Table 1 Accumulating and splitting DCJ operations

$A_{\mathcal{A}}^{\mathcal{A}}\succ B$

A→B

Accumulate labels of an $\mathcal{A}$-run

${\left(A_{\mathcal{A}}^{\mathcal{A}}\succ B\right)}^{-1}=B{\prec }_{\mathcal{A}}^{\mathcal{A}}A$

$A{\prec }_{\mathcal{B}}^{\mathcal{B}}B$

A→B

Inversely split label of a $\mathcal{B}$-run

${\left(A{\prec }_{\mathcal{B}}^{\mathcal{B}}B\right)}^{-1}=B_{\mathcal{B}}^{\mathcal{B}}\succ A$

$B_{\mathcal{B}}^{\mathcal{B}}\succ A$

B→A

Accumulate labels of a $\mathcal{B}$-run

${\left(B_{\mathcal{B}}^{\mathcal{B}}\succ A\right)}^{-1}=A{\prec }_{\mathcal{B}}^{\mathcal{B}}B$

$B{\prec }_{\mathcal{A}}^{\mathcal{A}}A$

B→A

Inversely split label of an $\mathcal{A}$-run

${\left(B{\prec }_{\mathcal{A}}^{\mathcal{A}}A\right)}^{-1}=A_{\mathcal{A}}^{\mathcal{A}}\succ B$