Product decomposition for surjective 2-block NCCA

It is known that injective Cellular Automata (CA) are surjective. In general, the converse is not true, and there are many algebraic CA counterexamples. However, there are interesting subclasses where this might be true. For example, if a surjective CA has entropy 0 then it is almost injective (Moothathu (2011)) and it is not known if it is actually injective. The author believes there are some sub-classes of potential preserving CA, including Number Conserving CA (NCCA), where there are no surjective but not injective CA. The subclass of NCCA, besides providing interesting mathematical structure, is used for discrete models in scientific disciplines where one simulates systems governed by conservation laws of mass or energy. Many papers have been published on traffic models using NCCA (for example see Maerivoet and Moor (2005)). The Moore-Myhill theorem says that a CA is surjective iff it is injective on homoclinic classes. Actually, it is easy to see that a NCCA is surjective iff it is bijective on homoclinic classes. This suggests that there might be a closer relationship between surjective NCCA and injective NCCA. So far, it is known that surjective NCCA have dense periodic points (Formenti and Grange (2003)). If it turns out that surjective NCCA are injective we would recover this result, since for bijective CA periodic points are dense.