         \Theta_{V,\mathrm{ free}}(A_0\cup A_0)         \Theta_{V,\mathrm{ free}}(B_0\cup B_0)         \over          \Theta_{V,\mathrm{ free}}(A_0\cup A_0)         \Theta_{V,\mathrm{ free}}(B_0)         \Theta_{V,\mathrm{ free}}(B_0)     }