Gordon and Jeffrey developed a type system for checking correspondence assertions. The correspondence assertions, proposed by Woo and Lam, state that when a certain event (called an ``end'' event) happens, the corresponding ``begin'' event must have occurred before. They can be used for checking authenticity in communication protocols. In this paper, we refine Gordon and Jeffrey's type system and develop a polynomial-time type inference algorithm, so that correspondence assertions can be verified fully automatically, without any type annotations. The main key idea that enables polynomial-time type inference is to introduce fractional effects; Without the fractional effects, the type inference problem is NP-hard.