[Zeke]

The tree may have pushed on the part of the fence that looks the best. The other part is falling INTO the neighbor's yard. And it looks from the gray that a sprinkler has caused most of the damage. I'd say it's a joint liability and th neighbors should seek the best and economical solution.

If that doesn't work, then one owner needs to do only what needs to be done to secure the yard.

There is a lot of neglect shown in the pic from both parties. Why start pointing fingers now?