There is an effective one-step cofinal reduction strategy for combinators
journal contributionposted on 01.01.1995 by Richard Statman
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Abstract: "In this note we shall construct an effective one-step reduction strategy for combinators. The construction clearly does not work for lambda calculus since it depends on the parallel residual property for combinators. Residuals of redexes are disjoint. However, it holds for a variety of combinatory reduction systems."