An internal collision already present in the pair

The scalar-sourced coordinate part of $\mathcal{O}$ contains a branch with schematic form

Two scalar contractions can join the stress slots at $z$ to the two scalar slots of the interaction at $y$. The resulting unintegrated expression contains two differentiated time-ordered scalar lines between $y$ and $z$, together with the already inherited retarded branch from $z$ to $x$.

The collision $y=z$ may occur while $x\ne z$. It is therefore a partial graph diagonal. A counterterm supported only where $x=y=z$ does not by its support alone normalize this internal collision. Other branches contain additional internal vertices. They require a joint check, not deletion because the final output is called binary.

This observation does not prove that every extension in C_{tot} fails. A proof of such failure would need an explicit unavoidable normalization incompatibility. None is inferred from the presence of the collision.