Splicing system, which is an abstraction of operations on DNA molecules, can be modelled mathematically under the framework of formal language theory and informational macromolecules. The recombinant behavior of the set of double-stranded DNA molecules under the influence of restriction enzyme and ligase further lead to the cut and paste phenomenon in splicing system. The theoretical study of splicing language has contributed to a new type of splicing language known as a second order limit language, which is an extension of limit language. Some types of splicing system can produce second order limit language. Y-G splicing system is chosen among other models to model the DNA splicing process as this model preserves the biological traits and presents the transparent behavior of the DNA splicing process. In this paper, the relation between second order limit language with simple splicing and semi-simple splicing system are presented.