 Once we have defined a reduction strategy, it is natural to ask whether one can improve it. If a term has a \(\beta\)-normal form, then a strategy will discover a normal form; but might there be a shorter \(\beta\)-reduction sequence that reaches the same normal form (or a term that is \(\alpha\)-convertible to that normal form)? This is the question of optimality. Defining optimal strategies and showing that they are optimal is generally considerably more difficult than simply defining a strategy. For more discussion, see (Barendregt, 1984 chapter 10).