The Desbot-Wilf classification conjecture for patterns in S_4

Let $S_4$ be the set of permutations of length $4$. For a permutation $\tau$, define its descent bottom set by

$$\operatorname{Desbot}(\tau)=\{\tau(i+1)\mid \tau(i)>\tau(i+1)\}.$$

Two patterns are Desbot-Wilf equivalent if their avoidance classes have the same $\operatorname{Desbot}$-distribution for every permutation length. The Desbot-Wilf classification conjecture. The non-singleton $\operatorname{Desbot}$-Wilf equivalence classes in $S_4$ are

$$\{2134,3412\},\quad \{2314,2413\},\quad \{2143,4312\},$$ $$\{1423,1342\},\quad \{3142,3241,4132,4213\}.$$

This is presented as equivalent to the preceding Destop classification by reverse complement; its general status is unresolved in the supplied text.