If the AI was smart it would use foot archers, especially elite units against HA units but it isn't and doesn't.
The best way to beat a HA unit is to get longer ranged missiles such as Longbow units or Byzantine Guard Archers. Put the archers on high ground and let the HA's come. You can drop three volleys on them before they can fire one in return because the high ground adds to the range advantage the foot units already have. The silly Cambarian circle is no help to the HA units if arrows fall short. If they charge they die. If they don't they run out of arrows and one or two units of sword/lance based light cavalry can clean them up. Even peasant archers on high ground can hold their own this way though they may need a couple of units with spears or pikes to protect them. Many of the elite archer units melee as well as horse archer units especially if they out number the HA units. Any elite archer unit just kills HA's
Since I generally use auto-resolve I don't ever build and HA unit in a game. The only battles I fight are custom battles. I can build a predominately infantry army that the computer cannot generally beat in auto-resolve out of infantry that is cheaper to maintain and easier to use. That's not really saying much.
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