strong fffz分析Part1

${\psi }_Z(0)=1$

${\psi }_Z[1](1)=2$

${\psi }_Z[1]({\psi }_Z[1](1))=3$

${\psi }_Z(1)=\omega$

${\psi }_Z[2](2)=\omega +1$

${\psi }_Z[2]({\psi }_Z(1))=\omega \times 2$

${\psi }_Z[2]({\psi }_Z[2](2))=\omega \times 2+1$

${\psi }_Z(2)={\omega }^2$

${\psi }_Z[\omega ](\omega )={\omega }^{\omega }$

${\psi }_Z[\omega ](\omega +1)={\omega }^{\omega +1}$

${\psi }_Z[\omega ]({\omega }^2)={\omega }^{{\omega }^2}$

${\psi }_Z[\omega ]({\psi }_Z[\omega ](\omega ))={\omega }^{{\omega }^{\omega }}$

${\psi }_Z(\omega )=(0)(1,1)$

${\psi }_Z(\omega +1)=(0)(1,1)(1)$

${\psi }_Z[\omega \times 2](\omega \times 2)=(0)(1,1)(1)(2)$

${\psi }_Z[\omega \times 2]({\omega }^{\omega })=(0)(1,1)(1)(2)(3)$

${\psi }_Z[\omega \times 2]({\psi }_Z(\omega ))=(0)(1,1)(1)(2,1)$

${\psi }_Z[\omega \times 2]({\psi }_Z[\omega \times 2](\omega \times 2))=(0)(1,1)(1)(2,1)(2)(3)$

${\psi }_Z(\omega \times 2)=(0)(1,1)(1,1)$

${\psi }_Z[{\omega }^2]({\omega }^2)=(0)(1,1)(2)$

${\psi }_Z[{\omega }^2,{\omega }^2+\omega ]({\omega }^2+\omega )=(0)(1,1)(2)(1)(2)$

${\psi }_Z[{\omega }^2]({\omega }^2+\omega )=(0)(1,1)(2)(1,1)$

${\psi }_Z[{\omega }^2]({\omega }^2\times 2)=(0)(1,1)(2)(1,1)(2)$

${\psi }_Z[{\omega }^2]({\omega }^3)=(0)(1,1)(2)(2)$

${\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\omega }^{\omega })=(0)(1,1)(2)(3)$

${\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\psi }_Z(\omega ))=(0)(1,1)(2)(3,1)$

${\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\omega }^{\omega }))=(0)(1,1)(2)(3,1)(4)(5)$

${\psi }_Z[{\omega }^2]({\omega }^{\omega })=(0)(1,1)(2,1)$

${\psi }_Z[{\omega }^2]({\omega }^{\omega }+\omega )=(0)(1,1)(2,1)(1,1)$

${\psi }_Z[{\omega }^2,{\omega }^{\omega }\times 2]({\omega }^{\omega }\times 2)=(0)(1,1)(2,1)(1,1)(2)(3)$

${\psi }_Z[{\omega }^2]({\omega }^{\omega }\times 2)=(0)(1,1)(2,1)(1,1)(2,1)$

${\psi }_Z[{\omega }^2]({\omega }^{\omega +1})=(0)(1,1)(2,1)(2)$

${\psi }_Z[{\omega }^2]({\omega }^{\omega +1}+{\omega }^{\omega })=(0)(1,1)(2,1)(2)(1,1)(2,1)$

${\psi }_Z[{\omega }^2]({\omega }^{\omega +2})=(0)(1,1)(2,1)(2)(2)$

${\psi }_Z[{\omega }^2,{\omega }^{\omega \times 2}]({\omega }^{\omega \times 2})=(0)(1,1)(2,1)(2)(3)$

${\psi }_Z[{\omega }^2,{\omega }^{\omega \times 2}]({\psi }_Z(\omega ))=(0)(1,1)(2,1)(2)(3,1)$

${\psi }_Z[{\omega }^2,{\omega }^{\omega \times 2}]({\psi }_Z[{\omega }^2,{\omega }^{\omega \times 2}]({\omega }^{\omega \times 2}))=(0)(1,1)(2,1)(2)(3,1)(4,1)(4)(5)$

${\psi }_Z[{\omega }^2]({\omega }^{\omega \times 2})=(0)(1,1)(2,1)(2,1)$

${\psi }_Z[{\omega }^2]({\omega }^{{\omega }^2})=(0)(1,1)(2,1)(3)$

${\psi }_Z[{\omega }^2]({\omega }^{{\omega }^2+\omega })=(0)(1,1)(2,1)(3)(2,1)$

${\psi }_Z[{\omega }^2]({\omega }^{{\omega }^3})=(0)(1,1)(2,1)(3)(3)$

${\psi }_Z[{\omega }^2,{\omega }^{{\omega }^{\omega }}]({\omega }^{{\omega }^{\omega }})=(0)(1,1)(2,1)(3)(4)$

${\psi }_Z[{\omega }^2,{\omega }^{{\omega }^{\omega }}]({\psi }_Z(\omega ))=(0)(1,1)(2,1)(3)(4,1)$

${\psi }_Z[{\omega }^2,{\omega }^{{\omega }^{\omega }}]({\psi }_Z[{\omega }^2,{\omega }^{{\omega }^{\omega }}]({\omega }^{{\omega }^{\omega }}))=(0)(1,1)(2,1)(3)(4,1)(5,1)(6)(7)$

${\psi }_Z[{\omega }^2]({\omega }^{{\omega }^{\omega }})=(0)(1,1)(2,1)(3,1)$

${\psi }_Z[{\omega }^2]({\omega }^{{\omega }^{\omega }+\omega })=(0)(1,1)(2,1)(3,1)(2,1)$

${\psi }_Z[{\omega }^2]({\omega }^{{\omega }^{\omega +1}})=(0)(1,1)(2,1)(3,1)(3)$

${\psi }_Z[{\omega }^2]({\omega }^{{\omega }^{\omega \times 2}})=(0)(1,1)(2,1)(3,1)(3,1)$

${\psi }_Z[{\omega }^2]({\omega }^{{\omega }^{{\omega }^2}})=(0)(1,1)(2,1)(3,1)(4)$

${\psi }_Z[{\omega }^2,{\omega }^{{\omega }^{{\omega }^{\omega }}}]({\omega }^{{\omega }^{{\omega }^{\omega }}})=(0)(1,1)(2,1)(3,1)(4)(5)$

${\psi }_Z[{\omega }^2]({\omega }^{{\omega }^{{\omega }^{\omega }}})=(0)(1,1)(2,1)(3,1)(4,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z(\omega ))=(0)(1,1)(2,2)$

${\psi }_Z[{\omega }^2]({\psi }_Z(\omega )+\omega )=(0)(1,1)(2,2)(1,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z(\omega )\times 2)=(0)(1,1)(2,2)(1,1)(2,2)$

${\psi }_Z[{\omega }^2]({\psi }_Z(\omega +1))=(0)(1,1)(2,2)(2)$

${\psi }_Z[{\omega }^2]({\psi }_Z(\omega +1)+{\psi }_Z(\omega ))=(0)(1,1)(2,2)(2)(1,1)(2,2)$

${\psi }_Z[{\omega }^2]({\psi }_Z(\omega +2))=(0)(1,1)(2,2)(2)(2)$

${\psi }_Z[{\omega }^2,{\psi }_Z[\omega \times 2](\omega \times 2)]({\psi }_Z[\omega \times 2](\omega \times 2))=(0)(1,1)(2,2)(2)(3)$

${\psi }_Z[{\omega }^2,{\psi }_Z[\omega \times 2](\omega \times 2)]({\psi }_Z(\omega \times 2))=(0)(1,1)(2,2)(2)(3,1)$

${\psi }_Z[{\omega }^2,{\psi }_Z[\omega \times 2](\omega \times 2)]({\psi }_Z[{\omega }^2,{\psi }_Z[\omega \times 2](\omega \times 2)]({\psi }_Z[\omega \times 2](\omega \times 2)))=(0)(1,1)(2,2)(2)(3,1)(4,2)(4)(5)$

${\psi }_Z[{\omega }^2]({\psi }_Z[\omega \times 2](\omega \times 2))=(0)(1,1)(2,2)(2,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[\omega \times 2](\omega \times 2+1))=(0)(1,1)(2,2)(2,1)(2)$

${\psi }_Z[{\omega }^2,{\psi }_Z[\omega \times 2](\omega \times 3)]({\psi }_Z[\omega \times 2](\omega \times 3))=(0)(1,1)(2,2)(2,1)(2)(3)$

${\psi }_Z[{\omega }^2]({\psi }_Z[\omega \times 2](\omega \times 3))=(0)(1,1)(2,2)(2,1)(2,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[\omega \times 2]({\omega }^2))=(0)(1,1)(2,2)(2,1)(3)$

${\psi }_Z[{\omega }^2,{\psi }_Z[\omega \times 2]({\omega }^{\omega })]({\psi }_Z[\omega \times 2]({\omega }^{\omega }))=(0)(1,1)(2,2)(2,1)(3)(4)$

${\psi }_Z[{\omega }^2]({\psi }_Z[\omega \times 2]({\omega }^{\omega }))=(0)(1,1)(2,2)(2,1)(3,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[\omega \times 2]({\omega }^{{\omega }^{\omega }}))=(0)(1,1)(2,2)(2,1)(3,1)(4,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[\omega \times 2]({\psi }_Z(\omega )))=(0)(1,1)(2,2)(2,1)(3,2)$

${\psi }_Z[{\omega }^2]({\psi }_Z[\omega \times 2]({\psi }_Z(\omega )+\omega ))=(0)(1,1)(2,2)(2,1)(3,2)(2,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[\omega \times 2]({\psi }_Z(\omega +1)))=(0)(1,1)(2,2)(2,1)(3,2)(3)$

${\psi }_Z[{\omega }^2,{\psi }_Z[\omega \times 2]({\psi }_Z[\omega \times 2](\omega \times 2))]({\psi }_Z[\omega \times 2]({\psi }_Z[\omega \times 2](\omega \times 2)))=(0)(1,1)(2,2)(2,1)(3,2)(3)(4)$

${\psi }_Z[{\omega }^2]({\psi }_Z[\omega \times 2]({\psi }_Z[\omega \times 2](\omega \times 2)))=(0)(1,1)(2,2)(2,1)(3,2)(3,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[\omega \times 2]({\psi }_Z[\omega \times 2]({\omega }^2)))=(0)(1,1)(2,2)(2,1)(3,2)(3,1)(4)$

${\psi }_Z[{\omega }^2]({\psi }_Z[\omega \times 2]({\psi }_Z[\omega \times 2]({\omega }^{\omega })))=(0)(1,1)(2,2)(2,1)(3,2)(3,1)(4,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[\omega \times 2]({\psi }_Z[\omega \times 2]({\psi }_Z(\omega )))=(0)(1,1)(2,2)(2,1)(3,2)(3,1)(4,2)$

${\psi }_Z[{\omega }^2]({\psi }_Z(\omega \times 2))=(0)(1,1)(2,2)(2,2)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2]({\omega }^2))=(0)(1,1)(2,2)(3)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2]({\omega }^2+\omega ))=(0)(1,1)(2,2)(3)(2,2)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2]({\omega }^3))=(0)(1,1)(2,2)(3)(3)$

${\psi }_Z[{\omega }^2,{\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\omega }^{\omega })]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\omega }^{\omega }))=(0)(1,1)(2,2)(3)(4)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\omega }^{\omega }))=(0)(1,1)(2,2)(3,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\omega }^{\omega +1}))=(0)(1,1)(2,2)(3,1)(3)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\omega }^{\omega \times 2}))=(0)(1,1)(2,2)(3,1)(3,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\omega }^{{\omega }^2}))=(0)(1,1)(2,2)(3,1)(4)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\omega }^{{\omega }^{\omega }}))=(0)(1,1)(2,2)(3,1)(4,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\psi }_Z(\omega )))=(0)(1,1)(2,2)(3,1)(4,2)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\psi }_Z[\omega \times 2](\omega \times 2)))=(0)(1,1)(2,2)(3,1)(4,2)(3,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\psi }_Z[\omega \times 2]({\omega }^2)))=(0)(1,1)(2,2)(3,1)(4,2)(3,1)(4)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\psi }_Z[\omega \times 2]({\omega }^{\omega })))=(0)(1,1)(2,2)(3,1)(4,2)(3,1)(4,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\psi }_Z[\omega \times 2]({\psi }_Z(\omega ))))=(0)(1,1)(2,2)(3,1)(4,2)(3,1)(4,2)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\psi }_Z[\omega \times 2]({\psi }_Z(\omega )+\omega )))=(0)(1,1)(2,2)(3,1)(4,2)(3,1)(4,2)(3,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\psi }_Z[\omega \times 2]({\psi }_Z(\omega +1))))=(0)(1,1)(2,2)(3,1)(4,2)(4)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\psi }_Z[\omega \times 2]({\psi }_Z[\omega \times 2](\omega \times 2))))=(0)(1,1)(2,2)(3,1)(4,2)(4,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\psi }_Z[\omega \times 2]({\psi }_Z[\omega \times 2]({\psi }_Z(\omega )))))=(0)(1,1)(2,2)(3,1)(4,2)(4,1)(5,2)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\psi }_Z(\omega \times 2)))=(0)(1,1)(2,2)(3,1)(4,2)(4,2)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\psi }_Z[{\omega }^2]({\omega }^2)))=(0)(1,1)(2,2)(3,1)(4,2)(5)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\omega }^{\omega })))=(0)(1,1)(2,2)(3,1)(4,2)(5,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\psi }_Z[{\omega }^2,{\omega }^{\omega }]({\psi }_Z(\omega ))))=(0)(1,1)(2,2)(3,1)(4,2)(5,1)(6,2)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2]({\omega }^{\omega }))=(0)(1,1)(2,2)(3,2)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2]({\omega }^{\omega }+\omega ))=(0)(1,1)(2,2)(3,2)(2,2)$

${\psi }_Z[{\omega }^2,{\psi }_Z[{\omega }^2,{\omega }^{\omega }\times 2]({\omega }^{\omega }\times 2)]({\psi }_Z[{\omega }^2,{\omega }^{\omega }\times 2]({\omega }^{\omega }\times 2))=(0)(1,1)(2,2)(3,2)(2,2)(3)(4)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega }\times 2]({\omega }^{\omega }\times 2))=(0)(1,1)(2,2)(3,2)(2,2)(3,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2]({\omega }^{\omega }\times 2))=(0)(1,1)(2,2)(3,2)(2,2)(3,2)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2]({\omega }^{\omega +1}))=(0)(1,1)(2,2)(3,2)(3)$

${\psi }_Z[{\omega }^2,{\psi }_Z[{\omega }^2,{\omega }^{\omega \times 2}]({\omega }^{\omega \times 2})]({\psi }_Z[{\omega }^2,{\omega }^{\omega \times 2}]({\omega }^{\omega \times 2}))=(0)(1,1)(2,2)(3,2)(3)(4)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2,{\omega }^{\omega \times 2}]({\omega }^{\omega \times 2}))=(0)(1,1)(2,2)(3,2)(3,1)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2]({\omega }^{\omega \times 2}))=(0)(1,1)(2,2)(3,2)(3,2)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2]({\omega }^{{\omega }^2}))=(0)(1,1)(2,2)(3,2)(4)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2]({\omega }^{{\omega }^{\omega }}))=(0)(1,1)(2,2)(3,2)(4,2)$

${\psi }_Z[{\omega }^2]({\psi }_Z[{\omega }^2]({\psi }_Z(\omega )))=(0)(1,1)(2,2)(3,3)$

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