Complete rewriting system

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Template:Rewriting system property

Definition

Symbol-free definition

A rewriting system is said to be complete if it satisfies the following equivalent conditions:

  1. It is finitely terminating and the equivalence relation generated by the rewriting system has exactly one irreducible in every equivalence class.
  2. It is finitely terminating and confluent.
  3. It is finitely terminating and locally confluent.