 The importance of normalization led to a whole range of questions (and an extensive literature of answers). How does the order of the reduction steps (i.e., a reduction strategy) affect finding the nf (if there is one)? Are there combinatory bases that guarantee the existence of normal forms for every combinator over that base? To quickly illustrate possible answers to our sample questions, we start with noting that if there is no combinator with a duplicative effect in a base, then all combinators over that base strongly normalize. This is a very easy answer, and as a concrete base, we could have, for example, \(\{\textsf{B},\textsf{C},\textsf{K}\}\) or \(\{\textsf{B}, \textsf{C},\textsf{I}\}\), which have some independent interest in view of their connection to simply typed calculi. However, these bases are far from being combinatorially complete and even a fixed point combinator is undefinable in them.