Abbreviation: GEAlg
A \emph{generalized effect algebra} is a separation algebra that is
\emph{positive}: $x\cdot y=e$ implies $x=e=y$.
A \emph{generalized effect algebra} is of the form $\langle A,+,0\rangle$ where $+:A^2\to A\cup\{*\}$ is a partial operation such that
$+$ is \emph{commutative}: $x+y\ne *$ implies $x+y=y+x$
$+$ is \emph{associative}: $x+y\ne *$ implies $(x+y)+z=x+(y+z)$
$0$ is an \emph{identity}: $x+0=x$
$+$ is \emph{cancellative}: $x+y=x+z$ implies $y=z$ and
$+$ is \emph{positive}: $x+y=0$ implies $x=0$.
Let $\mathbf{A}$ and $\mathbf{B}$ be generalized effect algebra. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: $h(e)=e$ and if $x + y\ne *$ then $h(x + y)=h(x) + h(y)$.
Example 1:
$\begin{array}{lr}
f(1)= &1\\ f(2)= &1\\ f(3)= &2\\ f(4)= &5\\ f(5)= &12\\ f(6)= &35\\ f(7)= &119\\ f(8)= &496\\ f(9)= &2699\\ f(10)= &21888\\ f(11)= &292496\\
\end{array}$