initialize the rightRree, leftTree, rightTreeMin, and leftTreeMax to null
    loop while root != null (root should not become null, but this protects against null parameter)
        if x < root
            check for root's left child null.  If so, x not in tree, break loop.
            if x < root's left child we have zig zig (left) so do a single rotate (left) at root
                check for (new) root's left child null.  If so, x not in tree, break loop.
            add root to rightRree at its minimum node - update the rightTreeMin to point to this node
            update the new working root:  set root to root's left child
        if x > root
            check for root's right child null.  If so, x not in tree, break loop.
            if x > root's right child we have zig zig (right) so do a single rotate (right) at root
                check for (new) root's right child null.  If so, x not in tree, break loop.
            add root to leftTree at its maximum node - update the leftTreeMax to point to this node
            update the new working root:  set root to root's right child
        otherwise we have found x at root.  break.
    reassemble
        if the left tree is not null, hang root's left child onto its maximum and set root's left child = the left tree.
        if the right tree is not null, hang root's right child onto its minimum and set root's right child = the right tree.
    return root