Some readers have noticed a problem with the construction in Lemma 2. The claim of item 1, CHAIN(p, n) \otimes INC(p) = CHAIN(p, n + 1), is not correct as it stands in the paper.
The chain has to be lengthened at the end, not the beginning. In this case, we can not lengthen the end itself by copying the last node, since the last node doesn't have a loop. So our only chance is to copy the next to last node. But that we can do. But it leads to a different event model, though:
e1: p /\ ~\gamma_0 /\ ~\gamma_1 (this one matches all nodes except the last two)

V
e2: p /\ \gamma_1 (this matches only the next to last node)

V
e3: p /\ \gamma_1 (we make another copy of the next to last node)

V
e4: p /\ \gamma_0 (this matches the last node only)
where all nodes have loops except e4. So the intuition is that we cut the input chain at the next to last node and insert another node there.