Universal deformation rings of string modules over a certain symmetric special biserial algebra

Let $k$ be an algebraically closed field, let $A$ be a finite dimensional $k$-algebra and let $V$ be a $A$-module with stable endomorphism ring isomorphic to $k$. If $A$ is self-injective then $V$ has a universal deformation ring $R(A,V)$, which is a complete local commutative Noetherian $k$-algebra with residue field $k$. Moreover, if $Lambda$ is also a Frobenius $k$-algebra then $R(A,V)$ is stable under syzygies. We use these facts to determine the universal deformation rings of string $Ar$-modules whose stable endomorphism ring isomorphic to $k$, where $Ar$ is a symmetric special biserial $k$-algebra that has quiver with relations depending on the four parameters $ bar{r}=(r_0,r_1,r_2,k)$ with $r_0,r_1,r_2geq 2$ and $kgeq 1$.