such order with finite subterm coefficients and for a finite signature is equivalent to an order using ordinals below ωω, that is, finite sequences of natural numbers of a fixed length. We show that this result does not hold when subterm coefficients are infinite. However, we prove that in this general case ordinals below \(\omega^{\omega^{\omega}}\) suffice. We also prove that both upper bounds are tight. We briefly discuss the significance of our results for the implementation of first-order theorem provers and describe relationships between the transfinite Knuth-Bendix orders and existing implementations of extensions of the Knuth-Bendix orders.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Laura Kovács
    • 1
  • Georg Moser
    • 2
  • Andrei Voronkov
    • 3
  1. 1.TU ViennaAustria
  2. 2.Institute of Computer ScienceUniversity of InnsbruckAustria
  3. 3.University of ManchesterUK

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