each other, called *tendons*. Tendons can be compressed into a BST structure that allows their traversal between the two endpoints in $O(1)$ steps.

We maintain $S$ as a root-containing subtree of our BST $T'$, called the *hand*. Due to the compression of the tendons, the relevant part of $S$ has size $O(k)$. The description so far, including the terminology, is identical to the one in [@CombineBST §2]. Our construction differs in the fact that it maintains the hand, i.e. the compressed representation of $S$ as a *balanced* BST. This guarantees the reachability of fingers in $O(\log{k})$ instead of $O(k)$ steps, i.e. property (1).

When a finger in $T$ moves or performs a rotation, the designation of some (pseudo)finger, or tendon nodes may change. Such changes can be viewed as the insertion or deletion of items in the tendons. As these operations happen only at certain places within the tendons, they can be implemented efficiently. We implement tendons with the same BST-based *deque* as [@CombineBST]. The construction appears to be folklore, we describe it in Appendix \[deque\_proof\] for completeness.

We depart again from [@CombineBST], as the operation affecting the (pseudo)finger and tendon nodes can trigger a re-balancing of the hand, which 