Closures of May and Must Convergence for Contextual Equivalence

We show on an abstract level that contextual equivalence in non-deterministic program calculi defined by mayand must-convergence is maximal in the following sense. Using also all the test predicates generated by the Boolean, foralland existential closure of mayand mustconvergence does not change the contextual equivalence. The situation is different if mayand total must-convergence is used, where an expression totally must-converges if all reductions are finite and terminate with a value: There is an infinite sequence of test-predicates generated by the Boolean, foralland existential closure of mayand total mustconvergence, which also leads to an infinite sequence of different contextual equalities.