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We consider about calculating $M$th moments of a given polynomial in freeindependent semicircular elements in free probability theory. By a naiveapproach, this calculation requires exponential time with respect to $M$. Weexplicitly give an algorithm for calculating them in polynomial time byrearranging Sch\"utzenberger's algorithm.

Pseudo-Polynomial Time Algorithm for Computing Moments of Polynomials in Free Semicircular Elements