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In this letter, the use of adaptive source transmission with amplify-and-forward relaying is proposed. Three different adaptive techniques are considered: (i) optimal simultaneous power and rate adaptation; (ii) constant power with optimal rate adaptation; (iii) channel inversion with fixed rate. The capacity upper bounds of these adaptive protocols are derived for the amplify-and-forward cooperative system over both independent and identically distributed (i.i.d.) Rayleigh fading and non-i.i.d. Rayleigh fading environments. The capacity analysis is based on an upper bound on the effective received signal-to-noise ratio (SNR). The tightness of the upper bound is validated by the use of a lower bound and by Monte Carlo simulation. It is shown that at high SNR the optimal simultaneous power and rate adaptation and the optimal rate adaptation with constant power provide roughly the same capacity. Channel inversion is shown to suffer from a deterioration in capacity relative to the other adaptive techniques.