Basis sets for combinator calculus
It's easy to make other bases by switching out the combinators from one basis with ones that do something similar. For example, starting with BCKW, you can switch $C$ for $T = (\lambda x y. y x)$ (since both switch terms around) and $W$ for $\omega = (\lambda x. x x)$ (since both duplicate things). You know this is still a basis because you can recover $C$ and $W$ from it: $C = B(T(B B T))(B B T)$ and $W = C(B \omega(B B T))$.