Consider the Car machine.
is a step of Car; 
is not.
is an execution fragment of
Car.
and 
are executions, but 
and
are not.
and 
are traces of
Car but 
and 
are not.
and 
are traces of
Car but 
and 
are not.
Finally, using the event-based definition of trace, we have
In both cases the empty sequence is a member of the behavior.