  A word is called a reset word for a deterministic finite automaton if it maps
all the states of the automaton to a unique state. Deciding about the existence
of a reset word of a given maximum length for a given automaton is known to be
an NP-complete problem. We prove that it remains NP-complete even if restricted
to Eulerian automata with binary alphabets, as it has been conjectured by
Martyugin (2011).
