On the asymptotic solution of a special type recurrence relations and the Kullmann–Luckhardt's technology

The problem of solving recurrence relations that arise in the analysis of the computational complexity of recursive algorithms is discussed. The research is only related to splitting algorithms, namely, DPLL-algorithms, which are named after the author's names by the first letters (Davis, Putman, Logemann, Loveland), and are designed to solve the problem SAT. The technology by Kullmann–Luckhardt, which is traditionally used in the analysis of the computational complexity of splitting algorithms, is explored. A theorem containing an upper estimate for the algorithm time is proved in the case of balanced splitting. The theorem extends the capabilities of the Kullmann–Luckhardt's technology.