Are special biserial algebras homologically tame

A finite dimensional algebra is said to be homologically tame provided the little and the big finitistic dimension are equal and finite. The question formulated in the title has been discussed by Birge Huisgen-Zimmermann in the paper "Representation-tame algebras need not be homologically tame", by looking for any r > 0 at a sequence of algebras \Lambda_m with big finitistic dimension r+m. As we will show, also the little finitistic dimension of \Lambda_m is r+m. It follows that contrary to her hope, all her algebras \Lambda_m are homologically tame.