BMS分析：修订间差异

←上一编辑下一编辑→

可视化wikitext

2025年7月9日 (三) 01:57的版本

目前使用的OCF为M型，后续补充BOCF

1：单行BMS（PrSS）

$\emptyset = 0$

$(0) = 1$

$(0) (0) = 2$

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

$(0) (1) = (0) (0) (0) (0) (0) . . . = ω$

$(0) (1) (0) = ω + 1$

$(0) (1) (0) (0) = ω + 2$

$(0) (1) (0) (1) = ω \times 2$

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

$(0) (1) (1) = (0) (1) (0) (1) (0) (1) . . . = ω^{2}$

$(0) (1) (1) (0) = ω^{2} + 1$

$(0) (1) (1) (0) (1) = ω^{2} + ω$

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

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

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

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

$(0) (1) (1) (1) = ω^{3}$

$(0) (1) (1) (1) (1) = ω^{4}$

$(0) (1) (2) = (0) (1) (1) (1) (1) . . . = ω^{ω}$

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

$(0) (1) (2) (1) = ω^{ω + 1}$

$(0) (1) (2) (1) (1) = ω^{ω + 2}$

$(0) (1) (2) (1) (1) (1) = ω^{ω + 3}$

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

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

$(0) (1) (2) (2) = ω^{ω^{2}}$

$(0) (1) (2) (2) (1) = ω^{ω^{2} + 1}$

$(0) (1) (2) (2) (1) (2) = ω^{ω^{2} + ω}$

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

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

$(0) (1) (2) (2) (2) = ω^{ω^{3}}$

$(0) (1) (2) (2) (2) (2) = ω^{ω^{4}}$

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

$(0) (1) (2) (3) (4) = ω^{ω^{ω^{ω}}}$

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

$(0) (1, 1) = (0) (1) (2) (3) (4) (5) (6) . . . = ε_{0}$

2：双行BMS

$(0) (1, 1) = ε_{0}$

$(0) (1, 1) (0, 0) = ε_{0} + 1$

$(0) (1, 1) (0, 0) (1, 0) = ε_{0} + ω$

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

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

$(0) (1, 1) (1, 0) = ε_{0} \times ω$

$(0) (1, 1) (1, 0) (1, 0) = ε_{0} \times ω^{2}$

$(0) (1, 1) (1, 0) (2, 0) = ε_{0} \times ω^{ω}$

$(0) (1, 1) (1, 0) (2, 0) (3, 0) = ε_{0} \times ω^{ω^{ω}}$

$(0) (1, 1) (1, 0) (2, 1) = ε_{0}^{2}$

$(0) (1, 1) (1, 0) (2, 1) (1, 0) (2, 0) = ε_{0}^{2} \times ω$

$(0) (1, 1) (1, 0) (2, 1) (1, 0) (2, 0) (3, 0) = ε_{0}^{2} \times ω^{ω}$

$(0) (1, 1) (1, 0) (2, 1) (1, 0) (2, 1) = ε_{0}^{3}$

$(0) (1, 1) (1, 0) (2, 1) (1, 0) (2, 1) (1, 0) (2, 1) = ε_{0}^{4}$

$(0) (1, 1) (1, 0) (2, 1) (2, 0) = ε_{0}^{ω}$

$(0) (1, 1) (1, 0) (2, 1) (2, 0) (1, 0) (2, 1) = ε_{0}^{ω + 1}$

$(0) (1, 1) (1, 0) (2, 1) (2, 0) (1, 0) (2, 1) (1, 0) (2, 1) = ε_{0}^{ω + 2}$

$(0) (1, 1) (1, 0) (2, 1) (2, 0) (1, 0) (2, 1) (2, 0) = ε_{0}^{ω \times 2}$

$(0) (1, 1) (1, 0) (2, 1) (2, 0) (1, 0) (2, 1) (2, 0) (1, 0) (2, 1) (2, 0) = ε_{0}^{ω \times 3}$

$(0) (1, 1) (1, 0) (2, 1) (2, 0) (2, 0) = ε_{0}^{ω^{2}}$

$(0) (1, 1) (1, 0) (2, 1) (2, 0) (3, 0) = ε_{0}^{ω^{ω}}$

$(0) (1, 1) (1, 0) (2, 1) (2, 0) (3, 0) (4, 0) = ε_{0}^{ω^{ω^{ω}}}$

$(0) (1, 1) (1, 0) (2, 1) (2, 0) (3, 1) = ε_{0}^{ε_{0}}$

$(0) (1, 1) (1, 0) (2, 1) (2, 0) (3, 1) (3, 0) (4, 1) = ε_{0}^{ε_{0}^{ε_{0}}}$

$(0) (1, 1) (1, 0) (2, 1) (2, 0) (3, 1) (3, 0) (4, 1) (4, 0) (5, 1) = ε_{0}^{ε_{0}^{ε_{0}^{ε_{0}}}}$

$(0) (1, 1) (1, 1) = ε_{1}$

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

$(0) (1, 1) (1, 1) (1, 0) = ε_{1} \times ω$

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

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

$(0) (1, 1) (1, 1) (1, 0) (2, 1) (2, 0) (3, 1) (3, 0) (4, 1) = ε_{1} \times ε_{0}^{ε_{0}}$

$(0) (1, 1) (1, 1) (1, 0) (2, 1) (2, 1) = ε_{1}^{2}$

$(0) (1, 1) (1, 1) (1, 0) (2, 1) (2, 1) (2, 0) = ε_{1}^{ω}$

$(0) (1, 1) (1, 1) (1, 0) (2, 1) (2, 1) (2, 0) (3, 1) = ε_{1}^{ε_{0}}$

$(0) (1, 1) (1, 1) (1, 0) (2, 1) (2, 1) (2, 0) (3, 1) (3, 1) = ε_{1}^{ε_{1}}$

$(0) (1, 1) (1, 1) (1, 0) (2, 1) (2, 1) (2, 0) (3, 1) (3, 1) (3, 0) (4, 1) (4, 1) = ε_{1}^{ε_{1}^{ε_{1}}}$

$(0) (1, 1) (1, 1) (1, 1) = ε_{2}$

$(0) (1, 1) (1, 1) (1, 1) (1, 1) = ε_{3}$

$(0) (1, 1) (2, 0) = ε_{ω}$

$(0) (1, 1) (2, 0) (1, 0) = ε_{ω} \times ω$

$(0) (1, 1) (2, 0) (1, 0) (2, 1) = ε_{ω} \times ε_{0}$

$(0) (1, 1) (2, 0) (1, 0) (2, 1) (2, 1) = ε_{ω} \times ε_{1}$

$(0) (1, 1) (2, 0) (1, 0) (2, 1) (2, 1) (2, 1) = ε_{ω} \times ε_{2}$

$(0) (1, 1) (2, 0) (1, 0) (2, 1) (2, 1) (2, 1) (2, 1) = ε_{ω} \times ε_{3}$

$(0) (1, 1) (2, 0) (1, 0) (2, 1) (3, 0) = ε_{ω}^{2}$

$(0) (1, 1) (2, 0) (1, 0) (2, 1) (3, 0) (2, 0) (3, 1) (4, 0) = ε_{ω}^{ε_{ω}}$

$(0) (1, 1) (2, 0) (1, 1) = ε_{ω + 1}$

$(0) (1, 1) (2, 0) (1, 1) (1, 1) = ε_{ω + 2}$

$(0) (1, 1) (2, 0) (1, 1) (1, 1) (1, 1) = ε_{ω + 3}$

$(0) (1, 1) (2, 0) (1, 1) (2, 0) = ε_{ω \times 2}$

$(0) (1, 1) (2, 0) (1, 1) (2, 0) (1, 1) (2, 0) = ε_{ω \times 3}$

$(0) (1, 1) (2, 0) (2, 0) = ε_{ω^{2}}$

$(0) (1, 1) (2, 0) (2, 0) (2, 0) = ε_{ω^{3}}$

$(0) (1, 1) (2, 0) (3, 0) = ε_{ω^{ω}}$

$(0) (1, 1) (2, 0) (3, 0) (4, 0) = ε_{ω^{ω^{ω}}}$

$(0) (1, 1) (2, 0) (3, 1) = ε_{ε_{0}}$

$(0) (1, 1) (2, 0) (3, 1) (1, 1) = ε_{ε_{0} + 1}$

$(0) (1, 1) (2, 0) (3, 1) (3, 1) = ε_{ε_{1}}$

$(0) (1, 1) (2, 0) (3, 1) (4, 0) = ε_{ε_{ω}}$

$(0) (1, 1) (2, 0) (3, 1) (4, 0) (5, 1) = ε_{ε_{ε_{0}}}$

$(0) (1, 1) (2, 0) (3, 1) (4, 0) (5, 1) (6, 0) (7, 1) = ε_{ε_{ε_{ε_{0}}}}$

$(0) (1, 1) (2, 1) = ζ_{0}$

$(0) (1, 1) (2, 1) (1, 0) (2, 1) (3, 1) = ζ_{0}^{2}$

$(0) (1, 1) (2, 1) (1, 0) (2, 1) (3, 1) (2, 0) (3, 1) (4, 1) = ζ_{0}^{ζ_{0}}$

$(0) (1, 1) (2, 1) (1, 1) = ε_{ζ_{0} + 1}$

$(0) (1, 1) (2, 1) (1, 1) (1, 0) (2, 1) (3, 1) (2, 1) = ε_{ζ_{0} + 1}^{2}$

$(0) (1, 1) (2, 1) (1, 1) (1, 1) = ε_{ζ_{0} + 2}$

$(0) (1, 1) (2, 1) (1, 1) (2, 0) = ε_{ζ_{0} + ω}$

$(0) (1, 1) (2, 1) (1, 1) (2, 0) (3, 1) = ε_{ζ_{0} + ε_{0}}$

$(0) (1, 1) (2, 1) (1, 1) (2, 0) (3, 1) (4, 1) = ε_{ζ_{0} \times 2}$

$(0) (1, 1) (2, 1) (1, 1) (2, 0) (3, 1) (4, 1) (3, 1) = ε_{ε_{ζ_{0} + 1}}$

$(0) (1, 1) (2, 1) (1, 1) (2, 0) (3, 1) (4, 1) (3, 1) (4, 0) (5, 1) (6, 1) (5, 1) = ε_{ε_{ε_{ζ + 1}}}$

$(0) (1, 1) (2, 1) (1, 1) (2, 1) = ζ_{1}$

$(0) (1, 1) (2, 1) (1, 1) (2, 1) (1, 1) = ε_{ζ_{1} + 1}$

$(0) (1, 1) (2, 1) (1, 1) (2, 0) = ε_{ζ_{1} + ω}$

$(0) (1, 1) (2, 1) (1, 1) (2, 1) (1, 1) (2, 1) = ζ_{2}$

$(0) (1, 1) (2, 1) (1, 1) (2, 1) (1, 1) (2, 1) (1, 1) (2, 1) = ζ_{3}$

$(0) (1, 1) (2, 1) (2, 0) = ζ_{ω}$

$(0) (1, 1) (2, 1) (2, 0) (2, 0) = ζ_{ω^{2}}$

$(0) (1, 1) (2, 1) (2, 0) (3, 1) = ζ_{ε_{0}}$

$(0) (1, 1) (2, 1) (2, 0) (3, 1) (4, 1) = ζ_{ζ_{0}}$

$(0) (1, 1) (2, 1) (2, 0) (3, 1) (4, 1) (4, 0) (5, 1) (6, 1) = ζ_{ζ_{ζ_{0}}}$

$(0) (1, 1) (2, 1) (2, 1) = η_{0}$

$(0) (1, 1) (2, 1) (2, 1) (1, 1) = ε_{η_{0} + 1}$

$(0) (1, 1) (2, 1) (2, 1) (1, 1) (2, 1) = ζ_{η_{0} + 1}$

$(0) (1, 1) (2, 1) (2, 1) (1, 1) (2, 1) (2, 0) (3, 1) (4, 1) (4, 1) (3, 1) (4, 1) = ζ_{ζ_{η_{0} + 1}}$

$(0) (1, 1) (2, 1) (2, 1) (1, 1) (2, 1) (2, 1) = η_{1}$

$(0) (1, 1) (2, 1) (2, 1) (1, 1) (2, 1) (2, 1) (1, 1) (2, 1) (2, 1) = η_{2}$

$(0) (1, 1) (2, 1) (2, 1) (2, 0) = η_{ω}$

$(0) (1, 1) (2, 1) (2, 1) (2, 1) = φ (4, 0) = ψ (Ω^{3})$

$(0) (1, 1) (2, 1) (3, 0) = φ (ω, 0) = ψ (Ω^{ω})$

$(0) (1, 1) (2, 1) (3, 0) (1, 1) = φ (1, φ (ω, 0) + 1) = ψ (Ω^{ω} + 1)$

$(0) (1, 1) (2, 1) (3, 0) (1, 1) (2, 1) = φ (2, φ (ω, 0) + 1) = ψ (Ω^{ω} + Ω)$

$(0) (1, 1) (2, 1) (3, 0) (1, 1) (2, 1) (2, 1) = φ (3, φ (ω, 0) + 1) = ψ (Ω^{ω} + Ω^{2})$

$(0) (1, 1) (2, 1) (3, 0) (1, 1) (2, 1) (3, 0) = φ (ω, 1) = ψ (Ω^{ω} \times 2)$

$(0) (1, 1) (2, 1) (3, 0) (1, 1) (2, 1) (3, 0) (1, 1) (2, 1) (3, 0) = φ (ω, 2) = ψ (Ω^{ω} \times 3)$

$(0) (1, 1) (2, 1) (3, 0) (2, 0) = φ (ω, ω) = ψ (Ω^{ω} \times ω)$

$(0) (1, 1) (2, 1) (3, 0) (2, 1) = φ (ω + 1, 0) = ψ (Ω^{ω + 1})$

$(0) (1, 1) (2, 1) (3, 0) (2, 1) (2, 1) = φ (ω + 2, 0) = ψ (Ω^{ω + 2})$

$(0) (1, 1) (2, 1) (3, 0) (2, 1) (2, 1) (2, 1) = φ (ω + 3, 0) = ψ (Ω^{ω + 3})$

$(0) (1, 1) (2, 1) (3, 0) (2, 1) (3, 0) = φ (ω \times 2, 0) = ψ (Ω^{ω \times 2})$

$(0) (1, 1) (2, 1) (3, 0) (2, 1) (3, 0) (2, 1) (3, 0) = φ (ω \times 3, 0) = ψ (Ω^{ω \times 3})$

$(0) (1, 1) (2, 1) (3, 0) (3, 0) = φ (ω^{2}, 0) = ψ (Ω^{ω^{2}})$

$(0) (1, 1) (2, 1) (3, 0) (4, 1) = φ (φ (1, 0), 0) = ψ (Ω^{ψ (0)})$

$(0) (1, 1) (2, 1) (3, 0) (4, 1) (5, 1) = φ (φ (2, 0), 0) = ψ (Ω^{ψ (Ω)})$

$(0) (1, 1) (2, 1) (3, 0) (4, 1) (5, 1) (6, 0) = φ (φ (ω, 0), 0) = ψ (Ω^{ψ (Ω^{ω})})$

$(0) (1, 1) (2, 1) (3, 0) (4, 1) (5, 1) (6, 0) (7, 1) (8, 1) (9, 0) = φ (φ (φ (ω, 0), 0), 0) = ψ (Ω^{ψ (Ω^{ψ (Ω^{ω})})})$

$(0) (1, 1) (2, 1) (3, 1) = φ (1, 0, 0) = Γ_{0} = ψ (Ω^{Ω})$

$(0) (1, 1) (2, 1) (3, 1) (1, 1) (2, 1) (3, 1) = φ (1, 0, 1) = Γ_{1} = ψ (Ω^{Ω} \times 2)$

$(0) (1, 1) (2, 1) (3, 1) (1, 1) (2, 1) (3, 1) (1, 1) (2, 1) (3, 1) = φ (1, 0, 2) = Γ_{2} = ψ (Ω^{Ω} \times 3)$

$(0) (1, 1) (2, 1) (3, 1) (2, 0) = φ (1, 0, ω) = Γ_{ω} = ψ (Ω^{Ω} \times ω)$

$(0) (1, 1) (2, 1) (3, 1) (2, 0) (3, 1) (4, 1) (5, 1) = φ (1, 0, φ (1, 0, 0)) = Γ_{Γ_{0}} = ψ (Ω^{Ω} \times ψ (Ω^{Ω}))$

$(0) (1, 1) (2, 1) (3, 1) (2, 0) (3, 1) (4, 1) (5, 1) (4, 0) (5, 1) (6, 1) (7, 1) = φ (1, 0, φ (1, 0, φ (1, 0, 0))) = Γ_{Γ_{Γ_{0}}} = ψ (Ω^{Ω} \times ψ (Ω^{Ω} \times ψ (Ω^{Ω})))$

$(0) (1, 1) (2, 1) (3, 1) (2, 1) = φ (1, 1, 0) = ψ (Ω^{Ω + 1})$

$(0) (1, 1) (2, 1) (3, 1) (2, 1) (2, 1) = φ (1, 2, 0) = ψ (Ω^{Ω + 2})$

$(0) (1, 1) (2, 1) (3, 1) (2, 1) (3, 0) = φ (1, ω, 0) = ψ (Ω^{Ω + ω})$

$(0) (1, 1) (2, 1) (3, 1) (2, 1) (3, 0) (4, 1) (5, 1) (6, 1) (5, 1) (6, 0) = φ (1, φ (1, ω, 0), 0) = ψ (Ω^{Ω + ψ (Ω^{Ω + ω})})$

$(0) (1, 1) (2, 1) (3, 1) (2, 1) (3, 1) = ψ (2, 0, 0) = ψ (Ω^{Ω \times 2})$

$(0) (1, 1) (2, 1) (3, 1) (2, 1) (3, 1) (2, 1) (3, 1) = ψ (3, 0, 0) = ψ (Ω^{Ω \times 3})$

$(0) (1, 1) (2, 1) (3, 1) (3, 0) = φ (ω, 0, 0) = ψ (Ω^{Ω \times ω})$

$(0) (1, 1) (2, 1) (3, 1) (3, 1) = φ (1, 0, 0, 0) = ψ (Ω^{Ω^{2}})$

$(0) (1, 1) (2, 1) (3, 1) (3, 1) (3, 1) = φ (1, 0, 0, 0, 0) = ψ (Ω^{Ω^{3}})$

$(0) (1, 1) (2, 1) (3, 1) (4, 0) = ψ (Ω^{Ω^{ω}})$

$(0) (1, 1) (2, 1) (3, 1) (4, 0) (5, 1) = ψ (Ω^{Ω^{ψ (0)}})$

$(0) (1, 1) (2, 1) (3, 1) (4, 0) (5, 1) (6, 1) = ψ (Ω^{Ω^{ψ (Ω)}})$

$(0) (1, 1) (2, 1) (3, 1) (4, 0) (5, 1) (6, 1) (7, 1) = ψ (Ω^{Ω^{ψ (Ω^{Ω})}})$

$(0) (1, 1) (2, 1) (3, 1) (4, 1) = ψ (Ω^{Ω^{Ω}})$

$(0) (1, 1) (2, 1) (3, 1) (4, 1) (5, 1) = ψ (Ω^{Ω^{Ω^{Ω}}})$

$(0) (1, 1) (2, 2) = ψ (ψ_{1} (0))$

$(0) (1, 1) (2, 2) (1, 1) = ψ (ψ_{1} (0) + 1)$

$(0) (1, 1) (2, 2) (1, 1) (2, 1) = ψ (ψ_{1} (0) + Ω)$

$(0) (1, 1) (2, 2) (1, 1) (2, 1) (3, 1) = ψ (ψ_{1} (0) + Ω^{Ω})$

$(0) (1, 1) (2, 2) (1, 1) (2, 2) = ψ (ψ_{1} (0) \times 2)$

$(0) (1, 1) (2, 2) (2, 0) = ψ (ψ_{1} (0) \times ω)$

$(0) (1, 1) (2, 2) (2, 1) = ψ (ψ_{1} (0) \times Ω)$

$(0) (1, 1) (2, 2) (2, 1) (3, 0) = ψ (ψ_{1} (0) \times Ω^{ω})$

$(0) (1, 1) (2, 2) (2, 1) (3, 1) = ψ (ψ_{1} (0) \times Ω^{Ω})$

$(0) (1, 1) (2, 2) (2, 1) (3, 2) = ψ (ψ_{1} (0)^{2})$

$(0) (1, 1) (2, 2) (2, 1) (3, 2) (3, 0) = ψ (ψ_{1} (0)^{ω})$

$(0) (1, 1) (2, 2) (2, 1) (3, 2) (3, 1) (4, 2) = ψ (ψ_{1} (0)^{ψ_{1} (0)})$

$(0) (1, 1) (2, 2) (2, 2) = ψ (ψ_{1} (1))$

$(0) (1, 1) (2, 2) (3, 0) = ψ (ψ_{1} (ω))$

$(0) (1, 1) (2, 2) (3, 1) (4, 2) = ψ (ψ_{1} (ψ_{1} (0)))$

$(0) (1, 1) (2, 2) (3, 2) = ψ (Ω_{2})$

$(0) (1, 1) (2, 2) (3, 2) (1, 1) = ψ (Ω_{2} + Ω)$

$(0) (1, 1) (2, 2) (3, 2) (1, 1) (2, 2) = ψ (Ω_{2} + ψ_{1} (0))$

$(0) (1, 1) (2, 2) (3, 2) (1, 1) (2, 2) (3, 1) (4, 2) = ψ (Ω_{2} + ψ_{1} (ψ_{1} (0)))$

$(0) (1, 1) (2, 2) (3, 2) (1, 1) (2, 2) (3, 2) = ψ (Ω_{2} + ψ_{1} (Ω_{2}))$

$(0) (1, 1) (2, 2) (3, 2) (2, 0) = ψ (Ω_{2} + ψ_{1} (Ω_{2}) \times ω)$

$(0) (1, 1) (2, 2) (3, 2) (2, 1) (3, 2) (4, 2) = ψ (Ω_{2} + ψ_{1} (Ω_{2})^{2})$

$(0) (1, 1) (2, 2) (3, 2) (2, 1) (3, 2) (4, 2) (3, 0) = ψ (Ω_{2} + ψ_{1} (Ω_{2})^{ω})$

$(0) (1, 1) (2, 2) (3, 2) (2, 1) (3, 2) (4, 2) (3, 1) (4, 2) (5, 2) = ψ (Ω_{2} + ψ_{1} (Ω_{2})^{ψ_{1} (Ω_{2})})$

$(0) (1, 1) (2, 2) (3, 2) (2, 2) = ψ (Ω_{2} + ψ_{1} (Ω_{2} + 1))$

$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 0) = ψ (Ω_{2} + ψ_{1} (Ω_{2} + ω))$

$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 1) (4, 2) (5, 2) = ψ (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2})))$

$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 1) (4, 2) (5, 2) (3, 0) = ψ (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2}) \times ω))$

$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 1) (4, 2) (5, 2) (4, 0) = ψ (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2})^{ω}))$

$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 1) (4, 2) (5, 2) (4, 1) (5, 2) (6, 2) = ψ (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2})^{ψ_{1} (Ω_{2})}))$

$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 1) (4, 2) (5, 2) (4, 2) = ψ (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2} + 1)))$

$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 1) (4, 2) (5, 2) (4, 2) (5, 0) = ψ (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2} + ω)))$

$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 1) (4, 2) (5, 2) (4, 2) (5, 0) (5, 1) (6, 2) (7, 2) = ψ (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2}))))$

$(0) (1, 1) (2, 2) (3, 2) (2, 2) (3, 2) = ψ (Ω_{2} \times 2)$

$(0) (1, 1) (2, 2) (3, 2) (3, 0) = ψ (Ω_{2} \times ω)$

$(0) (1, 1) (2, 2) (3, 2) (3, 1) (4, 2) (5, 2) = ψ (Ω_{2} \times ψ_{1} (Ω_{2}))$

$(0) (1, 1) (2, 2) (3, 2) (3, 2) = ψ (Ω_{2}^{2})$

$(0) (1, 1) (2, 2) (3, 2) (4, 0) = ψ (Ω_{2}^{ω})$

$(0) (1, 1) (2, 2) (3, 2) (4, 2) = ψ (Ω_{2}^{Ω_{2}})$

$(0) (1, 1) (2, 2) (3, 3) = ψ (ψ_{2} (0))$

$(0) (1, 1) (2, 2) (3, 3) (4, 3) = ψ (Ω_{3})$

$(0) (1, 1) (2, 2) (3, 3) (4, 4) = ψ (ψ_{3} (0))$

$(0) (1, 1, 1) = (0) (1, 1) (2, 2) (3, 3) \dots = ψ (Ω_{ω})$

3：三行BMS (0)(1,1,1)~(0)(1,1,1)(2,1,0)

三行之后BMS的行为复杂度急剧上升，因此部分节点的分析可能不会较为详细。

$(0) (1, 1, 1) = ψ (Ω_{ω})$

$(0) (1, 1, 1) (1, 1, 0) = ψ (Ω_{ω} + 1)$

$(0) (1, 1, 1) (1, 1, 0) (2, 0, 0) = ψ (Ω_{ω} + ω)$

$(0) (1, 1, 1) (1, 1, 0) (2, 1, 0) = ψ (Ω_{ω} + Ω)$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 0) = ψ (Ω_{ω} + ψ_{1} (0))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 0) (2, 2, 0) = ψ (Ω_{ω} + ψ_{1} (1))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 0) (3, 0, 0) = ψ (Ω_{ω} + ψ_{1} (ω))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 0) (3, 1, 0) (4, 2, 0) = ψ (Ω_{ω} + ψ_{1} (ψ_{1} (0)))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 0) (3, 2, 0) = ψ (Ω_{ω} + ψ_{1} (Ω_{2}))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 0) (3, 2, 0) (2, 0, 0) = ψ (Ω_{ω} + ψ_{1} (Ω_{2}) \times ω)$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 0) (3, 2, 0) (2, 1, 0) = ψ (Ω_{ω} + ψ_{1} (Ω_{2})^{ω})$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 0) (3, 2, 0) (2, 2, 0) = ψ (Ω_{ω} + ψ_{1} (Ω_{2} + 1))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 0) (3, 2, 0) (2, 2, 0) (3, 0, 0) = ψ (Ω_{ω} + ψ_{1} (Ω_{2} + ω))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 0) (3, 2, 0) (2, 2, 0) (3, 1, 0) (4, 2, 0) = ψ (Ω_{ω} + ψ_{1} (Ω_{2} + ψ_{1} (0)))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 0) (3, 2, 0) (2, 2, 0) (3, 2, 0) = ψ (Ω_{ω} + ψ_{1} (Ω_{2} \times 2))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 0) (3, 2, 0) (3, 0, 0) = ψ (Ω_{ω} + ψ_{1} (Ω_{2} \times ω))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 0) (3, 2, 0) (3, 2, 0) = ψ (Ω_{ω} + ψ_{1} (Ω_{2}^{2}))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 0) (3, 2, 0) (4, 2, 0) = ψ (Ω_{ω} + ψ_{1} (Ω_{2}^{Ω_{2}}))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 0) (3, 3, 0) = ψ (Ω_{ω} + ψ_{1} (ψ_{2} (0)))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 0) (3, 3, 0) (4, 4, 0) = ψ (Ω_{ω} + ψ_{1} (ψ_{3} (0)))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 1) = ψ (Ω_{ω} + ψ_{1} (Ω_{ω}))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 1) (2, 2, 0) = ψ (Ω_{ω} + ψ_{1} (Ω_{ω} + 1))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 1) (2, 2, 0) (3, 0, 0) = ψ (Ω_{ω} + ψ_{1} (Ω_{ω} + ω))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 1) (2, 2, 0) (3, 1, 0) (4, 2, 0) = ψ (Ω_{ω} + ψ_{1} (Ω_{ω} + ψ_{1} (0)))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 1) (2, 2, 0) (3, 1, 0) (4, 2, 0) (5, 3, 0) = ψ (Ω_{ω} + ψ_{1} (Ω_{ω} + ψ_{1} (ψ_{2} (0))))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 1) (2, 2, 0) (3, 1, 0) (4, 2, 1) = ψ (Ω_{ω} + ψ_{1} (Ω_{ω} + ψ_{1} (Ω_{ω})))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 1) (2, 2, 0) (3, 2, 0) = ψ (Ω_{ω} + Ω_{2})$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 1) (2, 2, 0) (3, 3, 0) = ψ (Ω_{ω} + ψ_{2} (0))$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 1) (2, 2, 0) (3, 3, 1) (3, 3, 0) (4, 3, 0) = ψ (Ω_{ω} + Ω_{3})$

$(0) (1, 1, 1) (1, 1, 0) (2, 2, 1) (2, 2, 0) (3, 3, 1) (3, 3, 0) (4, 4, 0) = ψ (Ω_{ω} + ψ_{3} (0))$

$(0) (1, 1, 1) (1, 1, 1) = ψ (Ω_{ω} \times 2)$

$(0) (1, 1, 1) (2, 0, 0) = ψ (Ω_{ω} \times ω)$

$(0) (1, 1, 1) (2, 1, 0) = ψ (Ω_{ω} \times Ω)$

@@ 第183行： / 第183行： @@
 <math>(0)(1,1)(2,0)(3,0)=\varepsilon_{\omega^\omega}</math>
-<math>(0)(1,1)(2,0)(3,0)(4)=\varepsilon_{\omega^{\omega^\omega}}</math>
+<math>(0)(1,1)(2,0)(3,0)(4,0)=\varepsilon_{\omega^{\omega^\omega}}</math>
 <math>(0)(1,1)(2,0)(3,1)=\varepsilon_{\varepsilon_0}</math>
@@ 第263行： / 第263行： @@
 <math>(0)(1,1)(2,1)(3,0)(1,1)(2,1)(2,1)=\varphi(3,\varphi(\omega,0)+1)=\psi(\Omega^\omega+\Omega^2)</math>
-<math>(0)(1,1)(2,1)(3)(1,1)(2,1)(3,0)=\varphi(\omega,1)=\psi(\Omega^\omega\times2)</math>
+<math>(0)(1,1)(2,1)(3,0)(1,1)(2,1)(3,0)=\varphi(\omega,1)=\psi(\Omega^\omega\times2)</math>
 <math>(0)(1,1)(2,1)(3,0)(1,1)(2,1)(3,0)(1,1)(2,1)(3,0)=\varphi(\omega,2)=\psi(\Omega^\omega\times3)</math>
@@ 第416行： / 第416行： @@
 <math>(0)(1,1,1)=(0)(1,1)(2,2)(3,3)\cdots=\psi(\Omega_\omega)</math>
+==== 3：三行BMS (0)(1,1,1)~(0)(1,1,1)(2,1,0) ====
+三行之后BMS的行为复杂度急剧上升，因此部分节点的分析可能不会较为详细。
+<math>(0)(1,1,1)=\psi(\Omega_\omega)</math>
+<math>(0)(1,1,1)(1,1,0)=\psi(\Omega_\omega+1)</math>
+<math>(0)(1,1,1)(1,1,0)(2,0,0)=\psi(\Omega_\omega+\omega)</math>
+<math>(0)(1,1,1)(1,1,0)(2,1,0)=\psi(\Omega_\omega+\Omega)</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,0)=\psi(\Omega_\omega+\psi_1(0))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,0)(2,2,0)=\psi(\Omega_\omega+\psi_1(1))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,0)(3,0,0)=\psi(\Omega_\omega+\psi_1(\omega))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,0)(3,1,0)(4,2,0)=\psi(\Omega_\omega+\psi_1(\psi_1(0)))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)=\psi(\Omega_\omega+\psi_1(\Omega_2))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(2,0,0)=\psi(\Omega_\omega+\psi_1(\Omega_2)\times\omega)</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(2,1,0)=\psi(\Omega_\omega+\psi_1(\Omega_2)^\omega)</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(2,2,0)=\psi(\Omega_\omega+\psi_1(\Omega_2+1))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(2,2,0)(3,0,0)=\psi(\Omega_\omega+\psi_1(\Omega_2+\omega))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(2,2,0)(3,1,0)(4,2,0)=\psi(\Omega_\omega+\psi_1(\Omega_2+\psi_1(0)))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(2,2,0)(3,2,0)=\psi(\Omega_\omega+\psi_1(\Omega_2\times2))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(3,0,0)=\psi(\Omega_\omega+\psi_1(\Omega_2\times\omega))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(3,2,0)=\psi(\Omega_\omega+\psi_1(\Omega_2^2))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,0)(3,2,0)(4,2,0)=\psi(\Omega_\omega+\psi_1(\Omega_2^{\Omega_2}))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,0)(3,3,0)=\psi(\Omega_\omega+\psi_1(\psi_2(0)))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,0)(3,3,0)(4,4,0)=\psi(\Omega_\omega+\psi_1(\psi_3(0)))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,1)=\psi(\Omega_\omega+\psi_1(\Omega_\omega))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)=\psi(\Omega_\omega+\psi_1(\Omega_\omega+1))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,0,0)=\psi(\Omega_\omega+\psi_1(\Omega_\omega+\omega))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,1,0)(4,2,0)=\psi(\Omega_\omega+\psi_1(\Omega_\omega+\psi_1(0)))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,1,0)(4,2,0)(5,3,0)=\psi(\Omega_\omega+\psi_1(\Omega_\omega+\psi_1(\psi_2(0))))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,1,0)(4,2,1)=\psi(\Omega_\omega+\psi_1(\Omega_\omega+\psi_1(\Omega_\omega)))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,2,0)=\psi(\Omega_\omega+\Omega_2)</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,3,0)=\psi(\Omega_\omega+\psi_2(0))</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,3,1)(3,3,0)(4,3,0)=\psi(\Omega_\omega+\Omega_3)</math>
+<math>(0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,3,1)(3,3,0)(4,4,0)=\psi(\Omega_\omega+\psi_3(0))</math>
+<math>(0)(1,1,1)(1,1,1)=\psi(\Omega_\omega\times2)</math>
+<math>(0)(1,1,1)(2,0,0)=\psi(\Omega_\omega\times\omega)</math>
+<math>(0)(1,1,1)(2,1,0)=\psi(\Omega_\omega\times\Omega)</math>
 [[分类:分析]]