Disproving Confluence of Term Rewriting Systems by Interpretation and Ordering

  • Takahito Aoto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8152)


In order to disprove confluence of term rewriting systems, we develop new criteria for ensuring non-joinability of terms based on interpretation and ordering. We present some instances of the criteria which are amenable for automation, and report on an implementation of a confluence disproving procedure based on these instances. The experiments reveal that our method is successfully applied to automatically disprove confluence of some term rewriting systems, on which state-of-the-art automated confluence provers fail. A key idea to make our method effective is the introduction of usable rules—this allows one to decompose the constraint on rewrite rules into smaller components that depend on starting terms.


Confluence Non-Joinability Interpretation Ordering Term Rewriting Systems 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Takahito Aoto
    • 1
  1. 1.RIECTohoku UniversitySendaiJapan

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