Abaye transmits the tradition according to Aba Shaul.

He reports 14 steps of the Avodah, starting with the Ma'arachah Gedolah and concluding with the evening Tamid.

Each step in his order is justified in the subsequent Gemara.

That the Ma'arachah Gedolah comes first is inferred from a Beraisa which draws from the Pasuk that there are two Ma'arachos.

Question: Perhaps the Ma'arachah Sheiniyah should come first?

Answer: We should give first priority to that which has more Kaparah (the Ma'arachah Gedolah).

Question: Perhaps we should give priority to the Ma'arachah from which we take coals within for the Ketores?

Answer: Still, more Kaparah takes precedence.

Alternate Answer: In the absence of coals from the second Ma'arachah, we would bring in coals from the first.

That the Ma'arachah Sheiniyah precedes the Sidur two Gezirei Eitzim is derived from "Alehah" which singles out one Ma'arachah, thus inferring the existence of two Ma'arachos already.

Question: But "Alehah" is needed for its own Halachah?

Answer: "Alehah" appears twice in the Pasuk.

That the two Gezirei Eitzim precede the Dishun Mizbe'ach Penimi is derived in spite of the presence of "ba'Boker ba'Boker" by both the Dishun and the two Gezirei Eitzim as we give precedence to a Machshir.

Question: How are the Gezirei Eitzim a Machshir for the Ketores, given that the coals for the Ketores were taken from the Ma'arachah Sheiniyah, not the Ma'arachah Gedolah?!

Answer #1: Eitzim have the status of Machshir.

Answer #2: Once involved with the Ma'arachah, we complete it.

Answer #3: In the absence of coals from the second Ma'arachah, we would bring in coals from the first.

That the Dishun precedes the Hatavah of the five Neiros is part of Abaye's tradition, for which he did not know a reason.

Rava taught the reason for the precedence is in order not to pass over Mitzvos (based on Resh Lakish) since he encounters the Mizbe'ach ha'Zahav first upon entry into the Heichal.

The Beraisa teaches the positions of each of the Keilim in the Heichal.

Question: Let the Mizbe'ach be in line between the Shulchan and the Menorah (and not slightly off- line to the East)?

Answer: The Pasuk teaches that there must be a direct line of sight between the Menorah and the Shulchan.

Rava learned from Resh Lakish an application to Tefilin, requiring a person to place the Shel Yad first.

That the Hatavas Chamesh Neiros precedes the Tamid, and;

That the Tamid precedes the Hatavas Sh'tei Neiros is derived from the (otherwise superfluous) words "ba'boker ba'Boker" which appear by the Hatavas Chamesh Neiros.

There are three "Boker" references by the Hatavas Chamesh Neiros, whereas the Tamid has two (giving the Hatavah precedence).

Even though both the Tamid and the Hatavas Sh'tei Neiros each have two "Boker" references, we give precedence to the Tamid since it is Mechaper.

Question: Perhaps one "Boker" should be sent to Dishun Mizbe'ach ha'Penimi and it will then precede the Tamid and a second "Boker" should be sent to the Tamid, placing it before the five Neiros (precedence given to the Mechaper)?

This (which will result in the five Neiros being prepared right before the two Neiros with no intervening Avodah) can work according to Resh Lakish.

However, it will not work according to R. Yochanan (given his D'rashah to separate the Hatavos)!

Question: The "ba'Boker is not superfluous (to place the Gezirei Eitzim before the second Ma'arachah)?

Answer: "Alehah" has already taught us that both Ma'arachos precede the Ketores!

Question: Why do the five Neiros before the two?

Answer: Once we begin, we do the majority.

Question: Then let us do six?!

Answer: The second Hatavah is spoken of in the plural.

That the two Neiros precede the Ketores is seen in the Pasuk.

That the Ketores precedes the Eivarim is based on the presence of two words "Boker" over the presence of one.

That the Eivarim precede the Minchah is derived from the prefix "ha'Olah", meaning that the Olas ha'Tamid is offered first.