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