title: If a timed automaton always terminates then there exists a trace with a maximum length?
body: <p>Hi I have a theoretical question regarding timed automata and I would like to know if someone has already given an answer to it, since that would be usefull for my research. So my question is the following:</p>
  
  <p>Assume that you have a timed automaton that has an accepting state q_f (that has no successors) and you know that all the traces of the configuration (q,delta) (for a location q of the automaton and a clock valuation delta) always terminate, that is that they lead to q_f. Does that mean that there exists a trace of  that has a maximal length???(e.g the computation tree of (q,delta) has a finite depth)</p>