The Turing tape can be initialised to any desired length before starting processing. But it is preferable to allow the machine to run on a simulated infinite tape: in other words, to assume that any uninitialised tape space contains symbol 3 (the blank symbol in the (2, 18) UTM ), represented by creature type Cephalid. This is accomplished by having the ends of the currently-initialised tape marked by two special tokens, one green Lhurgoyf and one white Rat. Suppose we’ve exhausted all the initialised tape to the left. This means that the casting of Infest
on turn T1 kills the Lhurgoyf rather than one of the normal tape types. This does not directly trigger any of the normal Reanimators/Necromancers. Instead, Bob has another Rotlung Reanimator
hacked  to read “Whenever Rotlung Reanimator or another Lhurgoyf dies, create a 2/2 green Lhurgoyf creature token”, and Alice has a Rotlung Reanimator
hacked to read “Whenever Rotlung Reanimator or another Lhurgoyf dies, create a 2/2 black Cephalid creature token.” Bob’s trigger will resolve first, then Alice’s.
First, Bob’s Reanimator trigger creates a new Lhurgoyf just to the left of the current head. (Alice’s Illusory Gains
triggers and gives her control of this new Lhurgoyf, but that will soon change.) We have one copy of Shared Triumph
set to Lhurgoyf (“Creatures of the chosen type get +1/+1”) so this token arrives as a 3/3.
Second, Alice’s Reanimator trigger now creates a 2/2 black Cephalid under Alice’s control. The same two copies of Dread of Night
as before are giving all black creatures -2/-2, so the black Cephalid will arrive as a 0/0 and immediately die.
The death of this Cephalid triggers one of the regular phasing Reanimators of Bob’s just as if a tape cell containing symbol 3 had been read: a new 2/2 token is created and Illusory Gains
moves to that new token. The green Lhurgoyf token serving as an end-of-tape marker has been recreated one step over to the left.
The situation for the white Rat representing the right-hand end of the tape is exactly equivalent. Bob has a Rotlung Reanimator
hacked to read “Whenever Rotlung Reanimator or another Rat dies, create a 2/2 white Rat creature token”; Alice has a Rotlung Reanimator hacked to read “Whenever Rotlung Reanimator or another Rat dies, create a 2/2 black Cephalid creature token”; and we have another Shared Triumph
set to Rat.