Wastlund's half-\bound conjecture for sorting permutations by block transpositions

Let an $n$-permutation be a permutation of the entries $1,2,\ldots,n$, and let a block transposition interchange two adjacent blocks of entries. A series of such operations sorts a permutation if it transforms it into the increasing permutation $12\cdots n$.

Wastlund's conjecture. If $n\neq 13$ and $n\neq 15$, then every $n$-permutation can be sorted by at most

$$\lceil (n+1)/2 \rceil$$

block transpositions.

The conjecture proposes a sharp upper bound matching the known lower bound for the decreasing permutation $n(n-1)\cdots 21$. The supplied text gives no resolution status for the conjecture.