Hierarchical structures have became a common data structure in modern applications, thus the needs to process them efficiently has increased. In this paper we provide a full description of a mathematical model of complex tree integration, whicha allows the representation of various types of hierarchical structures and integration tasks. We use this model to show that it is possible to decompose some integration tasks by splitting them into subtasks. Thanks to this procedure it is possible to solve large integration tasks faster, without the need to develop new, less computationally complex, algorithms. Decomposition is an important step towards developing methods of multi-stage integration of hierarchical structures.
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