—Embedded computer systems are characterized by the presence of a processor running application-specific dedicated software. A large number of these systems must satisfy real-time constraints. This paper examines the problem of determining the extreme (best and worst) case bounds on the running time of a given program on a given processor. This has several applications in the design of embedded systems with real-time constraints. An important aspect of this problem is determining which paths in the program are exercised in the extreme cases. The state-of-theart solution here relies on an explicit enumeration of program paths. This solution runs out of steam rather quickly since the number of feasible program paths is typically exponential in the size of the program. We present a solution for this problem that does not require an explicit enumeration of program paths, i.e., the paths are considered implicitly. This solution is implemented in the program cinderella (in recognition of ...