The preservation of interleaving equivalences

In recent years, though many attempts have been made to solve whether equivalences are preserved under action refinement, this problem still needs to be further investigated. The usual approach to the preservation problem is: given some well-established equivalence notion which is not preserved under refinement, is there a way of adding some restricted conditions under consideration such that preservation of this equivalence in the restricted setting is obtained? Generally, one investigates how to restrict the concept of action refinement such that these equivalences are preserved under the restricted refinement. In this paper, in another way, we investigate how to find the class of suitable systems satisfying that the established equivalences on them are preserved under no restricted refinement. Interleaving trace equivalence and interleaving bisimulation equivalence which are not preserved under refinement are showed that they are preserved under refinement in the systems in which there are not causal independence relations or all the transitions are bundle action transitions.