Venter Non-Tail: is G non-increasing or non-decreasing?

In the first paragraph of "Formal Definition", it's stated that G(x) is a non-decreasing function. In particular, G(0) = 0 and G(1) = 1. Then, in the very next sentence, that G[S(y)] is a survival function itself because it is non-increasing and starts at 1 an goes to 0, meaning G(0) = 1 and G(1) = 0. This same contradiction is stated a few pages later when Venter discusses the Wang transform in more detail.



Which is it? Or what am I missing here?

Venter Non-Tail: is G non-increasing or non-decreasing?