  The complexity of a well-quasi-order (wqo) can be measured through three
ordinal invariants: the width as a measure of antichains, height as a measure
of chains, and maximal order type as a measure of bad sequences.
  We study these ordinal invariants for the finitary powerset, i.e., the
collection Pf(A) of finite subsets of a wqo A ordered with the Hoare embedding
relation. We show that the invariants of Pf(A) cannot be expressed as a
function of the invariants of A, and provide tight upper and lower bounds for
them.
  We then focus on a family of well-behaved wqos, for which these invariants
can be computed compositionally, using a newly defined ordinal invariant called
the approximate maximal order type. This family is built from multiplicatively
indecomposable ordinals, using classical operations such as disjoint unions,
products, finite words, finite multisets, and the finitary powerset
construction.
