According to the increaing-Bruhat-path-explanation of Kazhdan-Lusztig $R$-polynomials(in fact $\tilde{R}$-polynomials), and the fact that $[q^{l(x,y)}]\tilde{R}_{x,y}(q)=1$, there is a unique increasing maximal path in any Bruhat interval under any reflection order. I wonder if there is any direct explanation.