When compiling to combinators, an implementation may equally choose one system or the other, or both, as it helps shorten the encodings of functions.
For example, the encodings of C exclusively in terms of S,K,I, as well as of S in B,C,W,K are long and complicated, as can be seen below, while their corresponding computational machine implementations are equally trivial.
It can be worth it to add additional interpretation rules, allowing for much shorter code which can lead to more efficient execution.
In fact, S(Kx)yz = Bxyz and Sx(Ky)z = Cxyz, as is easily verified.
[2] The combinators B, C, K and W correspond to four well-known axioms of sentential logic: Function application corresponds to the rule modus ponens: The axioms AB, AC, AK and AW, and the rule MP are complete for the implicational fragment of intuitionistic logic.