Consider binary trees with some abstract values at the leaves. A tree t2 is said to be "derivable" from a tree t1 iff the set of values in the leaves of t2 is included in the set of values in the leaves of t1. In particular, some values can be removed and some can be duplicated.
I'm looking for a minimal set of somewhat "natural" operations on binary trees that can be composed to transform a tree into any of its derivable trees.
By natural I mean operations which are local to the root of the tree or its vicinity, happen in constant time, and can be somewhat visualized.
For instance, swapping the left and right subtree of the root of performing AVL like rotations would qualify as natural operations.