  Given a special biserial algebra $\Lambda$ over an algebraically closed
field, let $\mathrm{rad}_\Lambda$ denote the radical of its module category.
The authors showed with Sinha that the stable rank of a special biserial
algebra $\Lambda$, i.e., the least ordinal $\gamma$ satisfying
$\mathrm{rad}_\Lambda^\gamma=\mathrm{rad}_\Lambda^{\gamma+1}$, is strictly
bounded above by $\omega^2$. We use finite automata to give simple algorithmic
proofs, complete with their time complexity analyses, of two key ingredients in
the proof of this result--the first one states that certain linear orders
called hammocks associated with such algebras are \emph{finite description
linear orders}, i.e., they lie in the smallest class of linear orders that
contains finite linear orders and $\omega$, and that is closed under
isomorphisms, order-reversals, binary sums, co-lexicographic products and
finitary shuffles. We also document a complete proof of the result that the
class of order types(=order-isomorphism classes) of finite description linear
orders coincides with that of languages of finite automata under inorder.
