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Suppose $\Lambda$ is a special biserial algebra over an algebraically closedfield. Schr\"oer showed that if $\Lambda$ is domestic then the radical of thecategory of finitely generated (left) $\Lambda$-modules is nilpotent, and theleast ordinal, denoted $\mathrm{st}(\Lambda)$, where the decreasing sequence ofpowers of the radical stabilizes satisfies $\mathrm{st}(\Lambda)<\omega^2$.With Gupta and Sardar, the third author conjectured that if $\Lambda$ has atleast one band then $\omega\le\mathrm{st}(\Lambda)<\omega^2$ even when$\Lambda$ is non-domestic. In this paper we settle this conjecture in theaffirmative. We also describe an algorithm to compute $\mathrm{st}(\Lambda)$ upto a finite error. We also show that for each $\omega\leq\alpha<\omega^2$ thereis a finite-dimensional tame representation type algebra $\Gamma$ with$\mathrm{st}(\Gamma)=\alpha$.

On the stable radical of the module category for special biserial algebras