  The commutator length $cl_G(g)$ of an element $g \in [G,G]$ in the commutator
subgroup of a group $G$ is the least number of commutators needed to express
$g$ as their product.
  If $G$ is a non-abelian free groups, then given an integer $n \in \mathbb{N}$
and an element $g \in [G,G]$ the decision problem which determines if $cl_G(g)
\leq n$ is NP-complete. Thus, unless P=NP, there is no algorithm that computes
$cl_G(g)$ in polynomial time in terms of $|g|$, the wordlength of $g$. This
statement remains true for groups which have a retract to a non-abelian free
group, such as non-abelian right-angled Artin groups.
  We will show these statements by relating commutator length to the
\emph{cyclic block interchange distance} of words, which we also show to be
NP-complete.
