I would like to find an upper bound of
$\text{Pr}\{a^{u_1+u_2+u_3+u_4}+a^{l_1+l_2+l_3+l_4}\leq a^{u_1+u_2+l_1+l_2}+a^{u_3+u_4+l_3+l_4}\}$,
where $a>1$ and $l_1,\cdots,l_4$ follows i.i.d Bernoulli$(p)$, $u_1,\cdots,u_4$ follows i.i.d. Bernoulli$(p(1+\delta))$ with $\delta>0$.
I tried Chernoff bound, but it looks very messy. Are there any specific concentration bounds that can be applied to this type of problem?