Revisiting Matrix Interpretations for Polynomial Derivational Complexity of Term Rewriting

  • Friedrich Neurauter
  • Harald Zankl
  • Aart Middeldorp
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6397)


Matrix interpretations can be used to bound the derivational complexity of term rewrite systems. In particular, triangular matrix interpretations over the natural numbers are known to induce polynomial upper bounds on the derivational complexity of (compatible) rewrite systems. Using techniques from linear algebra, we show how one can generalize the method to matrices that are not necessarily triangular but nevertheless polynomially bounded. Moreover, we show that our approach also applies to matrix interpretations over the real (algebraic) numbers. In particular, it allows triangular matrix interpretations to infer tighter bounds than the original approach.


Derivational complexity polynomial matrix interpretations 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Friedrich Neurauter
    • 1
  • Harald Zankl
    • 1
  • Aart Middeldorp
    • 1
  1. 1.Institute of Computer ScienceUniversity of InnsbruckAustria

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