The testing of a state-based system may involve the application of a number of adaptive test cases. Where the implementation under test (IUT) is deterministic, the response of the IUT to some adaptive test case γ1 could be capable of determining the response of the IUT to another adaptive test case $\gamma_2". Thus, the expected cost of applying a set of adaptive test cases depends upon the order in which they are applied. This paper explores properties of adaptive test cases and considers the problem of finding an order of application of the elements from some set of adaptive test cases, which minimises the expected cost of testing
