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The interaction between infinite reduction sequences and nfs deserves a more careful inspection though.
A slightly more complicated example of a term that has only infinite reduction sequences is Y CKI).
Both terms induce an infinite reduction sequence, that is, an infinite chain of successive one-step reductions.
If a is a variable, one can see that all finite reduction sequences commencing with KaΩ end at a, and there is exactly one infinite reduction sequence.
However, the existence of an infinite reduction sequence for a term does not imply that the term has no normal form (when the combinatory base is complete or contains a cancellator).
We design a strategy that, for any given term t in a fully extended OERS, constructs a longest reduction starting from t if t is strongly normalizing and otherwise constructs an infinite reduction.
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These authors address issues about the nature of infinite idealizations, reduction, and emergence.
If A ⊳η,1 B, then the length of B is strictly smaller than that of A. Thus, there can be no infinite η-reductions.
Then, using the symmetry reduction, the infinite series solutions are obtained.
A reduction to infinite dimensional systems was considered in [21, 23, 24].
According to Locke, who accepts the reductions, the infinite regress of wills can't get started (see Rickless 2000: 56 65; Garrett 2015: 269 274).
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