Can we compute ?  No.  Since applied to is

it would appear that

However, is undefined.  applied to would have the form

which is undefined.  Even worse, is false! At this equation gives . 

Referring back to their definitions, we see , , , and applied to are defined if , , and is distinct from all , and and is distinct from all , respectively.  Here, . 

Definition.  A pair is a suitable origin if
(1) and are free of nonpositive integers
(2) and are disjoint
(3) Integer elements of are
( and )

Definition.  A pair is accessible from a pair if there exists a proper sequence of shift and inverse shift operators , , , and such that