We consider a strongly coupled field theory with a critical point and a nonzero chemical potential at a finite temperature, which is dual to an asymptotically anti–de Sitter charged black hole. We study the evolution of the rescaled holographic subregion complexity near to and far from the critical point. We explain two distinct concepts of complexity in this theory and discuss that the state under study is complex based on how much information is needed to specify the state and is simple according to how many operations have to be done to reach the state. We justify the decreasing of the rescaled holographic subregion complexity with time using an increasing number of microstates of the mixed state and speculate about the description of the relative rescaled holographic subregion complexity of the initial state and the final state as a resource. We propose that in this process the complexity of the mixed state decreases and the complexity of the environment increases. We also observe that in this model the rescaled holographic subregion complexity is a good observable for probing the dynamical critical exponent.