If the MuSR data are grouped into the standard four transverse field groups the data should follow a cos(t) form in each group.
Data show the form cos(t) + offset where the offset is positive for all groups and approximately 1/4 of the initial asymmetry of the data. This prevents using fitting functions without an offset. There should be no physical reason for an offset and other analysis software gives an offset within error of zero.
An example run is musr00062260.nxs. The behaviour appears to be ubiquitous.
Seen in 3.8.x and 3.9.0 on Windows and 3.9.x on Linux.