If the tree is that close to the wall there is a good possibility that its roots are in your yard. Thats what happened to us, our neighbor had a tree that had branches hanging in our yard and we were constantly digging up, pulling or cuttung out small trees from thiers that were making themselves at home all over our yard and in planters. The roots from that tree were pretty much up and down our fence and into our yard, they were not that far down. If there is a place you can dig down a little ways and check, it might pay off and you will be able to use the answer about the copper nails. Good Luck!