Several formal systems has been proposed for reasoning about concurrent systems. the algebra of communicating processes (ACP) is proposed by J.A Bergstra and J. W. Klop, and algebraic system for such reasoning. in such formal systems,the equivalence between processes is the fundamental realtion for reasoning and several kinds of equivalence relations are based on behavior of processes. recently, the computational cost in execution of processes is considered to be one of the important factors in concurrent systems and beginning to interest to us. for example, the denial-of-service attacks are related to it closely. we developed a formal system for reasoning about computational costs of concurrent systems in the previous works, based on the milner's pi-calculus. in this paper, we investigate another system based on ACP.