concrete equality of group presentations

Question

Why does this equality hold? $$\begin{array}{rl} \langle a,c| &ca^{-1}cac^{-1}aca^{-1}c^{-1}ac^{-1}a^{-1}ca^{-1}c^{-1}a,\\ &ac^{-1}aca^{-1}cac^{-1}a^{-1}ca^{-1}c^{-1}ac^{-1}a^{-1}c\rangle\\ =\langle a,c| &aca^{-1}cac^{-1}aca^{-1}c^{-1}ac^{-1}a^{-1}ca^{-1}c^{-1}\rangle\\ \end{array}$$ I'm asking this cause I don't understand the last line of this calculation:

Answer 1

As Theo remarked in the comments, the relation in the second group is obtained from the first relation in the first group by conjugating with $a$.

The second relation in the first group is obtained from the first relation in the first group by inverting it and then conjugating with $c^{-1}a$.