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In this note we give a simple unifying proof of the undecidability of severaldiagrammatic properties of term rewriting systems that include: localconfluence, strong confluence, diamond property, subcommutative property, andthe existence of successor. The idea is to code configurations of TuringMachines into terms, and then define a suitable relation on those terms suchthat the termination of the Turing Machine becomes equivalent to thesatisfiability of the diagrammatic property.

A Note on a Unifying Proof of the Undecidability of Several Diagrammatic Properties of Term Rewriting Systems