I've been told that in a local group, one can find a word of length of $n=4$, i.e $w=g_1 g_2 g_3 g_4$, with two different meanings depending on how we put the parentheses. However I've also read that a well defined word has only one value, which means that I'm looking a word which is not well defined.
Can anyone give me a hint of such an example, or tell me whether my understanding of these basic facts is true?