Give two positions that are equivalent to each other and the transformation to get from one position
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When I say equivalent I mean that there is a function to convert any legal sequence of moves in one position to a specific legal sequence of moves in the other position and vice verse. So for example this position
is not equivalent to this position
as there is no function to uniquely convert a legal sequence of moves from one position into a legal sequence of moves in the other position as knights and bishops don't move in the same way.
The two positions you give don't need to be legal positions so long as they are equivalent in terms of legal sequences of moves.