We will prove that under the proper forcing axiom, the class of all Aronszajn lines behave like $\sigma$-scattered orders under the embeddability relation. In particular, we show that the class of better quasi order labeled fragmented Aronszajn lines is itself a better quasi order. Moreover, we show that every better quasi order labeled Aronszajn line can be expressed as a finite sum of labeled types which are algebraically indecomposable. By encoding lines with finite labeled trees, we are also able to deduce a decomposition result, that for every Aronszajn line $L$, there is an $n\in \omega$ such that for any finite colouring of $L$, there is a subset $L'$ of $L$ isomorphic to $L$ which uses no more than $n$ colours.