Abbreviation: ISRng$_1$
An \emph{idempotent semiring with identity} is a semirings with identity $\mathbf{S}=\langle S,\vee,\cdot,1 \rangle $ such that
$\vee$ is idempotent: $x\vee x=x$
Let $\mathbf{S}$ and $\mathbf{T}$ be idempotent semirings with identity. A morphism from $\mathbf{S}$ to $\mathbf{T}$ is a function $h:S\rightarrow T$ that is a homomorphism:
$h(x\vee y)=h(x)\vee h(y)$, $h(x\cdot y)=h(x)\cdot h(y)$, $h(1)=1$
Example 1:
$\begin{array}{lr}
f(1)= &1
f(2)= &1
f(3)= &
f(4)= &
f(5)= &
f(6)= &
\end{array}$