# Cycling in Simplex Method - Smallest Subscript Rule

Could someone explain to me how using the smallest subscript rule causes a cycling LP to terminate?

At the moment it looks to me that a program would use it to determine whether the matrix from the current iteration is the same as the original matrix as the smallest subscript rule allows the matrix to return to its original self. Or is it something else?

I don't see how the smallest subscript rule actually causes the method to terminate and stop cycling unless something like the above was implemented.

Degenerate LP Example:

z   x1    x2   x3   x4   s1   s2   s3 | RHS | Basic Variables| Ratio |
--------------------------------------|-----|----------------|-------|
1  -10    57    9   24    0    0    0 |  0  |        z       |       |
0  1/2 -11/2 -5/2    9    1    0    0 |  0  |       s1       |       |
0  1/2  -3/2 -1/2    1    0    1    0 |  0  |       s2       |       |
0    1     0    0    0    0    0    1 |  1  |       s3       |       |
----------------------------------------------------------------------


If someone could use this to demonstrate how the rule works I would be very grateful