  Weighted Timed Games (WTG for short) are the most widely used model to
describe controller synthesis problems involving real-time issues.
Unfortunately, they are notoriously difficult, and undecidable in general. As a
consequence, one-clock WTGs have attracted a lot of attention, especially
because they are known to be decidable when only non-negative weights are
allowed. However, when arbitrary weights are considered, despite several recent
works, their decidability status was still unknown. In this paper, we solve
this problem positively and show that the value function can be computed in
exponential time (if weights are encoded in unary).
