The pattern form conjecture for $(G_{1,1},X)$

Let $(G_{1,1},X)$ be the group–space pair whose patterns are being studied, and let a pattern be a sequence encoded by parenthesized blocks; within a block, $(0,-1)$ or $(1,0)$ denotes an arbitrary mixture of the indicated symbols. Pattern form conjecture. All patterns for $(G_{1,1},X)$ are of the form

$$(-1)(0,-1)(0)(1, 0)(1).$$

This conjecture is intended to identify the restricted class of patterns allowed by the rewriting moves and to support a description of those moves as rewrite rules. The supplied text does not establish the conjecture or provide evidence resolving it.