Let $S$ be finite and let $\Phi$ be a translation-invariant finite-range interaction on $S^{\mathbb Z}$ of range $r$. Present the model as a nearest-neighbour subshift on admissible $r$-blocks, with transition matrix $M$ whose entry $M_{uv}$ is the Boltzmann weight of the allowed overlap transition from block $u$ to block $v$, and with $M_{uv}=0$ for forbidden hard-constraint transitions. If this transfer matrix $M$ is irreducible and aperiodic, then there is a unique translation-invariant DLR Gibbs state. This measure is the equilibrium state for the corresponding locally constant potential on the associated subshift of finite type.