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    Chapter and Conference Paper

    Correctness of Context-Moving Transformations for Term Rewriting Systems

    Proofs by induction are often incompatible with functions in tail-recursive form as the accumulator changes in the course of unfolding the definitions. Context-moving and context-splitting (Giesl, 2000) for fu...

    Koichi Sato, Kentaro Kikuchi, Takahito Aoto in Logic-Based Program Synthesis and Transfor… (2015)

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    Chapter and Conference Paper

    Automated Proofs of Unique Normal Forms w.r.t. Conversion for Term Rewriting Systems

    The notion of normal forms is ubiquitous in various equivalent transformations. Confluence (CR), one of the central properties of term rewriting systems (TRSs), concerns uniqueness of normal forms

    Takahito Aoto, Yoshihito Toyama in Frontiers of Combining Systems (2019)

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    Chapter and Conference Paper

    Confluence and Commutation for Nominal Rewriting Systems with Atom-Variables

    Nominal rewriting was introduced as an extension of first-order term rewriting by a binding mechanism based on the nominal approach. Recently, a new format of nominal rewriting has been introduced where rewrit...

    Kentaro Kikuchi, Takahito Aoto in Logic-Based Program Synthesis and Transformation (2021)

  4. Chapter and Conference Paper

    A Critical Pair Criterion for Level-Commutation of Conditional Term Rewriting Systems

    The rewrite relation of a conditional term rewriting system (CTRS) can be divided into a hierarchy of rewrite relations of term rewriting systems (TRSs) by the depth of the recursive use of rewrite relation in...

    Ryota Haga, Yuki Kagaya, Takahito Aoto in Frontiers of Combining Systems (2023)