  Motivated by the success of bounded model checking framework for finite state
machines, Ouaknine and Worrell proposed a time-bounded theory of real-time
verification by claiming that restriction to bounded-time recovers decidability
for several key decision problem related to real-time verification. In support
of this theory, the list of undecidable problems recently shown decidable under
time-bounded restriction is rather impressive: language inclusion for timed
automata, emptiness problem for alternating timed automata, and emptiness
problem for rectangular hybrid automata. The objective of our study was to
recover decidability for general recursive timed automata---and perhaps for
recursive hybrid automata---under time-bounded restriction in order to provide
an appealing verification framework for powerful modeling environments such as
Stateflow/Simulink. Unfortunately, however, we answer this question in negative
by showing that time-bounded reachability problem stays undecidable for
recursive timed automata with five or more clocks. While the bad news continues
even when one considers well-behaved subclasses of recursive hybrid automata,
we recover decidability by considering recursive hybrid automata with bounded
context using a pass-by-reference mechanism, or by restricting the number of
variables to two, with rates in $\{0,1\}$.
