  In graph realization problems one is given a degree sequence and the task is
to decide whether there is a graph whose vertex degrees match to the given
sequence. This realization problem is known to be polynomial-time solvable when
the graph is directed or undirected. In contrary, we show NP-completeness for
the problem of realizing a given sequence of pairs of positive integers
(representing indegrees and outdegrees) with a directed acyclic graph,
answering an open question of Berger and M\"uller-Hannemann [FCT 2011].
Furthermore, we classify the problem as fixed-parameter tractable with respect
to the parameter "maximum degree".
