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I am having trouble figuring out what the difference equation or the system function for this system is? Here ''R'' represents the unit delay. The fact that the delay is not part of the feedback loop is confusing me.

Any suggestions will be much appreciated.

Thanks in advance!

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The signal after the summer is $e[n] = x[n]+y[n]$. In the feed-forward line a delay of 3 units is applied. Thus we have $$y[n] = \mathcal{R}(\mathcal{R}(\mathcal{R} (e[n]))) = x[n-3]+ y[n-3]$$. The equivalent transfer function is :$$ H(z) = \frac{Y(z)}{X(z)} = \frac{z^{-3}}{1-z^{-3}}$$

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