Barja–González–Naranjo modified Xiao conjecture for the relative irregularity

Let $f\colon S\to B$ be a non-isotrivial fibred surface of genus $g\geq 2$, and let $q_f$ denote its relative irregularity. The integer-valued upper bound is

$$\left\lceil \frac{g+1}{2}\right\rceil.$$

Barja–González–Naranjo's modified conjecture. For every non-isotrivial fibred surface $f\colon S\to B$ of genus $g\geq 2$,

$$q_f\leq \left\lceil \frac{g+1}{2}\right\rceil.$$

This modification is proposed after counterexamples to Xiao's original conjecture; the supplied text does not establish whether the modified conjecture has been resolved.