  Ten years ago, Gla{\ss}er, Pavan, Selman, and Zhang [GPSZ08] proved that if P
$\neq$ NP, then all NP-complete sets can be simply split into two NP-complete
sets.
  That advance might naturally make one wonder about a quite different
potential consequence of NP-completeness: Can the union of easy NP sets ever be
hard? In particular, can the union of two non-NP-complete NP sets ever be
NP-complete?
  Amazingly, Ladner [Lad75] resolved this more than forty years ago: If P
$\neq$ NP, then all NP-complete sets can be simply split into two
non-NP-complete NP sets. Indeed, this holds even when one requires the two
non-NP-complete NP sets to be disjoint.
  We present this result as a mini-tutorial. We give a relatively detailed
proof of this result, using the same technique and idea Ladner [Lad75] invented
and used in proving a rich collection of results that include many that are
more general than this result: delayed diagonalization. In particular, the
proof presented is based on what one can call team diagonalization (or if one
is being playful, perhaps even tag-team diagonalization): Multiple sets are
formed separately by delayed diagonalization, yet those diagonalizations are
mutually aware and delay some of their actions until their partner(s) have also
succeeded in some coordinated action.
  We relatedly note that, as a consequence of Ladner's result, if P $\neq$ NP,
there exist OptP functions f and g whose composition is NP-hard yet neither f
nor g is NP-hard.
