Finite test sets for morphisms which are square-free on some of Thue's square-free ternary words

Abstract: Let $S$ be one of ${aba,bcb}$ and ${aba, aca}$, and let $w$ be an infinite square-free word over $\Sigma={a,b,c}$ with no factor in $S$. Suppose that $f:\Sigma\rightarrow T^*$ is a non-erasing morphism. Word $f(w)$ is square-free if and only if $f$ is square-free on factors of $w$ of length 8 or less.