Help understanging ac signal connected to a charged capacitor (coupling capacitor)

(Assuming ideal elements) My friend is trying to convince me that the voltage across \$R_L\$ varies between 4 and 6, says the average value doesn't decrease and stays fixed at \$5V\$ forever. I'm not getting how this is possible -

^{simulate this circuit – Schematic created using CircuitLab}

The amplitude of the input ac signal varies between -1 and 1, always less than the capacitor voltage of \$5V\$. Wouldn't the capacitor see this low voltage and start discharging ? May I ask how the 1V input ac signal can put more charge into the capacitor so that the capacitor's voltage increases, even slighlty ? Makes not much sense to me. Highly appreciate any help. Thanks!

Answer

Yes, There is a DC path around the cap its going to discharge. DC response follows RC time-constant.