Complexity of Block edit distance with Swapping only Suppose I have distinct letters in an alphabet $\sum = \{a_1,a_2,...,a_n\}$. I also have two permutations of these letters, let's call them $A,B$. How can I find the Edit distance between $A$ and $B$ with block edit operations allowed?

To make it clearer, an example would be $\sum =\{a,b,c,d \}$. Two possible permutations are $A=``abcd",B=``dabc"$. The edit distance here would be $1$ because we can swap the block $``abc"$ with $``d"$ to get one string to the other.

Clearly, there won't be any deletions/insertions in this form of the problem, it will purely be swaps since the two strings are permutations of the same letters.

Now I know that the original edit-block problem with all operations is NP-Hard, however, would the restriction of only block swaps perhaps make this solvable in polynomial time? Most text I've read don't address this version and instead address variations of the original problem. Any help would be appreciated.
When one operation is exactly "removing a block and inserting it between two other positions", the problem of computing the string distance is known as Transposition Distance. It is NP-hard even if both input sequences are $p$-sequences, that is, if every letter occurs only once in each input sequence:

Laurent Bulteau, Guillaume Fertin, Irena Rusu:
Sorting by Transpositions Is Difficult. SIAM J. Discrete Math. 26(3): 1148-1180 (2012)