What is Supremal/Infimal Convolution

I'm currently reading a paper which mentions supremal and infimal convolutions. As I understood, they are upper and lower bounds for a joint distribution.

One of the formulas in that paper is as follows:

$$J^{v}(z) = sup\{max(F(x) + G(z-x) - 1,0) \}$$ where $$z = x + y$$

where $$F$$ and $$G$$ are defined as the CDFs of the $$X$$ and $$Y$$ distributions.

However for example if I have the following discrete distributions:

$$X = \{1,2,3,4\}$$

$$Y = \{3,5,7,9\}$$

For $$J^{v}(11)$$ we have two possible candidates as $$F(4),G(7)$$ and $$F(2),G(9)$$

$$max(F(4) + G(7) - 1,0) = 0.75$$ and $$max(F(2) + G(9) - 1,0) = 0.5$$, but how am i supposed to implement $$sup$$ operation ? If i need to sum the result, it would be meaningless since $$0.75 = 0.5 = 1.25$$.

How can i numerically calculate $$J^{v}(11)$$ ?