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of (but not the reflexive closure). In addition the normal forms of the strategy must be the same as the normal forms of the original rewriting system, i.e. for all , there exists a with iff .

A one step reduction strategy is one where . Otherwise it is a many step strategy.

A deterministic strategy is one where is a partial function, i.e. for each there is at most one such that . Otherwise it is a nondeterministic strategy.

Term rewriting

In a term rewriting system

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