  We compute the static potential of adjoint sources in SU(2) Yang-Mills theory
in four dimensions by numerical Monte Carlo simulations. Following a recent
calculation in 2+1 dimensions, we employ a variational approach involving
string and gluelump operators and obtain clear evidence for string breaking and
the saturation of the potential at large distances. For the string breaking
scale we find $r_b \approx 1.25{\rm fm}, 2.3 r_0$, or in units of the lightest
glueball, $r_b m_{0++} \approx 9.7$. We furthermore resolve the first
excitation of the flux-tube and observe its breaking as well. The result for
$r_b$ is in remarkable quantitative agreement with the three-dimensional one.
