^{+}[\{x_{m-2},b_{1},f_{1}\},i]=0$. The resulting homology $$HF^{+}({Y_{m,n}},\mathfrak{s}_{0}+\mu _{1}+\mu _{2})={\mathcal{T}^{+}}\oplus {\mathcal{T}^{+}}$$ is freely generated by the elements $[\{x_{m-2},b_{1},f_{2}\},i]$ and $[\{x_{m-2},b_{1},f_{1}\},i]$ for $i\geq 0$.

**Class $\mathfrak{s}_{0}-\mu _{1}-\mu _{2}$**\
We change the basepoint $z_{1}\in D_{5}$ for a new basepoint $z_{2}\in D_{2}$. By Lemma \[lemaz\], the $\sp $ structure $\mathfrak{s}_{0}-\mu _{1}-2\mu _{2}=\mathfrak{s}_{z_{1}}(\{x_{m},b_{2},f_{1}\})$ changes to $\mathfrak{s}_{0}-\mu _{1}-\mu _{2}=\mathfrak{s}_{z_{2}}(\{x_{m},b_{2},f_{1}\})$. In the new $\sp $ structure we have the same generators as in the $\sp $ structure $\mathfrak{s}_{0}-\mu _{1}-2\mu _{2}$, but the relative grading is now induced by the basepoint $z_{2}$: $$\xymatrix{
\{x_{m},b_{2},f_{2}\} \ar@{.>}[d]\\
\{x_{m},b_{2},f_{1}\}}$$ We already know that in the classes containing only two generators, the differential $\partial ^{\infty }$ is trivial. Therefore the resulting homology is $$HF^{+}({Y_{m,n}},\mathfrak{s}_{0}-\mu _{1}-\mu _{2})={\mathcal{T}^{+}}\oplus {\mathcal{T}^{+}}\;,$$ freely generated by the elements $[\{x_{m},b_{2},f_{2}\},i]$ and $[\{x_{m},b_{2},f_{1}\},i]$ for $i\geq 0$.

**Classes $\mathfrak{s}_{0}-i\mu _{1}-\mu _{2}$ for $2\leq i\leq m-2$**\
We change the basepoint $z_{1}\in D_{5}$ for a new basepoint $z_{2}\in D_{2}$. By Lemma \[lemaz\], the $\sp $ structure $\mathfrak{s}_{0}-i\mu _{1}-2\mu _{2}=\mathfrak{s}_{z_{1}}(\{x_{i-1},b_{1},f_{1}\})$ changes to $\mathfrak{s}_{0}-i\mu _{1}-\mu _{2}=\mathfrak{s}_{z_{2}}(\{x_{i-1},b_{1},f_{1}\})$. In the new $\sp $ structure we have the same generators as in the $\sp $ structure $\mathfrak{s}_{0}-i\mu _{1}-2\mu _{2}$, but the relative grading is now induced by the basepoint $z_{2}$: $$\xymatrix{
\{x_{i-1},b_{1},f_{2}\} \ar@{.>}[d]\\
\{x_{i-1},b_{1},f_{1}\}}$$ We already know that in the 