The factor-complexity and critical-exponent conjecture for morphic images of G

Let ${\mathbf G}=\gamma^\omega(0)$, where $\gamma=[01,2,02]$, and let $\mu$ be its critical exponent. For each morphism $h$ in Table~, consider the infinite word $h({\mathbf G})$. Morphic-image conjecture. For each such morphism $h$, the word $h({\mathbf G})$ has factor complexity $2n+1$ and critical exponent $\mu$. These are presented as open problems in the source; the conjecture concerns preservation of both invariants under the listed morphisms.