I'm curious about people's opinions on the following not-so-
hypothetical situation:

If you have two neighbors, call them Dan and Bob. There is a tree
whose trunk is on Dan's property, but there are branches that overhang
onto Bob's property, in fact, one branch hangs over Bob's pool causing
Bob some grief. The tree is mature, and existed before either moved
into their houses, Bob wants that branch (and several others)
trimmed, but Dan does not want to trim the tree on his property.
Who's responsibility is it to have the branch trimmed?

I know that Dan has no legal obligation to trim the tree, but is there
an implied moral obligation (it's Dan's tree therefore he should trim
it), or is it implied that the trim is for Bob's sole benefit,
therefore Bob should do it? (And splitting the cost does not seem to
be an option here).