TITLE: Free group in GAP
QUESTION [5 upvotes]: I know that in the free group $F$ with two generators $x$ and $y$, there is some word $w \in [F,F]$ such that $xy^2=x^{-2} y^{-3} x^{-2}(xy)^5 w$.
Is it possible to find $w$ using GAP?

REPLY [2 votes]: There is a recent preprint By Fialkovski and Ivanov that describes an algorithm for computing the commutator length of an element in a free group, and it also gives a minimal commutator representation of an element in $F'$.