In the finitely recursive process (FRP) model of discrete event systems (DES), concepts about processes and process operators have been introduced. An infinite set of process expressions or functions can be built recursively through function composition using a few elementary operators. Given any process realization, it is important to find out whether the process is bounded, i.e., whether it has a finite state realization. In the FRP setting this translates to the problem of finding out whether the set of post-process expressions is finite or not, In Cieslak and Varaiya (1990) it has been shown that the boundedness problem is undecidable for general FRP＇s, This paper investigates the decidability of the problem for subclasses of FRP, In Inan and Varaiya (1988), it was conjectured that the set of functions that can be recursively generated using the parallel composition operator (PCO) and different change operators [i.e., without using the Sequential Composition Operator (SCO)] will be finite and FRP＇s constructed over this set of functions will naturally be bounded. In the present work a counterexample has been provided to disprove the conjecture about the finiteness of the above set of functions. However, using a suitable post-process computation procedure, it has been shown here that the FRP＇s, built recursively over this set of functions, are bounded.