Benefit vs Damages
Question
If an animal is walking in the reshus harabim and eats from items there, it is classified as shein, the owner is patur from damages, but has to pay the benefit he received from not feeding his animal. If the animal turns his head to the side of the reshus harabim and eats items there, it is classified as keren, and if the animal is a tam, the owner pays half damages (chatzi nezek).
My question is: What happens if the chatzi nezek amount is less than the value the owner would pay for benefit in the case of shein? Do we say that the benefit amount is an overall minimum payment in all cases, or paying any amount of damages absolves the owner of paying for benefit?