Batman/Terminator: what do you think of this match-up?

I have been thinking of making a story between these two characters. I feel like the comic companies missed something when they didn't do it when the Superman vs Terminator comic came out. I mean they had Superman vs Predator. Batman fought Predator twice. Superman fought Alien. Batman fought alien at least once. Then they had the Terminator vs Superman comic, and Batman didn't even get mentioned in this. I think this could be a good story, if done right. What do y'all think?