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diskr-Wrela

Idea: If I have two relations R_1, R_t ∈ A × B where for each A and for each B the amount of elements incident to each one is the same between R_1 and R_2, and I am allowed to construct new relations R_n from R_{n-1} by transforming "aR_{n-1}b, cR_{n-1}d" to "aR_nd, cR_nb", are there any R_1, R_t where R_t can't be reached via such swaps from R_1? How to construct those?