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Confluence of Non-Left-Linear TRSs via Relative Termination

Dominik Klein, Nao Hirokawa

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Abstract

Abstract. We present a confluence criterion for term rewrite systems by relaxing termination requirements of Knuth and Bendix ’ confluence criterion, using joinability of extended critical pairs. Because computa-tion of extended critical pairs requires equational unification, which is undecidable, we give a sufficient condition for testing joinability auto-matically. 1

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Abstract. We present a confluence criterion for term rewrite systems by relaxing termination requirements of Knuth and Bendix ’ confluence criterion, using joinability of extended critical pairs. Because computa-tion of extended critical pairs requires equational unification, which is undecidable, we give a sufficient condition for testing joinability auto-matically. 1

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Available abstract

Abstract. We present a confluence criterion for term rewrite systems by relaxing termination requirements of Knuth and Bendix ’ confluence criterion, using joinability of extended critical pairs. Because computa-tion of extended critical pairs requires equational unification, which is undecidable, we give a sufficient condition for testing joinability auto-matically. 1

Key concepts: Confluence, Undecidable problem, Unification, Computer science, Term (time), Computation, Normalization property, Algorithm

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