  A left-variable word over an alphabet~$A$ is a word over~$A \cup \{\star\}$
whose first letter is the distinguished symbol~$\star$ standing for a
placeholder. The Ordered Variable Word theorem ($\mathsf{OVW}$), also known as
Carlson-Simpson's theorem, is a tree partition theorem, stating that for every
finite alphabet~$A$ and every finite coloring of the words over~$A$, there
exists a word $c_0$ and an infinite sequence of left-variable words $w_1, w_2,
\dots$ such that $\{ c_0 \cdot w_1[a_1] \cdot \dots \cdot w_k[a_k] : k \in
\mathbb{N}, a_1, \dots, a_k \in A \}$ is monochromatic.
  In this article, we prove that $\mathsf{OVW}$ is $\Pi^0_4$-conservative
over~$\mathsf{RCA}_0 + \mathsf{B}\Sigma^0_2$. This implies in particular that
$\mathsf{OVW}$ does not imply $\mathsf{ACA}_0$ over~$\mathsf{RCA}_0$. This is
the first principle for which the only known separation from~$\mathsf{ACA}_0$
involves non-standard models.
