Control Systems Signal Flow Graph and Block Diagram Block Diagram Reduction Technique

In the below figure, output C1 due to R1 and R2 is given by:

1
\(\rm\frac{G_1 R_1−G_1 G_3 G_4 R_2}{1−G_1 G_2 G_3 G_4}\)
2
\(\rm\frac{G_1 R_1−G_2 G_3 G_4 R_2}{1−G_1 G_2 G_3 G_4}\)
3
\(\rm\frac{G_1 R_1−G_1 G_3 G_2 R_2}{1−G_1 G_2 G_3 G_4}\)
4
\(\rm\frac{G_1 R_1−G_1 G_2 G_3 G_4 R_2}{1−G_1 G_2 G_3 G_4}\)
5
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