= Bad barrier array for the Rado order
{title2=$f(\{m,n\})=(m,n)$}
The <barrier in better-quasi-order theory> $[\omega]^2$ has shifts $\{m,n\}\triangleleft\{n,l\}$ for $m<n<l$. Map each pair to the corresponding element of the <Rado order>. Neither clause of $(m,n)\le_R(n,l)$ holds: the first coordinates differ, and the second coordinate of the first pair equals, rather than precedes, the first coordinate of the second. Thus this array is bad, although the <Rado order> is a <well-quasi-ordering>. It separates <better-quasi-ordering> from <well-quasi-ordering>.
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