In the second diagram a $2$-sheeted connected covering of the figure eight has been described. The image of the fundamental group of the covering space has the generators $a^2, b^2$ and $ab$ as claimed. But according to me the set of generators should include $ba$ as well. Could it be somehow possible to obtain $ba$ from the set of given generators $a^2, b^2$ and $ab\ $?
Any help would be greatly appreciated. Thanks for investing your valuable time on my question.