<human>: Provide a brief overview of the text.

My girlfriend has a male Jack Russell cross(neutered) who is about 10 years old, he's always been the only dog in the house until we decided to get another dog, a purebred male American Staffordshire Terrier(not neutered). Jack russell is an outside dog, Amstaff is an inside dog. 
They have always gotten along fine, apart from the Jack Russell occasionally lunging and growling at the Amstaff over food or treats. They have only had one scuffle before this, and it was quickly broken up by my girlfriend (also over food). 
Recently the Amstaff (now 7 1/2 months) has been getting quite aggressive towards the Jack Russell when it comes inside, to the point that it's attacked the Jack Russell 3 times in the last 2 days and we've had to separate them. The Amstaff shows very dominant body language before the fights, but the Jack Russell growls back and won't back down. 
I'm considering letting them just get it over with, as the Jack Russell has ended up on his back in the 5-10 second scuffles they have had, hoping it will submit if the battle goes on any longer. Will this encourage bad behaviour? Or is what needs to happen? I'm just worried the Amstaff (26kg) is gonna really hurt the old(10kg-ish) 
Jack Russell.
<bot>: Younger, bigger, more aggressive and dominant dog has started trying to bully the older dog into submission. Should I let them get it over with, or keep them separated?