  Convolutionless and convolution master equations are the two mostly used
physical descriptions of open quantum systems dynamics. We subject these
equations to time deformations: local dilations and contractions of time scale.
We prove that the convolutionless equation remains legitimate under any time
deformation (results in a completely positive dynamical map) if and only if the
original dynamics is completely positive divisible. Similarly, for a specific
class of convolution master equations we show that uniform time dilations
preserve positivity of the deformed map if the original map is positive
divisible. These results allow witnessing different types of non-Markovian
behavior: the absence of complete positivity for a deformed convolutionless
master equation clearly indicates that the original dynamics is at least weakly
non-Markovian; the absence of positivity for a class of time-dilated
convolution master equations is a witness of essentially non-Markovian original
dynamics.
