[Avodah] 13 Middot

[Arie Folger]

There exists a ma'hloqet rishonim about how to count the 13 Attributes of 
Divine Retribution (more correct nomenclature that ... Mercy, since it 
includes Din, as well). Rashi's scheme, mentioned also by Rabbenu Tam and 
Rabbi Eli'ezer Rokeach is well known, the other one comes from Rabbenu Nissim 
and, apparently, Rambam. Both opinions are recorded by Tos. Rosh haShanah 
17b.

The essential differences between the two schemes is whether to count "HaShem 
Hashem E-l" as one (RN) or three attributes (Rashi, RT) and whether to 
count "lo yenakeh (lesheeinam shavim)" as part of the 13 (RN).

However, all machzorim and siddurim that show Tashlikh with corresponding 13 
attributes count them according to a 3rd scheme. That one starts like Rabbenu 
Nissim, but instead of counting nakeh twice and also including "lo yenakeh", 
it divides erekh apayim and notzer chessed laalafim into two attributes each. 
This scheme is attributed to the Ari (so say Rebbe Scroll, and indeed, that 
is the way a highly Ari-Kabbalistically acquaintance of mine teaches the 13 
Middot), though I have no source to study this.

1) Can anyone explain the logic behind splitting erekh apayim and notzer 
chessed laalafim, respectively?
2) Why is it, that the Ari's scheme particularly caught on for Tashlikh, even 
as the same ma'hzorim will use Rashi & RT's scheme for seli'hot?
3) Where is the Ari's scheme first recorded (I assume in 'Etz 'Hayim)?
4) Can anyone mail me a reference, or if possible, a scan/excerpt from etext?

Yasher koach,

Arie Folger