it only in the following case. Let $\ud{a}$ and $\ud{b}$ be words (or strings). Then $$\ud{a}\prec\ud{b}\quad\text{iff $\exists$ $\ud{c}\in\tA^*$,
$\exists$ $k\geq 0$ such that $\ud{a}=\ud{c}a_k\cdots$,
$\ud{b}=\ud{c}b_k\cdots$ and $a_k<b_k$.}$$ If $\ud{a}\prec\ud{b}$ then neither $\ud{a}$ is a prefix of $\ud{b}$, nor $\ud{b}$ is a prefix of $\ud{a}$.

In subsection \[subsectionfollower\] we introduce one of the main tool for studying the shift-space $\BSigma(\ud{u},\ud{v})$, the follower-set graph. In subsection \[subsectionalgo\] we give an algorithm which assigns to a pair of strings $(\ud{u},\ud{v})$ a pair of real numbers $(\bar{\alpha},\bar{\beta})\in [0,1]\times[1,\infty)$. Finally in subsection \[topological\] we compute the topological entropy of the shift space $(\ud{u},\ud{v})$.

Follower-set graph $\cG(\ud{u},\ud{v})$ {#subsectionfollower}
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We associate to $\BSigma(\ud{u},\ud{v})$ a graph $\cG(\ud{u},\ud{v})$, called the [follower-set graph]{} (see [@LiM]), as well as an equivalent graph $\overline{\cG}(\ud{u},\ud{v})$. The graph $\overline{\cG}(\ud{u},\ud{v})$ has been systematically studied by Hofbauer in his works about piecewise monotone one-dimensional dynamical systems; see [@Ho1], [@Ho2] and [@Ho3] in the context of this paper, as well as [@Ke] and [@BrBr]. Our presentation differs from that of Hofbauer, but several proofs are directly inspired by [@Ho2] and [@Ho3].

We denote by $\cL(\ud{u},\ud{v})$ the [language of]{} $\BSigma(\ud{u},\ud{v})$, that is the set of words, which are factors of $\ud{x}\in \BSigma(\ud{u},\ud{v})$ (including the empty word $\epsilon$). 