Do you see how flat the roof is, I mean, used to be? In fact, right at the drip line, where the water drains away from the house directly onto the deck, that's where the deck began to get the wettest. What a dumb idea to drain the roof onto the deck. Why not a gutter and a downspout? Why not shed the water and the tree leaves and twigs away from the deck entirely? Well, let's do that. Surprise, more demolition.
Time to tear the roof off the sucker!