I haven't done proofs in a little while, but I would think that a simple counterexample proof would be enough here.
Start with the assertion that R1 is a subset of R2 (strict or not shouldn't matter).
Note that R1 can produce the following string (assuming +
means OR, so R1 can produce either 01
or 10
in any pattern infinitely):
10 01
You can observe that it is impossible to produce this string in R2, since R2 is defined such that it must have either only 01
pairs, or only 10
pairs.
Therefore, since R1 can produce strings outside of the domain of R2, it is impossible for R1 to be a subset, strict or not, of R2.