Do perks count towards the points spent on a style for the purpose of gaining more perk slots?

Question

When using the style rules in GURPS (Martial Arts, Shooting Styles, Magic Styles) do points spent on perks provided by the style count toward points spent on "components" of that style in order to gain more slots for style perks or is it only skills, techniques, and spells that count?

If so, does the perk have to have been acquired from that style, or could it be an identical perk purchased from another style?

If I spend 10 points on the skills and techniques of Italian School Fencing and buy the perk Off Hand Weapon Training (Rapier) that it provides, have I now spent 11 points on "components of the style" or only 10?

If I also have 9 points in the skills and techniques of La Verdadera Destreza which also provides Off Hand Weapon Training (Rapier) does that mean I have 10 points spent on "components of the style" and therefore can buy another perk it provides such as Sure-Footed (Uneven).

Answer 1

No, points spent on perks do not contribute to "points spent on the style's abilities." Style Perks on p. 142 of Martial Arts makes this clear:

Anyone may buy one Style Perk per 20 points in combat skills. A martial artist who has Style Familiarity may further buy one of that style’s perks per 10 points he has in its techniques and required skills; see Components of a Style (pp. 141-143). For example, 40 points in style abilities would allow two general perks plus four style-specific ones.

Perks are not Skills or Techniques, they are (tiny) Advantages.