After passing the last ice protecting a server, the next step (4) is to approach the server. The runner then has the choose if they wish to continue or jack out. If they choose to continue, both players have a chance to use paid abilities and rez cards before moving onto the "successful run" trigger which is where Hokusai Grid and Bernice Mai trigger if rezzed. Then the runner accesses the server.
1. Runner starts, names server.
If there's ICE, goto 2.
If no ice, goto 4.
2. Approach outermost ICE.
2.1. Paid ability can be used
2.2. Jack out (Goto 6, cannot jack out if first piece of ICE encountered this run) or continue to 2.3.
2.3. Approached ICE can be rezzed
Paid ability can be used
cards can be rezzed.
2.4. Check if ICE is rezzed.
If rezzed, goto 3.
If unrezzed, and there's another piece of ICE, goto 2.
If unrezzed, and there's no more ICE, go to 4.
3. Runner Encounters Ice if rezzed.
3.1. Icebreakers can interact, Paid abilities can be used
3.2. Resolve all unbroken subroutines
...Either the run ends, goto 6
Or it continues, and there's another piece of ICE, goto 2.
Or it continues, and there's no more ICE, go to 4.
4. Runner approaches attacked server
4.1. Paid abilities can be used.
4.2. Runner decides:
To jack out, go to 6
or to continue, go to 4.3
4.3. Paid abilities may be used, cards may be rezzed.
4.4. Run is successful. Trigger abilities if any.
4.5. Access cards. Trigger abilities if any.
Agenda : Stolen (Unless additional cost)
Trash cost present : may be paid to trash
Everything not trashed or stolen is returned to server.
5. Run ends. Trigger abilities if any.
6. Run is unsuccessful. Trigger abilities if any.