On a question of Remeslennikov (Q2710435)

In this short note the author answers in the negative a question of Remeslennikov by giving a counterexample. The question which is Question F16 of the list of ``Open problems in combinatorial group theory'' of \textit{G. Baumslag, A. G. Myasnikov} and \textit{V. Shpilrain} (world-wide-web: \url{http://zebra.sci.ccny.cuny.edu/web/}) is the following:NEWLINENEWLINENEWLINELet \(R\) be the normal closure of an element \(r\) in a free group \(F\) with the natural length function, and suppose that \(s\) is a (non-identity) element of minimal length in \(R\). Is it true that \(s\) is conjugate to one of the following elements: \(r\), \(r^{-1}\), \([r,f]\), or \([r^{-1},f]\), for some element \(f\)?NEWLINENEWLINENEWLINEThe author, to present his counterexample, takes the free group \(F_2\) on the two free generators \(a\), \(b\) and \(r=ba^tb^2a^t\), where \(t\geq 3\). He then proves that the element \(s=[b^3,a]\) is of minimal length in the normal closure \(R\) of \(r\) in \(F_2\) and is not conjugate to \(r^{\pm 1}\) or \([r^{\pm 1},f]\), for any \(f\in F_2\).