Low-dimensional relative K-theory computation for the coordinate axes

Let $A=\mathbb{Z}[x,y]/(xy)$ and let $I=(x,y)$. The low-dimensional relative K-theory conjecture.

$$K_9(A,I)\cong \mathbb{Z}/2\oplus\mathbb{Z}/2\oplus\mathbb{Z}/16\oplus\mathbb{Z}/3\oplus\mathbb{Z}/3$$

and

$$K_{13}(A,I)\cong \mathbb{Z}/2\oplus\mathbb{Z}/2\oplus\mathbb{Z}/8\oplus\mathbb{Z}/8\oplus\mathbb{Z}/3\oplus\mathbb{Z}/3\oplus\mathbb{Z}/9\oplus\mathbb{Z}/5\oplus\mathbb{Z}/5.$$

These computations reduce to calculations of equivariant topological cyclic homology groups, with the unresolved parts supplied by the subsequent conjectures on the relevant $C_4$-Tate spectral sequences.