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In this paper, we investigate the performance of a cooperative network with adaptive decode-and-forward (DF) relaying over time-selective frequency-flat Rayleigh fading channels. In adaptive DF relaying, only a subset of the available relays with "good" channels are allowed to participate in the relaying phase. The destination combines the direct and the relayed signals using maximal ratio combining technique. Pilot-symbol-assisted modulation (PSAM) is used for the estimation of time-varying fading channel coefficients. For the system under consideration, we derive an exact closed-form expression for the average bit error rate. Such closed form solutions are highly desirable because they allow for rapid and efficient evaluation of system performance. We further present computer simulations to validate our analytical results.