The response time of a rule-based program is deened as the maximum number of rule rings before a xed point of the program is reached from a start state. In this paper, we present several principles which make use of two relations, potential-trigger and suppression, for deriving tight response-time bounds. While the computation of these two relations is costly in general, we show how they can be eeciently approximated by reening the necessary/suucient conditions for these relations to be satissed. A response-time analyzer based on the theories in this paper has been implemented to analyze programs whose potential-trigger relations are acyclic. We demonstrate the analysis process with an example program which has innnite state space. Our analyzer takes only seconds to derive a tight bound on the example pro-gram's response time.
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