# nLab termination

Let $(X,\rightarrow)$ be an abstract rewriting system ie. a set equipped with a binary relation $\rightarrow$.

Then $\rightarrow$ is terminating, strongly normalizing or noetherian iff there doesn’t exist any infinite reduction $x_{1} \rightarrow x_{2} \rightarrow ... \rightarrow x_{n} \rightarrow ...$

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