Data Sufficiency

how many integers are there between, but not including, integers r and s?

(1) s - r = 10
(2) there are 9 integers between, but not including, r + 1 and s + 1

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Counting numbers between r and s (including both of them) I'd say the count is s - r + 1
and using (1) s - r = 10 then between them there are 11 integers but since the stem question
asks r and s not to be included then, 11 - 2 = 9.

As I understand (2) it says integers between s + 1 and r + 1 not including those is 9
therefore 9 is the number of integers between r and s including them so, not including them
as the stem question asks, I'd say the number of integers between r and s is 9 - 2 = 7.

Since the statements contradict each other it'd make me think there is a mistake in
the reasoning I applied.

Could someone please help?

thanks