Before revision:  The subshift X_0 \Omega_0 is proper due to some horizontal fracture of 0's or 1's in tilings in \Omega_0 and we believe that \Omega_0\setminus X_0 is a null set . Algorithms are provided to find markers, recognizable substitutions and sheering topological conjugacy from a set of Wang tiles.
After revision:  The subshift X_0 \Omega_0 is proper due to some horizontal fracture of 0's or 1's in tilings in \Omega_0 and we believe that \Omega_0\setminus X_0 is a null set for any shift-invariant probability measure on \Omega_0. The proof is based on twelve elementary steps where ten of them are using the same procedure allowing to desubstitute Wang tilings from the existence of a subset of marker tiles. The two other steps are adding decorations to deal with fault lines and are changing the base of the \mathbb{Z Algorithms are provided to find markers, recognizable substitutions and sheering topological conjugacy from a set of Wang tiles.