A Factorisation Theorem in Rewriting Theory

Some computations on a symbolic term M are more judicious than others, for instance the leftmost outermost derivations in the λ-calculus. In order to characterise generically that kind of judicious computations, [M] introduces the notion of external derivations in its axiomatic description of Rewriting Systems: a derivation e : M → P is said to be external when the derivation e; f : M → Q is standard whenever the derivation f : P → Q is standard.

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