If $(X,m)$ is a median algebra, then for each $x\in X$, define an operation $\wedge_{x}$ by letting $y\wedge_{x}z=m(x,y,z)$. Then $(X,\wedge_{x})$ is a meet-semilattice with least element $x$. Define the ordering $\leq_{x}$ on $X$ where $y\leq_{x}z$ iff $y=y\wedge_{x}z=m(x,y,z)$. An unrooted lobs...