10. R0_out, Y_in
11. R1_out, Xor, Z_in, Y_in
12. Z_out, Y_in, Xor, Z_in
13. Z_out, R1_in, Xor, Z_in
14. Z_out, R0_in

Your answer need not necessarily be this short to receive full marks, although it should be fairly close. (However, even if you interpreted the admonition to "use this algorithm" as stating that the values must be stored back into R0 and R1 as we go, I don't think it makes the above any longer, you just add an extra something_out to each line.)

Guide to the above:

• after step 10, Y contains [R0]
• after step 11, Z contains [R0] XOR [R1] and Y contains [R1]
• after step 12, Z contains [R0] XOR [R1] XOR [R1], which is [R0], and Y contains [R0] XOR [R1]
• after step 13, R1 contains [R0] as desired, and Z contains [R0] XOR [R1] XOR [R0], which is [R1]
• after step 14, R0 contains [R1] as desired.