  The objective of this work is to study how active galactic nuclei (AGN)
influence star formation in host galaxies. We present a detailed investigation
of the star-formation history and conditions of a $z=2.57$ massive radio galaxy
based on VLT/X-SHOOTER and ALMA observations. The deep rest-frame ultraviolet
spectrum contains photospheric absorption lines and wind features indicating
the presence of OB-type stars. The most significantly detected photospheric
features are used to characterize the recent star formation: neither
instantaneous nor continuous star-formation history is consistent with the
relative strength of the Si II $\lambda$1485 and S V $\lambda$1502 absorption.
Rather, at least two bursts of star formation took place in the recent past, at
$6^{+1}_{-2}$ Myr and $\gtrsim20$ Myr ago, respectively. We deduce a molecular
H$_{2}$ gas mass of $(3.9\pm1.0)\times10^{10}$ M$_{\odot}$ based on ALMA
observations of the [C I] $^3$P$_{2}$-$^3$P$_{1}$ emission. The molecular gas
mass is only 13 % of its stellar mass. Combined with its high star-formation
rate of ($1020^{+190}_{-170}$) Myr, this implies a high star-formation
efficiency of $(26\pm8$) Gyr$^{-1}$ and a short depletion time of $(38\pm12)$
Myr. We attribute the efficient star formation to compressive gas motions in
order to explain the modest velocity dispersions ($\leqslant$ 55 km s$^{-1}$)
of the photospheric lines and of the star-forming gas traced by [C I]. Because
of the likely very young age of the radio source, our findings suggest that
vigorous star formation consumes much of the gas and works in concert with the
AGN to remove any residual molecular gas, and eventually quenching star
formation in massive galaxies.
