$\ell_{\Gamma}$ the rightmost vertical line intersecting $\Gamma$; note that $\ell_{\Gamma}$ is a grid column.

Let $\Gamma_0$ and $\Gamma_1$ be two [order-preserving strictly-upward straight-line planar grid]{}drawings of $T$. We inductively construct a morph $\mathcal M$ from $\Gamma_0$ to $\Gamma_1$ as follows.

In the base case $n=1$; then $\mathcal M$ is the linear morph $\langle \Gamma_0,\Gamma_1\rangle$.

In the inductive case $n>1$. Let $l=l^{\rightarrow}_T$ be the rightmost leaf of $T$. Let $\pi=p(l)$ be the parent of $l$. Let $T'$ be the $(n-1)$-node tree obtained from $T$ by removing the node $l$ and the edge $(\pi,l)$. Let $\Gamma'_0$ and $\Gamma'_1$ be the drawings of $T'$ obtained from $\Gamma_0$ and $\Gamma_1$, respectively, by removing the node $l$ and the edge $(\pi,l)$. Inductively compute a $k$-step upward planar morph $\mathcal M'=\langle \Gamma'_0=\Delta'_1,\Delta'_2,\dots,\Delta'_{k}=\Gamma'_1\rangle$.

We now construct a morph $\mathcal M=\langle \Gamma_0,\Delta_1,\Delta_2,\dots,\Delta_k,\Gamma_1\rangle$. For each $i=2,3,\dots,k-1$, we define $\Delta_i$ as the drawing obtained from $\Delta'_i$ by placing $l$ one unit below $\pi$ and one unit to the right of $\ell_{\Delta'_i}$. Further, we define $\Delta_1$ ($\Delta_{k}$) as the drawing obtained from $\Delta'_1$ (resp. from $\Delta'_k$) by placing $l$ one unit below $\pi$ and one unit to the right of $\ell_{\Gamma_0}$ (resp. $\ell_{\Gamma_1}$). Note that the point at which $l$ is 