Homotopy between composites associated in different ways

Statement

Existential version

Suppose $f_1,f_2,f_3$ are loops based at a point $x_0$ in a topological space $X$. We can consider two differently associated products of these three loops:

$a=(f_1*f_2)*f_3,b=f_1*(f_2*f_3)$

$a$ and $b$ are homotopic loops, i.e., they are in the same homotopy class of loops based at $x_0$.

Constructive/explicit version

Fill this in later