This paper discusses the transformation power of Burstall and Darlington's folding/unfolding system, i.e. what kind of programs can be derived from a given one. A necessary condition of derivability is proved. The notion of inherent complexity of recursive functions in introduced. A bound on efficiency gain by folding/unfolding transformations is obtained for all reasonable computation models. The well-known partial correctness and incompleteness of the system are corollaries of the result. Examples of underivability are given, e.g. binary searching cannot be derived from linear searching, merge sorting cannot be derived from insert sorting.

In 1979, Klop (1980), answering a question raised by Mann in 1972, showed that the extension of λ-calculus with subjective pairing is not confluent. We refer to Klop (1980) and Barendregt (1981, revised 1984) for a perspective. The term presented by Klop to provide a counterexample is fairly simple, but the proof of non-confluence, although intuitively quite simple, involves some technical properties. Among others, a suitable standardization result on derivations in the extended system is needed in the proof. Klop's proof was revisited by Bunder (1985), who seemingly used less technical apparatus than Klop, starting with the same term as Klop. Although Bunder's proof does not explicitly use a standardization result, his proof proceeds internally with some rearrangements of derivations, so that it is fair to say that some standardization technique is present in Bunder (1985).

And Joktan begat Almodad, and Sheleph, and Hazarmaveth, and Jerah, and Handoram, and Uzal, and Diklah, and Obal, and Abimael, and Sheba, and Ophir, and Havilah, and Jobab: all these were the sons of Joktan.

— Genesis 10:26–29