Then we can find an infinite set $M$ and $I\subseteq [r]$ such that for any $x_1<x_2<\cdots <x_r$ in $M$, and $y_1<y_2<\cdots <y_r$ in $M$ we have $c(x_1{x}_2\cdots x_r)=c(y_1{y}_2\cdots y_r)$ if and only if $x_i=y_i$ for all $i\in I$.