Coevolutionary algorithms are variants of traditional evolutionary algorithms and are often considered more suitable for certain kinds of complex tasks than noncoevolutionary methods. One example is a general cooperative coevolutionary framework for function optimization. This paper presents a thorough and rigorous introductory analysis of the optimization potential of cooperative coevolution. Using the cooperative coevolutionary framework as a starting point, the CC (1+1) EA is defined and investigated from the perspective of the expected optimization time. The research concentrates on separability, a key property of objective functions. We show that separability alone is not sufficient to yield any advantage of the CC (1+1) EA over its traditional, non-coevolutionary counterpart. Such an advantage is demonstrated to have its basis in the increased explorative possibilities of the cooperative coevolutionary algorithm. For inseparable functions, the cooperative coevolutionary set-up can be harmful. We prove that for some objective functions the CC (1+1) EA fails to locate a global optimum with overwhelming probability, even in infinite time; however, inseparability alone is not sufficient for an objective function to cause difficulties. It is demonstrated that the CC (1+1) EA may perform equal to its traditional counterpart, and may even outperform it on certain inseparable functions.