16.9 (2006)

An element $g$ of a free group $F_n$ on the free generators $x_1, \dots, x_n$ is called a palindrome with respect to these generators if the reduced word representing $g$ is the same when read from left to right or from right to left. The palindromic length of an element $w \in F_n$ is the smallest number of palindromes in $F_n$ whose product is $w$. Is there an algorithm for finding the palindromic length of a given element of $F_n$?