Being able to reduce test suites without having to execute them for assessing the effects on their fault detection capabilities is quite appealing. In this direction, we proposed recently to characterize test suites via inferred decision trees and use these for comparisons in a reduction process. The equivalence relation underlying the comparisons plays obviously a significant role for the effectiveness achieved and efficiency experienced. In this paper, we explore five such relations that take different aspects into account and investigate their impact on test suite reduction, their effectiveness in fault detection, and computation time. We report corresponding results, and show as well as prove that the equivalence relations build a taxonomy.