The exponentially large sizes of state spaces have been a major obstacle in formal verification, which are due to high process concurrency, and large constants that are compared to clock variables and to discrete variables. We show how an intelligent permutation of reduction techniques and a good selection of data structures can be used to decrease the effect of the above explosion factors. First, a well-accepted experiment platform for the scalable verification of real time systems, called State-Graph Manipulators, is used to verify Wireless Transaction Protocol (WTP), which is a part of a fast permeating world standard, Wireless Application Protocol (WAP). Application results show how SGM handles large clock constants and large discrete constants efficiently. Second, a recently proposed Region Encoding Diagram (RED) technology is used to show how state-space size explosions due to high concurrency can be efficiently handled in WTP verification.