The behavior of the relativistic hadron (shower particle) multiplicity for 32 S-nucleus interactions is investigated. The experiment is carried out at 3.7A GeV (Dubna energy) and 200A GeV (SPS energy) to search for the incident energy effect on the interactions inside the 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 separated into groups according to the interactions with H, CNO, Em, and AgBr target nuclei. The separation of events, into these groups, is executed based on predictions of Glauber's multiple scattering theory. 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 GeV, the target size is the main parameter affecting the backward production of relativistic hadrons. The backward shower particle multiplicity can indicate the impact parameter. The incident energy is a principle 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 seen in the nuclear fireball model. The forward shower particle multiplicity distributions may behave in a similar trend at Dubna energy and SPS for low target sizes. For heavy target sizes, the SPS energy reveals the creation of hadrons with nearly equal probabilities over a wide range of multiplicity, extending to more than 300 hadrons per event. The data are analyzed in the framework of the FRITIOF model.