Hi
The Honda 2000i will run a 15000 btu AC for about 2 1/2 hours. When we tried it we were at sea level and the generator was brand new. Eight months later, in the mountains of Idaho it would not work. This after running for about 100 hours of use. I would think that running a 13500 btu AC would not be a problem except you will be running your generator at its maximum. When we ran our 15000 btu AC we turned everything else off (including fire alram, propane detector, 12VDC converter and anything else that draws current). We started the fan first and then the conpressor of the AC unit when we turned it on.
If you get another u2000i and run them in parallel you will get about 3500 watts which should run just about everything on your unit. I have tried this and it works great.
Good luck
Lee & Linda