  We construct, for the first time, the time-domain gravitational wave strain
waveform from the collapse of a strongly gravitating Abelian Higgs cosmic
string loop in full general relativity. We show that the strain exhibits a
large memory effect during merger, ending with a burst and the characteristic
ringdown as a black hole is formed. Furthermore, we investigate the waveform
and energy emitted as a function of string width, loop radius and string
tension $G\mu$. We find that the mass normalized gravitational wave energy
displays a strong dependence on the inverse of the string tension
$E_{\mathrm{GW}}/M_0\propto 1/G\mu$, with $E_{\mathrm{GW}}/M_0 \sim {\cal
O}(1)\%$ at the percent level, for the regime where $G\mu\gtrsim10^{-3}$.
Conversely, we show that the efficiency is only weakly dependent on the initial
string width and initial loop radii. Using these results, we argue that
gravitational wave production is dominated by kinematical instead of
geometrical considerations.
