The one on the left is definitely badly rotted. I'd probably pull that one out. I'm not familiar with the species, so I'm not sure if you could potentially cut above the rotted section, where the green top is, callous it, and get it to root? Someone else will have some better input there though. I'm not sure if that's a possibility.
The one on the right doesn't look so bad. I can't tell if it has rot at the base or if it's just slightly darker coloration. Does the base of that one feel soft at all?