In this transformation we present a rhythmically constrained audio style transfer technique for automatic mixing and mashing of two audio inputs. In this transformation the rhythmic and timbral features of both input signals are combined together through the use of an audio style transfer process that transforms the files so that they adhere to a larger metrical structure of the chosen input. This is accomplished by finding beat boundaries of both inputs and performing the transformation on beat-length audio segments. In order for the system to perform a mashup between two signals, we reformulate the previously used audio style transfer loss terms into three loss functions and enable them to be independent of the input. We measure and compare rhythmic similarities of the transformed and input audio signals using their rhythmic envelopes to investigate the influence of the tested transformation objectives.