Replacement-bijection conjecture for equivalent binary tree patterns

Let $s$ and $t$ be equivalent binary tree patterns, meaning that the binary trees avoiding $s$ and those avoiding $t$ are equinumerous. A top-down replacement, bottom-up replacement, and left--right reflection are the pattern transformations described in the paper, each inducing the corresponding transformation on binary trees.

Replacement-bijection conjecture. If $s$ and $t$ are equivalent, then there is a sequence of top-down replacements, bottom-up replacements, and left--right reflections that produces a bijection from binary trees avoiding $s$ to binary trees avoiding $t$.

The conjecture proposes that these explicit transformations generate all equivalences between binary tree pattern-avoidance classes. The paper states that the assertion holds computationally for patterns with at most $7$ leaves, while the general case remains open.