There is a close relation between the failures-divergences and the UTP models of CSP, but they are not equivalent. For example, miracles are not available in the failures-divergences model; the UTP theory is richer and can be used to give semantics to data-rich process algebras like
. Previously, we have defined functions that calculate the failures-divergences model of a CSP process characterised by a UTP relation. In this note, we use these functions to calculate the UTP characterisations of traces refinement and of the
relation that is widely used in testing. In addition, we prove that the combination of traces refinement and
corresponds to refinement of processes in
. This result is the basis for a formal testing technique based on
; as usual in testing, we restrict ourselves to divergence-free processes.