BMS分析

目前使用的OCF为M型，后续补充BOCF

1：单行BMS（PrSS）

$\varnothing =0$

$(0)=1$

$(0)(0)=2$

$(0)(0)(0)=3$

$(0)(1)=(0)(0)(0)(0)(0)...=\omega$

$(0)(1)(0)=\omega +1$

$(0)(1)(0)(0)=\omega +2$

$(0)(1)(0)(1)=\omega \times 2$

$(0)(1)(0)(1)(0)(1)=\omega \times 3$

$(0)(1)(1)=(0)(1)(0)(1)(0)(1)...={\omega }^2$

$(0)(1)(1)(0)={\omega }^2+1$

$(0)(1)(1)(0)(1)={\omega }^2+\omega$

$(0)(1)(1)(0)(1)(0)(1)={\omega }^2+\omega \times 2$

$(0)(1)(1)(0)(1)(1)={\omega }^2\times 2$

$(0)(1)(1)(0)(1)(1)(0)(1)={\omega }^2\times 2+\omega$

$(0)(1)(1)(0)(1)(1)(0)(1)(1)={\omega }^2\times 3$

$(0)(1)(1)(1)={\omega }^3$

$(0)(1)(1)(1)(1)={\omega }^4$

$(0)(1)(2)=(0)(1)(1)(1)(1)...={\omega }^{\omega }$

$(0)(1)(2)(0)(1)(2)={\omega }^{\omega }\times 2$

$(0)(1)(2)(1)={\omega }^{\omega +1}$

$(0)(1)(2)(1)(1)={\omega }^{\omega +2}$

$(0)(1)(2)(1)(1)(1)={\omega }^{\omega +3}$

$(0)(1)(2)(1)(2)={\omega }^{\omega \times 2}$

$(0)(1)(2)(1)(2)(1)(2)={\omega }^{\omega \times 3}$

$(0)(1)(2)(2)={\omega }^{{\omega }^2}$

$(0)(1)(2)(2)(1)={\omega }^{{\omega }^2+1}$

$(0)(1)(2)(2)(1)(2)={\omega }^{{\omega }^2+\omega }$

$(0)(1)(2)(2)(1)(2)(2)={\omega }^{{\omega }^2\times 2}$

$(0)(1)(2)(2)(1)(2)(2)(1)(2)(2)={\omega }^{{\omega }^2\times 3}$

$(0)(1)(2)(2)(2)={\omega }^{{\omega }^3}$

$(0)(1)(2)(2)(2)(2)={\omega }^{{\omega }^4}$

$(0)(1)(2)(3)=(0)(1)(2)(2)(2)(2)...={\omega }^{{\omega }^{\omega }}$

$(0)(1)(2)(3)(4)={\omega }^{{\omega }^{{\omega }^{\omega }}}$

$(0)(1)(2)(3)(4)(5)={\omega }^{{\omega }^{{\omega }^{{\omega }^{\omega }}}}$

$(0)(1,1)=(0)(1)(2)(3)(4)(5)(6)...={\epsilon }_0$

2：双行BMS

$(0)(1,1)={\epsilon }_0$

$(0)(1,1)(0)={\epsilon }_0+1$

$(0)(1,1)(0)(1)={\epsilon }_0+\omega$

$(0)(1,1)(0)(1,1)={\epsilon }_0\times 2$

$(0)(1,1)(0)(1,1)(0)(1,1)={\epsilon }_0\times 3$

$(0)(1,1)(1)={\epsilon }_0\times \omega$

$(0)(1,1)(1)(1)={\epsilon }_0\times {\omega }^2$

$(0)(1,1)(1)(2)={\epsilon }_0\times {\omega }^{\omega }$

$(0)(1,1)(1)(2)(3)={\epsilon }_0\times {\omega }^{{\omega }^{\omega }}$

$(0)(1,1)(1)(2,1)={\epsilon }_0^2$

$(0)(1,1)(1)(2,1)(1)(2)={\epsilon }_0^2\times \omega$

$(0)(1,1)(1)(2,1)(1)(2)(3)={\epsilon }_0^2\times {\omega }^{\omega }$

$(0)(1,1)(1)(2,1)(1)(2,1)={\epsilon }_0^3$

$(0)(1,1)(1)(2,1)(1)(2,1)(1)(2,1)={\epsilon }_0^4$

$(0)(1,1)(1)(2,1)(2)={\epsilon }_0^{\omega }$

$(0)(1,1)(1)(2,1)(2)(1)(2,1)={\epsilon }_0^{\omega +1}$

$(0)(1,1)(1)(2,1)(2)(1)(2,1)(1)(2,1)={\epsilon }_0^{\omega +2}$

$(0)(1,1)(1)(2,1)(2)(1)(2,1)(2)={\epsilon }_0^{\omega \times 2}$

$(0)(1,1)(1)(2,1)(2)(1)(2,1)(2)(1)(2,1)(2)={\epsilon }_0^{\omega \times 3}$

$(0)(1,1)(1)(2,1)(2)(2)={\epsilon }_0^{{\omega }^2}$

$(0)(1,1)(1)(2,1)(2)(3)={\epsilon }_0^{{\omega }^{\omega }}$

$(0)(1,1)(1)(2,1)(2)(3)(4)={\epsilon }_0^{{\omega }^{{\omega }^{\omega }}}$

$(0)(1,1)(1)(2,1)(2)(3,1)={\epsilon }_0^{{\epsilon }_0}$

$(0)(1,1)(1)(2,1)(2)(3,1)(3)(4,1)={\epsilon }_0^{{\epsilon }_0^{{\epsilon }_0}}$

$(0)(1,1)(1)(2,1)(2)(3,1)(3)(4,1)(4)(5,1)={\epsilon }_0^{{\epsilon }_0^{{\epsilon }_0^{{\epsilon }_0}}}$

$(0)(1,1)(1,1)={\epsilon }_1$

$(0)(1,1)(1,1)(0)(1,1)(1,1)={\epsilon }_1\times 2$

$(0)(1,1)(1,1)(1)={\epsilon }_1\times \omega$

$(0)(1,1)(1,1)(1)(2,1)={\epsilon }_1\times {\epsilon }_0$

$(0)(1,1)(1,1)(1)(2,1)(2)(3,1)={\epsilon }_1\times {\epsilon }_0^2$

$(0)(1,1)(1,1)(1)(2,1)(2)(3,1)(3)(4,1)={\epsilon }_1\times {\epsilon }_0^{{\epsilon }_0}$

$(0)(1,1)(1,1)(1)(2,1)(2,1)={\epsilon }_1^2$

$(0)(1,1)(1,1)(1)(2,1)(2,1)(2)={\epsilon }_1^{\omega }$

$(0)(1,1)(1,1)(1)(2,1)(2,1)(2)(3,1)={\epsilon }_1^{{\epsilon }_0}$

$(0)(1,1)(1,1)(1)(2,1)(2,1)(2)(3,1)(3,1)={\epsilon }_1^{{\epsilon }_1}$

$(0)(1,1)(1,1)(1)(2,1)(2,1)(2)(3,1)(3,1)(3)(4,1)(4,1)={\epsilon }_1^{{\epsilon }_1^{{\epsilon }_1}}$

$(0)(1,1)(1,1)(1,1)={\epsilon }_2$

$(0)(1,1)(1,1)(1,1)(1,1)={\epsilon }_3$

$(0)(1,1)(2)={\epsilon }_{\omega }$

$(0)(1,1)(2)(1)={\epsilon }_{\omega }\times \omega$

$(0)(1,1)(2)(1)(2,1)={\epsilon }_{\omega }\times {\epsilon }_0$

$(0)(1,1)(2)(1)(2,1)(2,1)={\epsilon }_{\omega }\times {\epsilon }_1$

$(0)(1,1)(2)(1)(2,1)(2,1)(2,1)={\epsilon }_{\omega }\times {\epsilon }_2$

$(0)(1,1)(2)(1)(2,1)(2,1)(2,1)(2,1)={\epsilon }_{\omega }\times {\epsilon }_3$

$(0)(1,1)(2)(1)(2,1)(3)={\epsilon }_{\omega }^2$

$(0)(1,1)(2)(1)(2,1)(3)(2)(3,1)(4)={\epsilon }_{\omega }^{{\epsilon }_{\omega }}$

$(0)(1,1)(2)(1,1)={\epsilon }_{\omega +1}$

$(0)(1,1)(2)(1,1)(1,1)={\epsilon }_{\omega +2}$

$(0)(1,1)(2)(1,1)(1,1)(1,1)={\epsilon }_{\omega +3}$

$(0)(1,1)(2)(1,1)(2)={\epsilon }_{\omega \times 2}$

$(0)(1,1)(2)(1,1)(2)(1,1)(2)={\epsilon }_{\omega \times 3}$

$(0)(1,1)(2)(2)={\epsilon }_{{\omega }^2}$

$(0)(1,1)(2)(2)(2)={\epsilon }_{{\omega }^3}$

$(0)(1,1)(2)(3)={\epsilon }_{{\omega }^{\omega }}$

$(0)(1,1)(2)(3)(4)={\epsilon }_{{\omega }^{{\omega }^{\omega }}}$

$(0)(1,1)(2)(3,1)={\epsilon }_{{\epsilon }_0}$

$(0)(1,1)(2)(3,1)(1,1)={\epsilon }_{{\epsilon }_0+1}$

$(0)(1,1)(2)(3,1)(3,1)={\epsilon }_{{\epsilon }_1}$

$(0)(1,1)(2)(3,1)(4)={\epsilon }_{{\epsilon }_{\omega }}$

$(0)(1,1)(2)(3,1)(4)(5,1)={\epsilon }_{{\epsilon }_{{\epsilon }_0}}$

$(0)(1,1)(2)(3,1)(4)(5,1)(6)(7,1)={\epsilon }_{{\epsilon }_{{\epsilon }_{{\epsilon }_0}}}$

$(0)(1,1)(2,1)={\zeta }_0$

$(0)(1,1)(2,1)(1)(2,1)(3,1)={\zeta }_0^2$

$(0)(1,1)(2,1)(1)(2,1)(3,1)(2)(3,1)(4,1)={\zeta }_0^{{\zeta }_0}$

$(0)(1,1)(2,1)(1,1)={\epsilon }_{{\zeta }_0+1}$

$(0)(1,1)(2,1)(1,1)(1)(2,1)(3,1)(2,1)={\epsilon }_{{\zeta }_0+1}^2$

$(0)(1,1)(2,1)(1,1)(1,1)={\epsilon }_{{\zeta }_0+2}$

$(0)(1,1)(2,1)(1,1)(2)={\epsilon }_{{\zeta }_0+\omega }$

$(0)(1,1)(2,1)(1,1)(2)(3,1)={\epsilon }_{{\zeta }_0+{\epsilon }_0}$

$(0)(1,1)(2,1)(1,1)(2)(3,1)(4,1)={\epsilon }_{{\zeta }_0\times 2}$

$(0)(1,1)(2,1)(1,1)(2)(3,1)(4,1)(3,1)={\epsilon }_{{\epsilon }_{{\zeta }_0+1}}$

$(0)(1,1)(2,1)(1,1)(2)(3,1)(4,1)(3,1)(4)(5,1)(6,1)(5,1)={\epsilon }_{{\epsilon }_{{\epsilon }_{\zeta +1}}}$

$(0)(1,1)(2,1)(1,1)(2,1)={\zeta }_1$

$(0)(1,1)(2,1)(1,1)(2,1)(1,1)={\epsilon }_{{\zeta }_1+1}$

$(0)(1,1)(2,1)(1,1)(2)={\epsilon }_{{\zeta }_1+\omega }$

$(0)(1,1)(2,1)(1,1)(2,1)(1,1)(2,1)={\zeta }_2$

$(0)(1,1)(2,1)(1,1)(2,1)(1,1)(2,1)(1,1)(2,1)={\zeta }_3$

$(0)(1,1)(2,1)(2)={\zeta }_{\omega }$

$(0)(1,1)(2,1)(2)(2)={\zeta }_{{\omega }^2}$

$(0)(1,1)(2,1)(2)(3,1)={\zeta }_{{\epsilon }_0}$

$(0)(1,1)(2,1)(2)(3,1)(4,1)={\zeta }_{{\zeta }_0}$

$(0)(1,1)(2,1)(2)(3,1)(4,1)(4)(5,1)(6,1)={\zeta }_{{\zeta }_{{\zeta }_0}}$

$(0)(1,1)(2,1)(2,1)={\eta }_0$

$(0)(1,1)(2,1)(2,1)(1,1)={\epsilon }_{{\eta }_0+1}$

$(0)(1,1)(2,1)(2,1)(1,1)(2,1)={\zeta }_{{\eta }_0+1}$

$(0)(1,1)(2,1)(2,1)(1,1)(2,1)(2)(3,1)(4,1)(4,1)(3,1)(4,1)={\zeta }_{{\zeta }_{{\eta }_0+1}}$

$(0)(1,1)(2,1)(2,1)(1,1)(2,1)(2,1)={\eta }_1$

$(0)(1,1)(2,1)(2,1)(1,1)(2,1)(2,1)(1,1)(2,1)(2,1)={\eta }_2$

$(0)(1,1)(2,1)(2,1)(2)={\eta }_{\omega }$

$(0)(1,1)(2,1)(2,1)(2,1)=\phi (4,0)=\psi ({\mathrm{\Omega }}^3)$

$(0)(1,1)(2,1)(3)=\phi (\omega ,0)=\psi ({\mathrm{\Omega }}^{\omega })$

$(0)(1,1)(2,1)(3)(1,1)=\phi (1,\phi (\omega ,0)+1)=\psi ({\mathrm{\Omega }}^{\omega }+1)$

$(0)(1,1)(2,1)(3)(1,1)(2,1)=\phi (2,\phi (\omega ,0)+1)=\psi ({\mathrm{\Omega }}^{\omega }+\mathrm{\Omega })$

$(0)(1,1)(2,1)(3)(1,1)(2,1)(2,1)=\phi (3,\phi (\omega ,0)+1)=\psi ({\mathrm{\Omega }}^{\omega }+{\mathrm{\Omega }}^2)$

$(0)(1,1)(2,1)(3)(1,1)(2,1)(3)=\phi (\omega ,1)=\psi ({\mathrm{\Omega }}^{\omega }\times 2)$

$(0)(1,1)(2,1)(3)(1,1)(2,1)(3)(1,1)(2,1)(3)=\phi (\omega ,2)=\psi ({\mathrm{\Omega }}^{\omega }\times 3)$

$(0)(1,1)(2,1)(3)(2)=\phi (\omega ,\omega )=\psi ({\mathrm{\Omega }}^{\omega }\times \omega )$

$(0)(1,1)(2,1)(3)(2,1)=\phi (\omega +1,0)=\psi ({\mathrm{\Omega }}^{\omega +1})$

$(0)(1,1)(2,1)(3)(2,1)(2,1)=\phi (\omega +2,0)=\psi ({\mathrm{\Omega }}^{\omega +2})$

$(0)(1,1)(2,1)(3)(2,1)(2,1)(2,1)=\phi (\omega +3,0)=\psi ({\mathrm{\Omega }}^{\omega +3})$

$(0)(1,1)(2,1)(3)(2,1)(3)=\phi (\omega \times 2,0)=\psi ({\mathrm{\Omega }}^{\omega \times 2})$

$(0)(1,1)(2,1)(3)(2,1)(3)(2,1)(3)=\phi (\omega \times 3,0)=\psi ({\mathrm{\Omega }}^{\omega \times 3})$

$(0)(1,1)(2,1)(3)(3)=\phi ({\omega }^2,0)=\psi ({\mathrm{\Omega }}^{{\omega }^2})$

$(0)(1,1)(2,1)(3)(4,1)=\phi (\phi (1,0),0)=\psi ({\mathrm{\Omega }}^{\psi (0)})$

$(0)(1,1)(2,1)(3)(4,1)(5,1)=\phi (\phi (2,0),0)=\psi ({\mathrm{\Omega }}^{\psi (\mathrm{\Omega })})$

$(0)(1,1)(2,1)(3)(4,1)(5,1)(6)=\phi (\phi (\omega ,0),0)=\psi ({\mathrm{\Omega }}^{\psi ({\mathrm{\Omega }}^{\omega })})$

$(0)(1,1)(2,1)(3)(4,1)(5,1)(6)(7,1)(8,1)(9)=\phi (\phi (\phi (\omega ,0),0),0)=\psi ({\mathrm{\Omega }}^{\psi ({\mathrm{\Omega }}^{\psi ({\mathrm{\Omega }}^{\omega })})})$

$(0)(1,1)(2,1)(3,1)=\phi (1,0,0)={\mathrm{\Gamma }}_0=\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }})$

$(0)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)=\phi (1,0,1)={\mathrm{\Gamma }}_1=\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }}\times 2)$

$(0)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)=\phi (1,0,2)={\mathrm{\Gamma }}_2=\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }}\times 3)$

$(0)(1,1)(2,1)(3,1)(2)=\phi (1,0,\omega )={\mathrm{\Gamma }}_{\omega }=\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }}\times \omega )$

$(0)(1,1)(2,1)(3,1)(2)(3,1)(4,1)(5,1)=\phi (1,0,\phi (1,0,0))={\mathrm{\Gamma }}_{{\mathrm{\Gamma }}_0}=\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }}\times \psi ({\mathrm{\Omega }}^{\mathrm{\Omega }}))$

$(0)(1,1)(2,1)(3,1)(2)(3,1)(4,1)(5,1)(4)(5,1)(6,1)(7,1)=\phi (1,0,\phi (1,0,\phi (1,0,0)))={\mathrm{\Gamma }}_{{\mathrm{\Gamma }}_{{\mathrm{\Gamma }}_0}}=\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }}\times \psi ({\mathrm{\Omega }}^{\mathrm{\Omega }}\times \psi ({\mathrm{\Omega }}^{\mathrm{\Omega }})))$

$(0)(1,1)(2,1)(3,1)(2,1)=\phi (1,1,0)=\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }+1})$

$(0)(1,1)(2,1)(3,1)(2,1)(2,1)=\phi (1,2,0)=\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }+2})$

$(0)(1,1)(2,1)(3,1)(2,1)(3)=\phi (1,\omega ,0)=\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }+\omega })$

$(0)(1,1)(2,1)(3,1)(2,1)(3)(4,1)(5,1)(6,1)(5,1)(6)=\phi (1,\phi (1,\omega ,0),0)=\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }+\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }+\omega })})$

$(0)(1,1)(2,1)(3,1)(2,1)(3,1)=\psi (2,0,0)=\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }\times 2})$

$(0)(1,1)(2,1)(3,1)(2,1)(3,1)(2,1)(3,1)=\psi (3,0,0)=\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }\times 3})$

$(0)(1,1)(2,1)(3,1)(3)=\phi (\omega ,0,0)=\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }\times \omega })$

$(0)(1,1)(2,1)(3,1)(3,1)=\phi (1,0,0,0)=\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^2})$

$(0)(1,1)(2,1)(3,1)(3,1)(3,1)=\phi (1,0,0,0,0)=\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^3})$

$(0)(1,1)(2,1)(3,1)(4)=\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\omega }})$

$(0)(1,1)(2,1)(3,1)(4)(5,1)=\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\psi (0)}})$

$(0)(1,1)(2,1)(3,1)(4)(5,1)(6,1)=\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\psi (\mathrm{\Omega })}})$

$(0)(1,1)(2,1)(3,1)(4)(5,1)(6,1)(7,1)=\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\psi ({\mathrm{\Omega }}^{\mathrm{\Omega }})}})$

$(0)(1,1)(2,1)(3,1)(4,1)=\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\mathrm{\Omega }}})$

$(0)(1,1)(2,1)(3,1)(4,1)(5,1)=\psi ({\mathrm{\Omega }}^{{\mathrm{\Omega }}^{{\mathrm{\Omega }}^{\mathrm{\Omega }}}})$

$(0)(1,1)(2,2)=\psi ({\psi }_1(0))$