In general, flat outputs of a nonlinear system may depend on the system's
state and input as well as on an arbitrary number of time derivatives of the
latter. If a flat output which also depends on time derivatives of the input is
known, one may pose the question whether there also exists a flat output which
is independent of these time derivatives, i.e., an (x,u)-flat output. Until
now, the question whether every flat system also possesses an (x,u)-flat output
has been open. In this contribution, this conjecture is disproved by means of a
counterexample. We present a two-input system which is differentially flat with
a flat output depending on the state, the input and first-order time
derivatives of the input, but which does not possess any (x,u)-flat output. The
proof relies on the fact that every (x,u)-flat two-input system can be exactly
linearized after an at most dim(x)-fold prolongation of one of its (new) inputs
after a suitable input transformation has been applied