The behavior of relativistic hadron multiplicity for 4He-nucleus interactions is investigated. The experiment is carried out at 2.1 A and 3.7 A GeV (Dubna energy) to search for the incident energy effect on the interactions inside different emulsion target nuclei. Data are presented in terms of the number of emitted relativistic hadrons in both forward and backward angular zones. The dependence on the target size is presented. For this purpose the statistical events are discriminated into groups according to the interactions with H, CNO, Em, and AgBr target nuclei. The separation of events, into the mentioned groups, is executed based on Glauber's multiple scattering theory approach. Features suggestive of a decay mechanism seem to be a characteristic of the backward emission of relativistic hadrons. The results strongly support the assumption that the relativistic hadrons may already be emitted during the de-excitation of the excited target nucleus, in a behavior like that of compound-nucleus disintegration. Regarding the limiting fragmentation hypothesis beyond 1 A GeV, the target size is the main parameter affecting the backward production of the relativistic hadron. The incident energy is a principal factor responsible for the forward relativistic hadron production, implying that this system of particle production is a creation system. However, the target size is an effective parameter as well as the projectile size considering the geometrical concept regarded in the nuclear fireball model. The data are analyzed in the framework of the FRITIOF model.