SGH与FGH对照：修订间差异
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<nowiki>\begin{align} & f_{\omega^\omega}(n)\sim\psi(\Omega^{\Omega^\omega})\\&f_3(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+1)\\&f_4^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega)\\&f_5^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^2)\\&f_n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^\omega)\\&f_{\omega}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\psi(\Omega^{\Omega^\omega})})\\&f_{\omega}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega})\\&f_{\omega+1}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega+1})\\&f_{\omega+n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega+\omega})\\&f_{\omega\times2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega\times2})\\&f_{\omega\times n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega\times\omega})\\&f_{\omega^2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega^2})\\&f_{\omega^3}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega^3})\\&f_{\omega^n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}\times2)\\&f_{\omega^n}^2(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}\times3)\\&f_{\omega^n}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}\times\omega)\\&f_{\omega^n+1}(f_{\omega^\omega}(n))=f_{\omega^n}^{f_{\omega^\omega}(n)}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}\times\psi(\Omega^{\Omega^\omega}))\\&f_{\omega^n+1}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+1})\\&f_{\omega^n+2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+2})\\&f_{\omega^n+n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+\omega})\\&f_{\omega^n+\omega}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+\Omega})\\&f_{\omega^n+\omega\times2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+\Omega\times2})\\&f_{\omega^n+\omega^2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+\Omega^2})\\&f_{\omega^n\times2}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega\times2})\\&f_{\omega^n\times3}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega\times3})\\&f_{\omega^n\times n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega\times\omega})\\&f_{\omega^{n+1}}(f_{\omega^\omega}(n))=f_{\omega^n\times f_{\omega^\omega}(n)}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}})\\&f_{\omega^n}(f_{\omega^{n+1}}(f_{\omega^\omega}(n)))\sim\psi(\Omega^{\Omega^{\omega+1}}+\Omega^{\Omega^\omega})\\&f_{\omega^n+1}^n(f_{\omega^{n+1}}(f_{\omega^\omega}(n)))\sim\psi(\Omega^{\Omega^{\omega+1}}+\Omega^{\Omega^\omega+1})\\&f_{\omega^n\times n}(f_{\omega^{n+1}}(f_{\omega^\omega}(n)))\sim\psi(\Omega^{\Omega^{\omega+1}}+\Omega^{\Omega^\omega\times\omega})\\&f_{\omega^{n+1}}^2(f_{\omega^\omega}(n))=f_{\omega^n\times f_{\omega^{n+1}}(f_{\omega^\omega}(n))}(f_{\omega^{n+1}}(f_{\omega^\omega}(n)))\sim\psi(\Omega^{\Omega^{\omega+1}}\times2)\\&f_{\omega^{n+1}}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}}\times\omega)\\&f_{\omega^{n+1}+1}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}+1})\\&f_{\omega^{n+1}+\omega^n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}+\Omega^\omega})\\&f_{\omega^{n+1}\times2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}\times2})\\&f_{\omega^{n+1}\times n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}\times\omega})\\&f_{\omega^{n+2}}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+2}})\\&f_{\omega^{n\times2}}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega\times2}})\\&f_{\omega^{n^2}}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega^2}})\\&f_{\omega^{f_3(n)}}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\psi(0)}})\\&f_{\omega^\omega}^2(n)=f_{\omega^{f_{\omega^\omega}(n)}}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\psi(\Omega^{\Omega^\omega})}})\\&f_{\omega^\omega}^3(n)\sim\psi(\Omega^{\Omega^{\psi(\Omega^{\Omega^{\psi(\Omega^{\Omega^\omega})}})}})\\&f_{\omega^\omega+1}(n)=f_{\omega^\omega}^n(n)\sim\psi(\Omega^{\Omega^{\Omega}})\\&f_{\omega^\omega+2}(n)\sim\psi(\Omega^{\Omega^\Omega+1})\\&f_{\omega^\omega+3}(n)\sim\psi(\Omega^{\Omega^\Omega+2})\\&f_{\omega^\omega+\omega}(n)\sim\psi(\Omega^{\Omega^\Omega+\omega})\\&f_{\omega^\omega+\omega+1}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega})\\&f_{\omega^\omega+\omega\times2}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega+\omega})\\&f_{\omega^\omega+\omega\times2+1}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega\times2})\\&f_{\omega^\omega+\omega^2}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega\times\omega})\\&f_{\omega^\omega+\omega^2+1}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega^2})\\&f_{\omega^\omega+\omega^3+1}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega^3})\\&f_{\omega^\omega\times2}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega^\omega})\\&f_{\omega^\omega\times2+1}(n)\sim\psi(\Omega^{\Omega^\Omega\times2})\\&f_{\omega^\omega\times3+1}(n)\sim\psi(\Omega^{\Omega^\Omega\times3})\\&f_{\omega^{\omega+1}}(n)\sim\psi(\Omega^{\Omega^\Omega\times\omega})\\&f_{\omega^{\omega+1}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega+1}})\\&f_{\omega^{\omega+1}+\omega+1}(n)\sim\psi(\Omega^{\Omega^{\Omega+1}+\Omega})\\&f_{\omega^{\omega+1}+\omega^\omega+1}(n)\sim\psi(\Omega^{\Omega^{\Omega+1}+\Omega^\Omega})\\&f_{\omega^{\omega+1}\times2+1}(n)\sim\psi(\Omega^{\Omega^{\Omega+1}\times2})\\&f_{\omega^{\omega+2}}(n)\sim\psi(\Omega^{\Omega^{\Omega+1}\times\omega})\\&f_{\omega^{\omega+2}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega+2}})\\&f_{\omega^{\omega\times2}}(n)\sim\psi(\Omega^{\Omega^{\Omega+\omega}})\\&f_{\omega^{\omega\times2}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega\times2}})\\&f_{\omega^{\omega\times3}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega\times3}})\\&f_{\omega^{\omega^2}}(n)\sim\psi(\Omega^{\Omega^{\Omega\times\omega}})\\&f_{\omega^{\omega^2}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^2}})\\&f_{\omega^{\omega^2}\times2+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^2}\times2})\\&f_{\omega^{\omega^2+1}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^2+1}})\\&f_{\omega^{\omega^2+\omega}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^2+\Omega}})\\&f_{\omega^{\omega^2\times2}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^2\times2}})\\&f_{\omega^{\omega^3}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^3}})\\&f_{\omega^{\omega^\omega}}(n)\sim\psi(\Omega^{\Omega^{\Omega^\omega}})\\&f_{\omega^{\omega^\omega}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^\Omega}})\\&f_{\omega^{\omega^{\omega^\omega}}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^{\Omega^\Omega}}})\\&f_{\psi(0)}(n)\sim\psi(\psi_1(0))\\&f_3(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+1)\\&f_4^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega)\\&f_n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^\omega)\\&f_\omega(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\psi(\psi_1(0))})\\&f_\omega^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega})\\&f_{\omega+1}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega+1})\\&f_{\omega\times2}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega\times2})\\&f_{\omega^\omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega^\Omega})\\&f_{\omega^\omega+1}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega^\Omega+1})\\&f_{\omega^{\omega^\omega}}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega^{\Omega^\Omega}})\\&f_{\omega^{\omega^{\omega^\omega}}}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega^{\Omega^{\Omega^\Omega}}})\\&f_{\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times2)\\&f_{\psi(0)[n]}^2(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times3)\\&f_{\psi(0)[n]}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\omega)\\&f_{\psi(0)[n]+1}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\psi(\psi_1(0)))\\&f_{\psi(0)[n]+1}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega)\\&f_{\psi(0)[n]}(f_{\psi(0)[n]+1}^n(f_{\psi(0)}(n)))\sim\psi(\psi_1(0)\times\Omega+\psi_1(0))\\&f_{\psi(0)[n]+1}^{n+1}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega+\psi_1(0)\times\psi(\psi_1(0)\times\Omega))\\&f_{\psi(0)[n]+1}^{n\times2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega\times2)\\&f_{\psi(0)[n]+2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega\times\psi(\psi_1(0)))\\&f_{\psi(0)[n]+2}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega^2)\\&f_{\psi(0)[n]+n}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega^\omega)\\&f_{\psi(0)[n]+\omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega^\Omega)\\&f_{\psi(0)[n]\times2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^2)\\&f_{\psi(0)[n]\times n}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^\omega)\\&f_{\psi(0)[n]\times \omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^\Omega)\\&f_{\psi(0)[n]\times \omega^2}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\Omega^2})\\&f_{\psi(0)[n]\times \omega^\omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\Omega^\Omega})\\&f_{\psi(0)[n]^2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)})\\&f_{\psi(0)[n]^2+\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)+1})\\&f_{\psi(0)[n]^2\times2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)\times2})\\&f_{\psi(0)[n]^2\times n}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)\times\omega})\\&f_{\psi(0)[n]^2\times \omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)\times\Omega})\\&f_{\psi(0)[n]^3}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^2})\\&f_{\psi(0)[n]^n}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^\omega})\\&f_{\psi(0)[n]^\omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^\Omega})\\&f_{\psi(0)[n]^{\psi(0)[n]}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}})\\&f_{\psi(0)[n+1]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}})\\&f_{\psi(0)[n+1]+\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}+1})\\&f_{\psi(0)[n+1]+\psi(0)[n]^2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}+\psi_1(0)})\\&f_{\psi(0)[n+1]+\psi(0)[n]^\omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}+\psi_1(0)^\Omega})\\&f_{\psi(0)[n+1]\times2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}\times2})\\&f_{\psi(0)[n+1]\times\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)+1}})\\&f_{\psi(0)[n+1]\times\psi(0)[n]^2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)+2}})\\&f_{\psi(0)[n+1]^2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)\times2}})\\&f_{\psi(0)[n+1]^{\psi(0)[n]}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^2}})\\&f_{\psi(0)[n+1]^{\psi(0)[n]+1}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^2+\psi_1(0)}})\\&f_{\psi(0)[n+1]^{\psi(0)[n]\times2}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^2\times2}})\\&f_{\psi(0)[n+1]^{\psi(0)[n]^2}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^3}})\\&f_{\psi(0)[n+2]}(f_{\psi(0)}(n))=f_{\psi(0)[n+1]^{\psi(0)[n+1]}}(f_{\psi(0)}(n))=f_{\psi(0)[n+1]^{\psi(0)[n]^{\psi(0)[n]}}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^{\psi_1(0)}}})\\&f_{\psi(0)[n+3]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^{\psi_1(0)^{\psi_1(0)}}}})\\&f_{\psi(0)[n\times2]}(f_{\psi(0)}(n))\sim\psi(\psi_1(1))\\&f_{\psi(0)[n]}(f_{\psi(0)[n\times2]}(f_{\psi(0)}(n)))\sim\psi(\psi_1(1)+\psi_1(0))\\&f_{\psi(0)[n\times2]}^2(f_{\psi(0)}(n))\sim\psi(\psi_1(1)\times2)\\&f_{\psi(0)[n\times2]+\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)\times\psi_1(0))\\&f_{\psi(0)[n\times2]+\psi(0)[n+1]}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)\times\psi_1(0)^{\psi_1(0)^{\psi_1(0)}})\\&f_{\psi(0)[n\times2]\times2}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)^2)\\&f_{\psi(0)[n\times2]\times\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)^{\psi_1(0)})\\&f_{\psi(0)[n\times2]^2}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)^{\psi_1(1)})\\&f_{\psi(0)[n\times2]^3}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)^{\psi_1(1)^2})\\&f_{\psi(0)[n\times2+1]}(f_{\psi(0)}(n))=f_{\psi(0)[n\times2]^{\psi(0)[n\times2]}}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)^{\psi_1(1)^{\psi_1(1)}})\\&f_{\psi(0)[n\times3]}(f_{\psi(0)}(n))\sim\psi(\psi_1(2))\\&f_{\psi(0)[n^2]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\omega))\\&f_{\psi(0)[n^2+n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\omega+1))\\&f_{\psi(0)[n^3]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\omega^2))\\&f_{\psi(0)[n^n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\omega^\omega))\\&f_{\psi(0)[f_3(n)]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\psi(0)))\\&f_{\psi(0)}^2(n)=f_{\psi(0)[f_{\psi(0)}(n)]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\psi(\psi_1(0))))\\&f_{\psi(0)[n]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)))\times\psi_1(0))\\&f_{\psi(0)[n\times2]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)))\times\psi_1(1))\\&f_{\psi(0)[f_{\psi(0)}(n)]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)))^2)\\&f_{\psi(0)[f_{\psi(0)}(n)+1]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)))^{\psi_1(\psi(\psi_1(0)))^{\psi_1(\psi(\psi_1(0)))}})\\&f_{\psi(0)[f_{\psi(0)}(n)+n]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0))+1))\\&f_{\psi(0)[f_{\psi(0)}(n)\times2]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0))\times2))\\&f_{\psi(0)[f_3(f_{\psi(0)}(n))]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)+1)))\\&f_{\psi(0)[f_{\psi(0)[n]}(f_{\psi(0)}(n))]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)\times2)))\\&f_{\psi(0)[f_{\psi(0)[n\times2]}(f_{\psi(0)}(n))]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(1))))\\&f_{\psi(0)[f_{\psi(0)[n^2]}(f_{\psi(0)}(n))]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(\omega))))\\&f_{\psi(0)}^3(n)\sim\psi(\psi_1(\psi(\psi_1(\psi(\psi_1(0))))))\\&f_{\psi(0)+1}(n)\sim\psi(\psi_1(\Omega))\\&f_{\psi(0)[n]}(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)+\psi_1(0))\\&f_{\psi(0)[n\times2]}(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)+\psi_1(1))\\&f_{\psi(0)[f_{\psi(0)}(n)]}(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)+\psi_1(\psi(\psi_1(0))))\\&f_{\psi(0)}(f_{\psi(0)+1}(n))=f_{\psi(0)[f_{\psi(0)+1}(n)]}(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)+\psi_1(\psi(\psi_1(\Omega))))\\&f_{\psi(0)}^2(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)+\psi_1(\psi(\psi_1(\Omega)+\psi_1(\psi(\psi_1(\Omega))))))\\&f_{\psi(0)}^n(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)\times2)\\&f_{\psi(0)}^{n^2}(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)\times\omega)\\&f_{\psi(0)+1}^2(n)\sim\psi(\psi_1(\Omega)\times\psi(\psi_1(\Omega)))\\&f_{\psi(0)+2}(n)\sim\psi(\psi_1(\Omega)\times\Omega)\\&f_{\psi(0)+3}(n)\sim\psi(\psi_1(\Omega)\times\Omega^2)\\&f_{\psi(0)+\omega}(n)\sim\psi(\psi_1(\Omega)\times\Omega^\omega)\\&f_{\psi(0)+\omega+1}(n)\sim\psi(\psi_1(\Omega)\times\Omega^\Omega)\\&f_{\psi(0)+\omega^\omega+1}(n)\sim\psi(\psi_1(\Omega)\times\Omega^{\Omega^\Omega})\\&f_{\psi(0)\times2}(n)\sim\psi(\psi_1(\Omega)\times\psi_1(0))\\&f_{\psi(0)\times2+1}(n)\sim\psi(\psi_1(\Omega)^2)\\&f_{\psi(0)\times3+1}(n)\sim\psi(\psi_1(\Omega)^3)\\&f_{\psi(0)\times\omega}(n)\sim\psi(\psi_1(\Omega)^\omega)\\&f_{\psi(0)\times\omega+1}(n)\sim\psi(\psi_1(\Omega)^\Omega)\\&f_{\psi(0)^2}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(0)})\\&f_{\psi(0)^2+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)})\\&f_{\psi(0)^2+\psi(0)+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)+1})\\&f_{\psi(0)^2\times2+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)\times2})\\&f_{\psi(0)^3+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)^2})\\&f_{\psi(0)^\omega+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)^\Omega})\\&f_{\psi(0)^{\psi(0)}}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)^{\psi_1(0)}})\\&f_{\psi(0)^{\psi(0)}+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)^{\psi_1(\Omega)}})\\&f_{\psi(1)}(n)\sim\psi(\psi_1(\Omega+1))\\&f_{\psi(0)[n]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)+\psi_1(0))\\&f_{\psi(0)}^n(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)+\psi_1(\Omega))\\&f_{\psi(0)^{\psi(0)}}^n(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)+\psi_1(\Omega)^{\psi_1(\Omega)^{\psi_1(\Omega)}})\\&f_{\psi(1)[n]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times2)\\&f_{\psi(1)[n]}^2(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times3)\\&f_{\psi(1)[n]+1}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times\psi(\psi_1(\Omega+1)))\\&f_{\psi(1)[n]+1}^n(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times\Omega)\\&f_{\psi(1)[n]+\psi(0)[n]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times\psi_1(0))\\&f_{\psi(1)[n]+\psi(0)}^n(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times\psi_1(\Omega))\\&f_{\psi(1)[n]\times2}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)^2)\\&f_{\psi(1)[n]\times\psi(0)[n]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)^{\psi_1(0)})\\&f_{\psi(1)[n]^2}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)^{\psi_1(\Omega+1)})\\&f_{\psi(1)[n+1]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)^{\psi_1(\Omega+1)^{\psi_1(\Omega+1)}})\\&f_{\psi(1)[n\times2]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+2))\\&f_{\psi(1)}^2(n)\sim\psi(\psi_1(\Omega+\psi(\psi_1(\Omega))))\\&f_{\psi(1)+1}(n)\sim\psi(\psi_1(\Omega\times2))\\&f_{\psi(1)+2}(n)\sim\psi(\psi_1(\Omega\times2)\times\Omega)\\&f_{\psi(1)+\psi(0)+1}(n)\sim\psi(\psi_1(\Omega\times2)\times\psi_1(\Omega))\\&f_{\psi(1)\times2+1}(n)\sim\psi(\psi_1(\Omega\times2)^2)\\&f_{\psi(1)\times{\psi(0)}+1}(n)\sim\psi(\psi_1(\Omega\times2)^{\psi_1(\Omega)})\\&f_{\psi(1)^{2}+1}(n)\sim\psi(\psi_1(\Omega\times2)^{\psi_1(\Omega\times2)})\\&f_{\psi(1)^{\psi(1)}+1}(n)\sim\psi(\psi_1(\Omega\times2)^{\psi_1(\Omega\times2)^{\psi_1(\Omega\times2)}})\\&f_{\psi(2)}(n)\sim\psi(\psi_1(\Omega\times2+1))\\&f_{\psi(2)+1}(n)\sim\psi(\psi_1(\Omega\times3))\\&f_{\psi(3)}(n)\sim\psi(\psi_1(\Omega\times3+1))\\&f_{\psi(4)}(n)\sim\psi(\psi_1(\Omega\times4+1))\\&f_{\psi(\omega)}(n)\sim\psi(\psi_1(\Omega\times\omega))\\&f_{\psi(\omega)+1}(n)\sim\psi(\psi_1(\Omega^2))\\&f_{\psi(\omega)+2}(n)\sim\psi(\psi_1(\Omega^2)\times\Omega)\\&f_{\psi(\omega)\times2+1}(n)\sim\psi(\psi_1(\Omega^2)^2)\\&f_{\psi(\omega)^2+1}(n)\sim\psi(\psi_1(\Omega^2)^{\psi_1(\Omega^2)})\\&f_{\psi(\omega+1)}(n)\sim\psi(\psi_1(\Omega^2+1))\\&f_{\psi(\omega+1)+1}(n)\sim\psi(\psi_1(\Omega^2+\Omega))\\&f_{\psi(\omega+2)+1}(n)\sim\psi(\psi_1(\Omega^2+\Omega\times2))\\&f_{\psi(\omega\times2)+1}(n)\sim\psi(\psi_1(\Omega^2\times2))\\&f_{\psi(\omega^2)+1}(n)\sim\psi(\psi_1(\Omega^3))\\&f_{\psi(\omega^\omega)}(n)\sim\psi(\psi_1(\Omega^\omega))\\&f_{\psi(\omega^\omega)+1}(n)\sim\psi(\psi_1(\Omega^\Omega))\\&f_{\psi(\omega^{\omega^\omega})+1}(n)\sim\psi(\psi_1(\Omega^{\Omega^\Omega}))\\&f_{\psi(\psi(0))}(n)\sim\psi(\psi_1(\psi_1(0)))\\&f_{\psi(\psi(0))+1}(n)\sim\psi(\psi_1(\psi_1(\Omega)))\\&f_{\psi(\psi(1))+1}(n)\sim\psi(\psi_1(\psi_1(\Omega\times2)))\\&f_{\psi(\psi(\psi(0)))+1}(n)\sim\psi(\psi_1(\psi_1(\psi_1(\Omega))))\\&f_{\psi(\Omega)}(n)\sim\psi(\Omega_2)\\&f_{3}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+1)\\&f_{\omega}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\Omega^\Omega)\\&f_{\psi(0)[n]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(0))\\&f_{\psi(0)}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega))\\&f_{\psi(1)[n]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega+1))\\&f_{\psi(1)}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega\times2))\\&f_{\psi(\omega)}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega^2))\\&f_{\psi(\psi(0))}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\psi_1(\Omega)))\\&f_{\psi(\psi(\psi(0)))}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\psi_1(\psi_1(\Omega))))\\&f_{\psi(\Omega)[n]}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)\times\omega)\\&f_{\psi(\Omega)[n]+1}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)\times\Omega)\\&f_{\psi(\Omega)[n]\times2}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)^2)\\&f_{\psi(\Omega)[n]\times \omega}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)^\Omega)\\&f_{\psi(\Omega)[n]\times \psi(0)+1}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)^{\psi_1(\Omega)})\\&f_{\psi(\Omega)[n]^2}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)^{\psi_1(\Omega_2)})\\&f_{\psi(\Omega)[n]^{\psi(\Omega)[n]}}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)^{\psi_1(\Omega_2)^{\psi_1(\Omega_2)}})\\&f_{\psi(\psi(\Omega)[n-1]+1)[n]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+1))\\&f_{\psi(\psi(\Omega)[n-1]+1)}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\Omega))\\&f_{\psi(\psi(\Omega)[n-1]+n)}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\Omega\times\omega))\\&f_{\psi(\psi(\Omega)[n-1]+\omega)}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\Omega^2))\\&f_{\psi(\psi(\Omega)[n-1]+\psi(0))}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega)))\\&f_{\psi(\psi(\Omega)[n-1]+\psi(\psi(0)))}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\psi_1(\Omega))))\\&f_{\psi(\Omega)[n+1]}(f_{\psi(\Omega)}(n))=f_{\psi(\psi(\Omega)[n])}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)))\\&f_{\psi(\psi(\Omega)[n]+1)}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)+1))\\&f_{\psi(\psi(\Omega)[n]\times2)}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)\times2))\\&f_{\psi(\psi(\Omega)[n]^2)}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)^2))\\&f_{\psi(\psi(\psi(\Omega)[n-1]+1))}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2+1)))\\&f_{\psi(\Omega)[n+2]}(f_{\psi(\Omega)}(n))=f_{\psi(\psi(\psi(\Omega)[n]))}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2))))\\&f_{\psi(\Omega)[n\times2]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2)\\&f_{\psi(\Omega)[n]}(f_{\psi(\Omega)[n\times2]}(f_{\psi(\Omega)}(n)))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2))\\&f_{\psi(\Omega)[n\times2]}^2(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2))\\&f_{\psi(\Omega)[n\times2]+1}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2)\times\Omega)\\&f_{\psi(\Omega)[n\times2]\times2}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2)^2)\\&f_{\psi(\Omega)[n\times2]^2}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2)^{\psi_!(\Omega_2\times2)})\\&f_{\psi(\psi(\Omega)[n\times2-1]+1)}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2+1))\\&f_{\psi(\Omega)[n\times2+1]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2+\psi_1(\Omega_2\times2)))\\&f_{\psi(\Omega)[n\times3]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times3)\\&f_{\psi(\Omega)[n^2]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\omega)\\&f_{\psi(\Omega)[n^2+1]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\omega+\psi_1(\Omega_2\times\omega+\psi_1(\Omega_2\times\omega)))\\&f_{\psi(\Omega)[n^2+n]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\omega+\Omega_2)\\&f_{\psi(\Omega)[n^3]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\omega^2)\\&f_{\psi(\Omega)[f_3(n)]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\psi(0))\\&f_{\psi(\Omega)}^2(n)=f_{\psi(\Omega)[f_{\psi(\Omega)}(n)]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\psi(\Omega_2))\\&f_{\psi(\Omega)}^3(n)\sim\psi(\Omega_2\times\psi(\Omega_2\times\psi(\Omega_2)))\\&f_{\psi(\Omega)+1}(n)=f_{\psi(\Omega)}^n(n)\sim\psi(\Omega_2\times\Omega)\\&f_{\psi(\Omega)}(f_{\psi(\Omega)+1}(n))\sim\psi(\Omega_2\times\Omega+\Omega_2\times\psi(\Omega_2\times\Omega))\\&f_{\psi(\Omega)}^n(f_{\psi(\Omega)+1}(n))\sim\psi(\Omega_2\times\Omega\times2)\\&f_{\psi(\Omega)+1}^2(n)\sim\psi(\Omega_2\times\Omega\times\psi(\Omega_2\times\Omega))\\&f_{\psi(\Omega)+2}(n)\sim\psi(\Omega_2\times\Omega^2)\\&f_{\psi(\Omega)+\omega}(n)\sim\psi(\Omega_2\times\Omega^\omega)\\&f_{\psi(\Omega)+\omega+1}(n)\sim\psi(\Omega_2\times\Omega^\Omega)\\&f_{\psi(\Omega)+\omega^\omega+1}(n)\sim\psi(\Omega_2\times\Omega^{\Omega^\Omega})\\&f_{\psi(\Omega)+\psi(0)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega))\\&f_{\psi(\Omega)+\psi(1)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega\times2))\\&f_{\psi(\Omega)+\psi(\psi(0))+1}(n)\sim\psi(\Omega_2\times\psi_1(\psi_1(\Omega)))\\&f_{\psi(\Omega)\times2}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2))\\&f_{\psi(\Omega)}^n(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)+\Omega_2\times\Omega)\\&f_{\psi(\Omega)+\psi(0)}^n(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)+\Omega_2\times\psi_1(\Omega))\\&f_{\psi(\Omega)+\psi(\Omega)[n]}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)\times2)\\&f_{\psi(\Omega)+\psi(\Omega)[n]}^2(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)\times3)\\&f_{\psi(\Omega)+\psi(\Omega)[n]+1}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)\times\psi(\Omega_2\times\psi_1(\Omega_2)))\\&f_{\psi(\Omega)+\psi(\Omega)[n]+1}^n(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)\times\Omega)\\&f_{\psi(\Omega)+\psi(\Omega)[n]\times2}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)^2)\\&f_{\psi(\Omega)+\psi(\psi(\Omega)[n-1]+1)[n]}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2+1))\\&f_{\psi(\Omega)+\psi(\Omega)[n+1]}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2+\psi_1(\Omega_2)))\\&f_{\psi(\Omega)+\psi(\Omega)[n\times2]}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2\times2))\\&f_{\psi(\Omega)\times2}^2(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi(\Omega_2\times\psi_1(\Omega_2))))\\&f_{\psi(\Omega)\times2+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega))\\&f_{\psi(\Omega)\times2}(f_{\psi(\Omega)\times2+1}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)+\Omega_2\times\psi_1(\Omega_2\times\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega))))\\&f_{\psi(\Omega)\times2}^n(f_{\psi(\Omega)\times2+1}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)\times2)\\&f_{\psi(\Omega)\times2+1}^2(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)\times\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)))\\&f_{\psi(\Omega)\times2+2}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)\times\Omega)\\&f_{\psi(\Omega)\times3}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)\times\psi_1(\Omega_2))\\&f_{\psi(\Omega)\times3+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^2)\\&f_{\psi(\Omega)\times\omega+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^\Omega)\\&f_{\psi(\Omega)\times\omega+\psi(\Omega)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^{\Omega+1})\\&f_{\psi(\Omega)\times\psi(0)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^{\psi_1(0)})\\&f_{\psi(\Omega)^2}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^{\psi_1(\Omega_2)})\\&f_{\psi(\Omega)^2+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^{\psi_1(\Omega_2\times\Omega)})\\&f_{\psi(\Omega)^{\psi(\Omega)}+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^{\psi_1(\Omega_2\times\Omega)^{\psi_1(\Omega_2\times\Omega)}})\\&f_{\psi(\Omega+1)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+1))\\&f_{\psi(\Omega+1)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\Omega))\\&f_{\psi(\Omega+2)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\Omega+1))\\&f_{\psi(\Omega+2)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\Omega\times2))\\&f_{\psi(\Omega+\omega)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\Omega^2))\\&f_{\psi(\Omega+\psi(0))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(0)))\\&f_{\psi(\Omega+\psi(0))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega)))\\&f_{\psi(\Omega+\psi(\Omega))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2)))\\&f_{\psi(\Omega+\psi(\Omega))[n\times2]}(f_{\psi(\Omega+\psi(\Omega))}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times2)))\\&f_{\psi(\Omega+\psi(\Omega))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times\Omega)))\\&f_{\psi(\Omega+\psi(\Omega)+1)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times\Omega)+1))\\&f_{\psi(\Omega+\psi(\Omega+1))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times\Omega+1)))\\&f_{\psi(\Omega+\psi(\Omega+\psi(\Omega)))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times\Omega))))\\&f_{\psi(\Omega\times2)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\Omega_2))\\&f_{\psi(\Omega\times2)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2))\\&f_{\psi(\Omega\times2)\times2+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2)^2)\\&f_{\psi(\Omega\times2+1)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2+1))\\&f_{\psi(\Omega\times2+1)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2+\Omega))\\&f_{\psi(\Omega\times2+\psi(\Omega\times2))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2+\psi_1(\Omega_2\times\Omega\times2)))\\&f_{\psi(\Omega\times3)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2+\Omega_2))\\&f_{\psi(\Omega\times3)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times3))\\&f_{\psi(\Omega\times\omega)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times\omega))\\&f_{\psi(\Omega\times\omega)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^2))\\&f_{\psi(\Omega\times\omega+1)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^2+1))\\&f_{\psi(\Omega\times\omega+\Omega)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^2+\Omega_2\times\Omega))\\&f_{\psi(\Omega\times\omega\times2)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^2\times2))\\&f_{\psi(\Omega\times\omega^2)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^3))\\&f_{\psi(\Omega\times\omega^\omega)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^\Omega))\\&f_{\psi(\Omega\times\psi(0))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(0)))\\&f_{\psi(\Omega\times\psi(0))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega)))\\&f_{\psi(\Omega\times\psi(1))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega+1)))\\&f_{\psi(\Omega\times\psi(\Omega))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2)))\\&f_{\psi(\Omega\times\psi(\Omega))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2\times\Omega)))\\&f_{\psi(\Omega\times\psi(\Omega+1))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2\times\Omega+1)))\\&f_{\psi(\Omega\times\psi(\Omega\times2))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2)))\\&f_{\psi(\Omega\times\psi(\Omega\times\psi(0)))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2\times\psi_1(0))))\\&f_{\psi(\Omega\times\psi(\Omega\times\psi(\Omega)))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2))))\\&f_{\psi(\Omega^2)}(n)\sim\psi(\Omega_2^2)\\&f_{\psi(\Omega^2)[n]}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\psi_1(\Omega^2_2))\\&f_{\psi(\Omega\times\psi(\Omega^2)[n-1]+1)}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\psi_1(\Omega^2_2+1))\\&\psi(\Omega^2)[n]=\psi(\Omega\times\psi(\Omega^2)[n-1]) \\&f_{\psi(\Omega\times\psi(\Omega^2)[n-1]+\Omega)[n]}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\Omega_2)\\&f_{\psi(\Omega\times\psi(\Omega^2)[n-1]+\Omega)}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\Omega_2\times\Omega)\\&f_{\psi(\Omega\times\psi(\Omega^2)[n-1]+\Omega\times\psi(\Omega))}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\Omega_2\times\psi_1(\Omega_2))\\&f_{\psi(\Omega^2)[n+1]}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\Omega_2\times\psi_1(\Omega_2^2))\\&f_{\psi(\Omega^2)[n\times2]}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2\times2)\\&f_{\psi(\Omega^2)+1}(n)\sim\psi(\Omega^2_2\times\Omega)\\&f_{\psi(\Omega^2)+2}(n)\sim\psi(\Omega^2_2\times\Omega^2)\\&f_{\psi(\Omega^2)+\psi(0)}(n)\sim\psi(\Omega^2_2\times\psi_1(0))\\&f_{\psi(\Omega^2)+\psi(\Omega)}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2))\\&f_{\psi(\Omega^2)+\psi(\Omega\times\psi(\Omega))}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2)))\\&f_{\psi(\Omega^2)\times2}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2))\\&f_{\psi(\Omega^2)\times2+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega))\\&f_{\psi(\Omega^2)^2+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega)^{\psi_1(\Omega^2_2\times\Omega)})\\&f_{\psi(\Omega^2+1)}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+1))\\&f_{\psi(\Omega^2+1)+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega))\\&f_{\psi(\Omega^2+\psi(\Omega^2))+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\psi_1(\Omega^2_2\times\Omega)))\\&f_{\psi(\Omega^2+\Omega)}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega_2))\\&f_{\psi(\Omega^2+\Omega)+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega_2\times\Omega))\\&f_{\psi(\Omega^2+\Omega\times2)+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega_2\times\Omega\times2))\\&f_{\psi(\Omega^2+\Omega\times\psi(0))+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega_2\times\psi_1(\Omega)))\\&f_{\psi(\Omega^2+\Omega\times\psi(\Omega^2))+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega_2\times\psi_1(\Omega_2^2\times\Omega)))\\&f_{\psi(\Omega^2\times2)}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega\times2))\\&f_{\psi(\Omega^2\times\omega)+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega^2))\\&f_{\psi(\Omega^2\times\psi(0))+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\psi_1(0)))\\&f_{\psi(\Omega^2\times\psi(\Omega^2))}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\psi_1(\Omega_2^2)))\\&f_{\psi(\Omega^2\times\psi(\Omega^2))+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\psi_1(\Omega_2^2\times\Omega)))\\&f_{\psi(\Omega^3)}(n)\sim\psi(\Omega_2^3)\\&f_{\psi(\Omega^4)}(n)\sim\psi(\Omega_2^4)\\&f_{\psi(\Omega^\omega)}(n)\sim\psi(\Omega_2^\omega)\\&f_{\psi(\Omega^\omega)+1}(n)\sim\psi(\Omega_2^\Omega)\\&f_{\psi(\Omega^\omega)+2}(n)\sim\psi(\Omega_2^\Omega\times\Omega)\\&f_{\psi(\Omega^\omega)\times2}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\omega))\\&f_{\psi(\Omega^\omega)\times2+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega))\\&f_{\psi(\Omega^\omega)\times2+2}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times\Omega)\\&f_{\psi(\Omega^\omega)^2+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)^{\psi_1(\Omega_2^\Omega)})\\&f_{\psi(\Omega^\omega+1)}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+1))\\&f_{\psi(\Omega^\omega+\psi(\Omega^\omega))+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)))\\&f_{\psi(\Omega^\omega+\Omega)+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\Omega_2\times\Omega))\\&f_{\psi(\Omega^\omega\times2)}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\Omega_2^\omega))\\&f_{\psi(\Omega^\omega\times2)+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times2))\\&f_{\psi(\Omega^\omega\times\psi(0))+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega)))\\&f_{\psi(\Omega^\omega\times\psi(\Omega^\omega))+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega^\Omega)))\\&f_{\psi(\Omega^{\omega+1})}(n)\sim\psi(\Omega_2^{\Omega+1})\\&f_{\psi(\Omega^{\omega\times2})+1}(n)\sim\psi(\Omega_2^{\Omega\times2})\\&f_{\psi(\Omega^{\omega^2})+1}(n)\sim\psi(\Omega_2^{\Omega^2})\\&f_{\psi(\Omega^{\omega^\omega})+1}(n)\sim\psi(\Omega_2^{\Omega^\Omega})\\&f_{\psi(\Omega^{\psi(0)})}(n)\sim\psi(\Omega_2^{\psi_1(0)})\\&f_{\psi(\Omega^{\psi(0)})+1}(n)\sim\psi(\Omega_2^{\psi_1(\Omega)})\\&f_{\psi(\Omega^{\psi(\Omega)})}(n)\sim\psi(\Omega_2^{\psi_1(\Omega_2)})\\&f_{\psi(\Omega^{\psi(\Omega^2)})}(n)\sim\psi(\Omega_2^{\psi_1(\Omega_2^2)})\\&f_{\psi(\Omega^{\psi(\Omega^{\psi(\Omega)})})}(n)\sim\psi(\Omega_2^{\psi_1(\Omega_2^{\psi_1(\Omega_2)})})\\&f_{\psi(\Omega^{\Omega})}(n)\sim\psi(\Omega_2^{\Omega_2})\\&f_{\psi(\Omega^{\Omega})+1}(n)\sim\psi(\Omega_2^{\Omega_2}\times\Omega)\\&f_{\psi(\Omega^{\Omega})\times2}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}))\\&f_{\psi(\Omega^{\Omega}+1)+1}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times\Omega+\Omega))\\&f_{\psi(\Omega^{\Omega}+\Omega)+1}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times\Omega+\Omega_2\times\Omega))\\&f_{\psi(\Omega^{\Omega}+\Omega^{\psi(\Omega^\Omega)})}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times\Omega+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}))\\&f_{\psi(\Omega^{\Omega}\times2)}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times\Omega\times2))\\&f_{\psi(\Omega^{\Omega}\times\psi(0))}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times\psi_1(0)))\\&f_{\psi(\Omega^{\Omega+1})}(n)\sim\psi(\Omega_2^{\Omega_2+1})\\&f_{\psi(\Omega^{\Omega+2})}(n)\sim\psi(\Omega_2^{\Omega_2+2})\\&f_{\psi(\Omega^{\Omega+\omega})+1}(n)\sim\psi(\Omega_2^{\Omega_2+\Omega})\\&f_{\psi(\Omega^{\Omega+\psi(\Omega^\Omega)})}(n)\sim\psi(\Omega_2^{\Omega_2+\psi_1(\Omega_2^{\Omega_2})})\\&f_{\psi(\Omega^{\Omega\times2})}(n)\sim\psi(\Omega_2^{\Omega_2\times2})\\&f_{\psi(\Omega^{\Omega^2})}(n)\sim\psi(\Omega_2^{\Omega_2^2})\\&f_{\psi(\Omega^{\Omega^\omega})}(n)\sim\psi(\Omega_2^{\Omega_2^\omega})\\&f_{\psi(\Omega^{\Omega^\omega})+1}(n)\sim\psi(\Omega_2^{\Omega_2^\Omega})\\&f_{\psi(\Omega^{\Omega^\Omega})}(n)\sim\psi(\Omega_2^{\Omega_2^{\Omega_2}})\\&f_{\psi(\psi_1(0))}(n)\sim\psi(\psi_2(0))\\&f_{\psi(\psi_1(0)\times\Omega)}(n)\sim\psi(\psi_2(0)\times\Omega_2)\\&f_{\psi(\psi_1(0)^2)}(n)\sim\psi(\psi_2(0)^2)\\&f_{\psi(\psi_1(0)^\Omega)}(n)\sim\psi(\psi_2(0)^{\Omega_2})\\&f_{\psi(\psi_1(0)^{\psi_1(0)})}(n)\sim\psi(\psi_2(0)^{\psi_2(0)})\\&f_{\psi(\psi_1(1))}(n)\sim\psi(\psi_2(1))\\&f_{\psi(\psi_1(\omega))+1}(n)\sim\psi(\psi_2(\Omega))\\&f_{\psi(\psi_1(\psi(0)))}(n)\sim\psi(\psi_2(\psi_1(0)))\\&f_{\psi(\psi_1(\psi(\Omega)))}(n)\sim\psi(\psi_2(\psi_1(\Omega_2)))\\&f_{\psi(\psi_1(\psi(\Omega^\Omega)))}(n)\sim\psi(\psi_2(\psi_1(\Omega_2^{\Omega_2})))\\&f_{\psi(\psi_1(\psi(\psi_1(0))))}(n)\sim\psi(\psi_2(\psi_1(\psi_2(0))))\\&f_{\psi(\psi_1(\Omega))}(n)\sim\psi(\psi_2(\Omega_2))\\&f_{\psi(\psi_1(\psi_1(0)))}(n)\sim\psi(\psi_2(\psi_2(0)))\\&f_{\psi(\Omega_2)}(n)\sim\psi(\Omega_3)\\&f_{\psi(\Omega_2)[n]}(f_{\psi(\Omega_2)}(n))\sim\psi(\Omega_3+\psi_2(\Omega_3))\\&f_{\psi(\Omega_2)[n+1]}(f_{\psi(\Omega_2)}(n))\sim\psi(\Omega_3+\psi_2(\Omega_3+\psi_2(\Omega_3)))\\&f_{\psi(\Omega_2)[n\times2]}(f_{\psi(\Omega_2)}(n))\sim\psi(\Omega_3\times2)\\&f_{\psi(\Omega_2)+1}(n)\sim\psi(\Omega_3\times\Omega)\\&f_{\psi(\Omega_2)+\psi(0)}(n)\sim\psi(\Omega_3\times\psi_1(0))\\&f_{\psi(\Omega_2)+\psi(\Omega)}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_2))\\&f_{\psi(\Omega_2)\times2}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3))\\&f_{\psi(\Omega_2)\times2+1}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega))\\&f_{\psi(\Omega_2)\times3+1}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega)^2)\\&f_{\psi(\Omega_2)^2+1}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega)^{\psi_1(\Omega_3\times\Omega)})\\&f_{\psi(\Omega_2+1)}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+1))\\&f_{\psi(\Omega_2+\Omega)}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+\Omega_2))\\&f_{\psi(\Omega_2+\psi_1(\Omega_2))}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+\psi_2(\Omega_3)))\\&f_{\psi(\Omega_2+\psi_1(\Omega_2))+1}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+\psi_2(\Omega_3\times\Omega)))\\&f_{\psi(\Omega_2+\psi_1(\Omega_2+1))}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+\psi_2(\Omega_3\times\Omega+1)))\\&f_{\psi(\Omega_2\times2)}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+\Omega_3))\\&f_{\psi(\Omega_2\times2)+1}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega\times2))\\&f_{\psi(\Omega_2\times\psi(\Omega_2))}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\psi_1(\Omega_3)))\\&f_{\psi(\Omega_2\times\Omega)}(n)\sim\psi(\Omega_3\times\Omega_2)\\&f_{\psi(\Omega_2\times\psi_1(0))}(n)\sim\psi(\Omega_3\times\psi_2(0))\\&f_{\psi(\Omega_2\times\psi_1(\Omega_2))}(n)\sim\psi(\Omega_3\times\psi_2(\Omega_3))\\&f_{\psi(\Omega_2^2)}(n)\sim\psi(\Omega_3^2)\\&f_{\psi(\Omega_2^{\Omega_2})}(n)\sim\psi(\Omega_3^{\Omega_3})\\&f_{\psi(\psi_2(0))}(n)\sim\psi(\psi_3(0))\\&f_{\psi(\Omega_3)}(n)\sim\psi(\Omega_4)\\&f_{\psi(\Omega_4)}(n)\sim\psi(\Omega_5)\\&\dots \\ \end{align}</nowiki> | <nowiki>\begin{align} & f_{\omega^\omega}(n)\sim\psi(\Omega^{\Omega^\omega})\\&f_3(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+1)\\&f_4^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega)\\&f_5^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^2)\\&f_n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^\omega)\\&f_{\omega}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\psi(\Omega^{\Omega^\omega})})\\&f_{\omega}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega})\\&f_{\omega+1}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega+1})\\&f_{\omega+n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega+\omega})\\&f_{\omega\times2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega\times2})\\&f_{\omega\times n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega\times\omega})\\&f_{\omega^2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega^2})\\&f_{\omega^3}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega^3})\\&f_{\omega^n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}\times2)\\&f_{\omega^n}^2(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}\times3)\\&f_{\omega^n}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}\times\omega)\\&f_{\omega^n+1}(f_{\omega^\omega}(n))=f_{\omega^n}^{f_{\omega^\omega}(n)}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}\times\psi(\Omega^{\Omega^\omega}))\\&f_{\omega^n+1}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+1})\\&f_{\omega^n+2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+2})\\&f_{\omega^n+n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+\omega})\\&f_{\omega^n+\omega}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+\Omega})\\&f_{\omega^n+\omega\times2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+\Omega\times2})\\&f_{\omega^n+\omega^2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+\Omega^2})\\&f_{\omega^n\times2}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega\times2})\\&f_{\omega^n\times3}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega\times3})\\&f_{\omega^n\times n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega\times\omega})\\&f_{\omega^{n+1}}(f_{\omega^\omega}(n))=f_{\omega^n\times f_{\omega^\omega}(n)}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}})\\&f_{\omega^n}(f_{\omega^{n+1}}(f_{\omega^\omega}(n)))\sim\psi(\Omega^{\Omega^{\omega+1}}+\Omega^{\Omega^\omega})\\&f_{\omega^n+1}^n(f_{\omega^{n+1}}(f_{\omega^\omega}(n)))\sim\psi(\Omega^{\Omega^{\omega+1}}+\Omega^{\Omega^\omega+1})\\&f_{\omega^n\times n}(f_{\omega^{n+1}}(f_{\omega^\omega}(n)))\sim\psi(\Omega^{\Omega^{\omega+1}}+\Omega^{\Omega^\omega\times\omega})\\&f_{\omega^{n+1}}^2(f_{\omega^\omega}(n))=f_{\omega^n\times f_{\omega^{n+1}}(f_{\omega^\omega}(n))}(f_{\omega^{n+1}}(f_{\omega^\omega}(n)))\sim\psi(\Omega^{\Omega^{\omega+1}}\times2)\\&f_{\omega^{n+1}}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}}\times\omega)\\&f_{\omega^{n+1}+1}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}+1})\\&f_{\omega^{n+1}+\omega^n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}+\Omega^\omega})\\&f_{\omega^{n+1}\times2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}\times2})\\&f_{\omega^{n+1}\times n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}\times\omega})\\&f_{\omega^{n+2}}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+2}})\\&f_{\omega^{n\times2}}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega\times2}})\\&f_{\omega^{n^2}}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega^2}})\\&f_{\omega^{f_3(n)}}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\psi(0)}})\\&f_{\omega^\omega}^2(n)=f_{\omega^{f_{\omega^\omega}(n)}}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\psi(\Omega^{\Omega^\omega})}})\\&f_{\omega^\omega}^3(n)\sim\psi(\Omega^{\Omega^{\psi(\Omega^{\Omega^{\psi(\Omega^{\Omega^\omega})}})}})\\&f_{\omega^\omega+1}(n)=f_{\omega^\omega}^n(n)\sim\psi(\Omega^{\Omega^{\Omega}})\\&f_{\omega^\omega+2}(n)\sim\psi(\Omega^{\Omega^\Omega+1})\\&f_{\omega^\omega+3}(n)\sim\psi(\Omega^{\Omega^\Omega+2})\\&f_{\omega^\omega+\omega}(n)\sim\psi(\Omega^{\Omega^\Omega+\omega})\\&f_{\omega^\omega+\omega+1}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega})\\&f_{\omega^\omega+\omega\times2}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega+\omega})\\&f_{\omega^\omega+\omega\times2+1}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega\times2})\\&f_{\omega^\omega+\omega^2}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega\times\omega})\\&f_{\omega^\omega+\omega^2+1}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega^2})\\&f_{\omega^\omega+\omega^3+1}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega^3})\\&f_{\omega^\omega\times2}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega^\omega})\\&f_{\omega^\omega\times2+1}(n)\sim\psi(\Omega^{\Omega^\Omega\times2})\\&f_{\omega^\omega\times3+1}(n)\sim\psi(\Omega^{\Omega^\Omega\times3})\\&f_{\omega^{\omega+1}}(n)\sim\psi(\Omega^{\Omega^\Omega\times\omega})\\&f_{\omega^{\omega+1}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega+1}})\\&f_{\omega^{\omega+1}+\omega+1}(n)\sim\psi(\Omega^{\Omega^{\Omega+1}+\Omega})\\&f_{\omega^{\omega+1}+\omega^\omega+1}(n)\sim\psi(\Omega^{\Omega^{\Omega+1}+\Omega^\Omega})\\&f_{\omega^{\omega+1}\times2+1}(n)\sim\psi(\Omega^{\Omega^{\Omega+1}\times2})\\&f_{\omega^{\omega+2}}(n)\sim\psi(\Omega^{\Omega^{\Omega+1}\times\omega})\\&f_{\omega^{\omega+2}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega+2}})\\&f_{\omega^{\omega\times2}}(n)\sim\psi(\Omega^{\Omega^{\Omega+\omega}})\\&f_{\omega^{\omega\times2}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega\times2}})\\&f_{\omega^{\omega\times3}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega\times3}})\\&f_{\omega^{\omega^2}}(n)\sim\psi(\Omega^{\Omega^{\Omega\times\omega}})\\&f_{\omega^{\omega^2}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^2}})\\&f_{\omega^{\omega^2}\times2+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^2}\times2})\\&f_{\omega^{\omega^2+1}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^2+1}})\\&f_{\omega^{\omega^2+\omega}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^2+\Omega}})\\&f_{\omega^{\omega^2\times2}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^2\times2}})\\&f_{\omega^{\omega^3}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^3}})\\&f_{\omega^{\omega^\omega}}(n)\sim\psi(\Omega^{\Omega^{\Omega^\omega}})\\&f_{\omega^{\omega^\omega}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^\Omega}})\\&f_{\omega^{\omega^{\omega^\omega}}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^{\Omega^\Omega}}})\\&f_{\psi(0)}(n)\sim\psi(\psi_1(0))\\&f_3(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+1)\\&f_4^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega)\\&f_n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^\omega)\\&f_\omega(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\psi(\psi_1(0))})\\&f_\omega^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega})\\&f_{\omega+1}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega+1})\\&f_{\omega\times2}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega\times2})\\&f_{\omega^\omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega^\Omega})\\&f_{\omega^\omega+1}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega^\Omega+1})\\&f_{\omega^{\omega^\omega}}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega^{\Omega^\Omega}})\\&f_{\omega^{\omega^{\omega^\omega}}}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega^{\Omega^{\Omega^\Omega}}})\\&f_{\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times2)\\&f_{\psi(0)[n]}^2(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times3)\\&f_{\psi(0)[n]}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\omega)\\&f_{\psi(0)[n]+1}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\psi(\psi_1(0)))\\&f_{\psi(0)[n]+1}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega)\\&f_{\psi(0)[n]}(f_{\psi(0)[n]+1}^n(f_{\psi(0)}(n)))\sim\psi(\psi_1(0)\times\Omega+\psi_1(0))\\&f_{\psi(0)[n]+1}^{n+1}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega+\psi_1(0)\times\psi(\psi_1(0)\times\Omega))\\&f_{\psi(0)[n]+1}^{n\times2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega\times2)\\&f_{\psi(0)[n]+2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega\times\psi(\psi_1(0)))\\&f_{\psi(0)[n]+2}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega^2)\\&f_{\psi(0)[n]+n}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega^\omega)\\&f_{\psi(0)[n]+\omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega^\Omega)\\&f_{\psi(0)[n]\times2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^2)\\&f_{\psi(0)[n]\times n}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^\omega)\\&f_{\psi(0)[n]\times \omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^\Omega)\\&f_{\psi(0)[n]\times \omega^2}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\Omega^2})\\&f_{\psi(0)[n]\times \omega^\omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\Omega^\Omega})\\&f_{\psi(0)[n]^2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)})\\&f_{\psi(0)[n]^2+\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)+1})\\&f_{\psi(0)[n]^2\times2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)\times2})\\&f_{\psi(0)[n]^2\times n}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)\times\omega})\\&f_{\psi(0)[n]^2\times \omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)\times\Omega})\\&f_{\psi(0)[n]^3}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^2})\\&f_{\psi(0)[n]^n}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^\omega})\\&f_{\psi(0)[n]^\omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^\Omega})\\&f_{\psi(0)[n]^{\psi(0)[n]}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}})\\&f_{\psi(0)[n+1]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}})\\&f_{\psi(0)[n+1]+\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}+1})\\&f_{\psi(0)[n+1]+\psi(0)[n]^2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}+\psi_1(0)})\\&f_{\psi(0)[n+1]+\psi(0)[n]^\omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}+\psi_1(0)^\Omega})\\&f_{\psi(0)[n+1]\times2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}\times2})\\&f_{\psi(0)[n+1]\times\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)+1}})\\&f_{\psi(0)[n+1]\times\psi(0)[n]^2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)+2}})\\&f_{\psi(0)[n+1]^2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)\times2}})\\&f_{\psi(0)[n+1]^{\psi(0)[n]}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^2}})\\&f_{\psi(0)[n+1]^{\psi(0)[n]+1}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^2+\psi_1(0)}})\\&f_{\psi(0)[n+1]^{\psi(0)[n]\times2}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^2\times2}})\\&f_{\psi(0)[n+1]^{\psi(0)[n]^2}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^3}})\\&f_{\psi(0)[n+2]}(f_{\psi(0)}(n))=f_{\psi(0)[n+1]^{\psi(0)[n+1]}}(f_{\psi(0)}(n))=f_{\psi(0)[n+1]^{\psi(0)[n]^{\psi(0)[n]}}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^{\psi_1(0)}}})\\&f_{\psi(0)[n+3]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^{\psi_1(0)^{\psi_1(0)}}}})\\&f_{\psi(0)[n\times2]}(f_{\psi(0)}(n))\sim\psi(\psi_1(1))\\&f_{\psi(0)[n]}(f_{\psi(0)[n\times2]}(f_{\psi(0)}(n)))\sim\psi(\psi_1(1)+\psi_1(0))\\&f_{\psi(0)[n\times2]}^2(f_{\psi(0)}(n))\sim\psi(\psi_1(1)\times2)\\&f_{\psi(0)[n\times2]+\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)\times\psi_1(0))\\&f_{\psi(0)[n\times2]+\psi(0)[n+1]}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)\times\psi_1(0)^{\psi_1(0)^{\psi_1(0)}})\\&f_{\psi(0)[n\times2]\times2}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)^2)\\&f_{\psi(0)[n\times2]\times\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)^{\psi_1(0)})\\&f_{\psi(0)[n\times2]^2}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)^{\psi_1(1)})\\&f_{\psi(0)[n\times2]^3}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)^{\psi_1(1)^2})\\&f_{\psi(0)[n\times2+1]}(f_{\psi(0)}(n))=f_{\psi(0)[n\times2]^{\psi(0)[n\times2]}}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)^{\psi_1(1)^{\psi_1(1)}})\\&f_{\psi(0)[n\times3]}(f_{\psi(0)}(n))\sim\psi(\psi_1(2))\\&f_{\psi(0)[n^2]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\omega))\\&f_{\psi(0)[n^2+n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\omega+1))\\&f_{\psi(0)[n^3]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\omega^2))\\&f_{\psi(0)[n^n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\omega^\omega))\\&f_{\psi(0)[f_3(n)]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\psi(0)))\\&f_{\psi(0)}^2(n)=f_{\psi(0)[f_{\psi(0)}(n)]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\psi(\psi_1(0))))\\&f_{\psi(0)[n]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)))\times\psi_1(0))\\&f_{\psi(0)[n\times2]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)))\times\psi_1(1))\\&f_{\psi(0)[f_{\psi(0)}(n)]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)))^2)\\&f_{\psi(0)[f_{\psi(0)}(n)+1]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)))^{\psi_1(\psi(\psi_1(0)))^{\psi_1(\psi(\psi_1(0)))}})\\&f_{\psi(0)[f_{\psi(0)}(n)+n]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0))+1))\\&f_{\psi(0)[f_{\psi(0)}(n)\times2]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0))\times2))\\&f_{\psi(0)[f_3(f_{\psi(0)}(n))]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)+1)))\\&f_{\psi(0)[f_{\psi(0)[n]}(f_{\psi(0)}(n))]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)\times2)))\\&f_{\psi(0)[f_{\psi(0)[n\times2]}(f_{\psi(0)}(n))]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(1))))\\&f_{\psi(0)[f_{\psi(0)[n^2]}(f_{\psi(0)}(n))]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(\omega))))\\&f_{\psi(0)}^3(n)\sim\psi(\psi_1(\psi(\psi_1(\psi(\psi_1(0))))))\\&f_{\psi(0)+1}(n)\sim\psi(\psi_1(\Omega))\\&f_{\psi(0)[n]}(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)+\psi_1(0))\\&f_{\psi(0)[n\times2]}(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)+\psi_1(1))\\&f_{\psi(0)[f_{\psi(0)}(n)]}(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)+\psi_1(\psi(\psi_1(0))))\\&f_{\psi(0)}(f_{\psi(0)+1}(n))=f_{\psi(0)[f_{\psi(0)+1}(n)]}(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)+\psi_1(\psi(\psi_1(\Omega))))\\&f_{\psi(0)}^2(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)+\psi_1(\psi(\psi_1(\Omega)+\psi_1(\psi(\psi_1(\Omega))))))\\&f_{\psi(0)}^n(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)\times2)\\&f_{\psi(0)}^{n^2}(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)\times\omega)\\&f_{\psi(0)+1}^2(n)\sim\psi(\psi_1(\Omega)\times\psi(\psi_1(\Omega)))\\&f_{\psi(0)+2}(n)\sim\psi(\psi_1(\Omega)\times\Omega)\\&f_{\psi(0)+3}(n)\sim\psi(\psi_1(\Omega)\times\Omega^2)\\&f_{\psi(0)+\omega}(n)\sim\psi(\psi_1(\Omega)\times\Omega^\omega)\\&f_{\psi(0)+\omega+1}(n)\sim\psi(\psi_1(\Omega)\times\Omega^\Omega)\\&f_{\psi(0)+\omega^\omega+1}(n)\sim\psi(\psi_1(\Omega)\times\Omega^{\Omega^\Omega})\\&f_{\psi(0)\times2}(n)\sim\psi(\psi_1(\Omega)\times\psi_1(0))\\&f_{\psi(0)\times2+1}(n)\sim\psi(\psi_1(\Omega)^2)\\&f_{\psi(0)\times3+1}(n)\sim\psi(\psi_1(\Omega)^3)\\&f_{\psi(0)\times\omega}(n)\sim\psi(\psi_1(\Omega)^\omega)\\&f_{\psi(0)\times\omega+1}(n)\sim\psi(\psi_1(\Omega)^\Omega)\\&f_{\psi(0)^2}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(0)})\\&f_{\psi(0)^2+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)})\\&f_{\psi(0)^2+\psi(0)+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)+1})\\&f_{\psi(0)^2\times2+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)\times2})\\&f_{\psi(0)^3+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)^2})\\&f_{\psi(0)^\omega+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)^\Omega})\\&f_{\psi(0)^{\psi(0)}}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)^{\psi_1(0)}})\\&f_{\psi(0)^{\psi(0)}+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)^{\psi_1(\Omega)}})\\&f_{\psi(1)}(n)\sim\psi(\psi_1(\Omega+1))\\&f_{\psi(0)[n]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)+\psi_1(0))\\&f_{\psi(0)}^n(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)+\psi_1(\Omega))\\&f_{\psi(0)^{\psi(0)}}^n(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)+\psi_1(\Omega)^{\psi_1(\Omega)^{\psi_1(\Omega)}})\\&f_{\psi(1)[n]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times2)\\&f_{\psi(1)[n]}^2(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times3)\\&f_{\psi(1)[n]+1}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times\psi(\psi_1(\Omega+1)))\\&f_{\psi(1)[n]+1}^n(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times\Omega)\\&f_{\psi(1)[n]+\psi(0)[n]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times\psi_1(0))\\&f_{\psi(1)[n]+\psi(0)}^n(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times\psi_1(\Omega))\\&f_{\psi(1)[n]\times2}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)^2)\\&f_{\psi(1)[n]\times\psi(0)[n]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)^{\psi_1(0)})\\&f_{\psi(1)[n]^2}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)^{\psi_1(\Omega+1)})\\&f_{\psi(1)[n+1]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)^{\psi_1(\Omega+1)^{\psi_1(\Omega+1)}})\\&f_{\psi(1)[n\times2]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+2))\\&f_{\psi(1)}^2(n)\sim\psi(\psi_1(\Omega+\psi(\psi_1(\Omega))))\\&f_{\psi(1)+1}(n)\sim\psi(\psi_1(\Omega\times2))\\&f_{\psi(1)+2}(n)\sim\psi(\psi_1(\Omega\times2)\times\Omega)\\&f_{\psi(1)+\psi(0)+1}(n)\sim\psi(\psi_1(\Omega\times2)\times\psi_1(\Omega))\\&f_{\psi(1)\times2+1}(n)\sim\psi(\psi_1(\Omega\times2)^2)\\&f_{\psi(1)\times{\psi(0)}+1}(n)\sim\psi(\psi_1(\Omega\times2)^{\psi_1(\Omega)})\\&f_{\psi(1)^{2}+1}(n)\sim\psi(\psi_1(\Omega\times2)^{\psi_1(\Omega\times2)})\\&f_{\psi(1)^{\psi(1)}+1}(n)\sim\psi(\psi_1(\Omega\times2)^{\psi_1(\Omega\times2)^{\psi_1(\Omega\times2)}})\\&f_{\psi(2)}(n)\sim\psi(\psi_1(\Omega\times2+1))\\&f_{\psi(2)+1}(n)\sim\psi(\psi_1(\Omega\times3))\\&f_{\psi(3)}(n)\sim\psi(\psi_1(\Omega\times3+1))\\&f_{\psi(4)}(n)\sim\psi(\psi_1(\Omega\times4+1))\\&f_{\psi(\omega)}(n)\sim\psi(\psi_1(\Omega\times\omega))\\&f_{\psi(\omega)+1}(n)\sim\psi(\psi_1(\Omega^2))\\&f_{\psi(\omega)+2}(n)\sim\psi(\psi_1(\Omega^2)\times\Omega)\\&f_{\psi(\omega)\times2+1}(n)\sim\psi(\psi_1(\Omega^2)^2)\\&f_{\psi(\omega)^2+1}(n)\sim\psi(\psi_1(\Omega^2)^{\psi_1(\Omega^2)})\\&f_{\psi(\omega+1)}(n)\sim\psi(\psi_1(\Omega^2+1))\\&f_{\psi(\omega+1)+1}(n)\sim\psi(\psi_1(\Omega^2+\Omega))\\&f_{\psi(\omega+2)+1}(n)\sim\psi(\psi_1(\Omega^2+\Omega\times2))\\&f_{\psi(\omega\times2)+1}(n)\sim\psi(\psi_1(\Omega^2\times2))\\&f_{\psi(\omega^2)+1}(n)\sim\psi(\psi_1(\Omega^3))\\&f_{\psi(\omega^\omega)}(n)\sim\psi(\psi_1(\Omega^\omega))\\&f_{\psi(\omega^\omega)+1}(n)\sim\psi(\psi_1(\Omega^\Omega))\\&f_{\psi(\omega^{\omega^\omega})+1}(n)\sim\psi(\psi_1(\Omega^{\Omega^\Omega}))\\&f_{\psi(\psi(0))}(n)\sim\psi(\psi_1(\psi_1(0)))\\&f_{\psi(\psi(0))+1}(n)\sim\psi(\psi_1(\psi_1(\Omega)))\\&f_{\psi(\psi(1))+1}(n)\sim\psi(\psi_1(\psi_1(\Omega\times2)))\\&f_{\psi(\psi(\psi(0)))+1}(n)\sim\psi(\psi_1(\psi_1(\psi_1(\Omega))))\\&f_{\psi(\Omega)}(n)\sim\psi(\Omega_2)\\&f_{3}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+1)\\&f_{\omega}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\Omega^\Omega)\\&f_{\psi(0)[n]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(0))\\&f_{\psi(0)}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega))\\&f_{\psi(1)[n]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega+1))\\&f_{\psi(1)}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega\times2))\\&f_{\psi(\omega)}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega^2))\\&f_{\psi(\psi(0))}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\psi_1(\Omega)))\\&f_{\psi(\psi(\psi(0)))}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\psi_1(\psi_1(\Omega))))\\&f_{\psi(\Omega)[n]}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)\times\omega)\\&f_{\psi(\Omega)[n]+1}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)\times\Omega)\\&f_{\psi(\Omega)[n]\times2}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)^2)\\&f_{\psi(\Omega)[n]\times \omega}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)^\Omega)\\&f_{\psi(\Omega)[n]\times \psi(0)+1}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)^{\psi_1(\Omega)})\\&f_{\psi(\Omega)[n]^2}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)^{\psi_1(\Omega_2)})\\&f_{\psi(\Omega)[n]^{\psi(\Omega)[n]}}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)^{\psi_1(\Omega_2)^{\psi_1(\Omega_2)}})\\&f_{\psi(\psi(\Omega)[n-1]+1)[n]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+1))\\&f_{\psi(\psi(\Omega)[n-1]+1)}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\Omega))\\&f_{\psi(\psi(\Omega)[n-1]+n)}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\Omega\times\omega))\\&f_{\psi(\psi(\Omega)[n-1]+\omega)}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\Omega^2))\\&f_{\psi(\psi(\Omega)[n-1]+\psi(0))}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega)))\\&f_{\psi(\psi(\Omega)[n-1]+\psi(\psi(0)))}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\psi_1(\Omega))))\\&f_{\psi(\Omega)[n+1]}(f_{\psi(\Omega)}(n))=f_{\psi(\psi(\Omega)[n])}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)))\\&f_{\psi(\psi(\Omega)[n]+1)}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)+1))\\&f_{\psi(\psi(\Omega)[n]\times2)}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)\times2))\\&f_{\psi(\psi(\Omega)[n]^2)}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)^2))\\&f_{\psi(\psi(\psi(\Omega)[n-1]+1))}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2+1)))\\&f_{\psi(\Omega)[n+2]}(f_{\psi(\Omega)}(n))=f_{\psi(\psi(\psi(\Omega)[n]))}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2))))\\&f_{\psi(\Omega)[n\times2]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2)\\&f_{\psi(\Omega)[n]}(f_{\psi(\Omega)[n\times2]}(f_{\psi(\Omega)}(n)))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2))\\&f_{\psi(\Omega)[n\times2]}^2(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2))\\&f_{\psi(\Omega)[n\times2]+1}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2)\times\Omega)\\&f_{\psi(\Omega)[n\times2]\times2}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2)^2)\\&f_{\psi(\Omega)[n\times2]^2}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2)^{\psi_!(\Omega_2\times2)})\\&f_{\psi(\psi(\Omega)[n\times2-1]+1)}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2+1))\\&f_{\psi(\Omega)[n\times2+1]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2+\psi_1(\Omega_2\times2)))\\&f_{\psi(\Omega)[n\times3]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times3)\\&f_{\psi(\Omega)[n^2]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\omega)\\&f_{\psi(\Omega)[n^2+1]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\omega+\psi_1(\Omega_2\times\omega+\psi_1(\Omega_2\times\omega)))\\&f_{\psi(\Omega)[n^2+n]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\omega+\Omega_2)\\&f_{\psi(\Omega)[n^3]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\omega^2)\\&f_{\psi(\Omega)[f_3(n)]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\psi(0))\\&f_{\psi(\Omega)}^2(n)=f_{\psi(\Omega)[f_{\psi(\Omega)}(n)]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\psi(\Omega_2))\\&f_{\psi(\Omega)}^3(n)\sim\psi(\Omega_2\times\psi(\Omega_2\times\psi(\Omega_2)))\\&f_{\psi(\Omega)+1}(n)=f_{\psi(\Omega)}^n(n)\sim\psi(\Omega_2\times\Omega)\\&f_{\psi(\Omega)}(f_{\psi(\Omega)+1}(n))\sim\psi(\Omega_2\times\Omega+\Omega_2\times\psi(\Omega_2\times\Omega))\\&f_{\psi(\Omega)}^n(f_{\psi(\Omega)+1}(n))\sim\psi(\Omega_2\times\Omega\times2)\\&f_{\psi(\Omega)+1}^2(n)\sim\psi(\Omega_2\times\Omega\times\psi(\Omega_2\times\Omega))\\&f_{\psi(\Omega)+2}(n)\sim\psi(\Omega_2\times\Omega^2)\\&f_{\psi(\Omega)+\omega}(n)\sim\psi(\Omega_2\times\Omega^\omega)\\&f_{\psi(\Omega)+\omega+1}(n)\sim\psi(\Omega_2\times\Omega^\Omega)\\&f_{\psi(\Omega)+\omega^\omega+1}(n)\sim\psi(\Omega_2\times\Omega^{\Omega^\Omega})\\&f_{\psi(\Omega)+\psi(0)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega))\\&f_{\psi(\Omega)+\psi(1)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega\times2))\\&f_{\psi(\Omega)+\psi(\psi(0))+1}(n)\sim\psi(\Omega_2\times\psi_1(\psi_1(\Omega)))\\&f_{\psi(\Omega)\times2}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2))\\&f_{\psi(\Omega)}^n(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)+\Omega_2\times\Omega)\\&f_{\psi(\Omega)+\psi(0)}^n(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)+\Omega_2\times\psi_1(\Omega))\\&f_{\psi(\Omega)+\psi(\Omega)[n]}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)\times2)\\&f_{\psi(\Omega)+\psi(\Omega)[n]}^2(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)\times3)\\&f_{\psi(\Omega)+\psi(\Omega)[n]+1}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)\times\psi(\Omega_2\times\psi_1(\Omega_2)))\\&f_{\psi(\Omega)+\psi(\Omega)[n]+1}^n(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)\times\Omega)\\&f_{\psi(\Omega)+\psi(\Omega)[n]\times2}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)^2)\\&f_{\psi(\Omega)+\psi(\psi(\Omega)[n-1]+1)[n]}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2+1))\\&f_{\psi(\Omega)+\psi(\Omega)[n+1]}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2+\psi_1(\Omega_2)))\\&f_{\psi(\Omega)+\psi(\Omega)[n\times2]}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2\times2))\\&f_{\psi(\Omega)\times2}^2(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi(\Omega_2\times\psi_1(\Omega_2))))\\&f_{\psi(\Omega)\times2+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega))\\&f_{\psi(\Omega)\times2}(f_{\psi(\Omega)\times2+1}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)+\Omega_2\times\psi_1(\Omega_2\times\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega))))\\&f_{\psi(\Omega)\times2}^n(f_{\psi(\Omega)\times2+1}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)\times2)\\&f_{\psi(\Omega)\times2+1}^2(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)\times\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)))\\&f_{\psi(\Omega)\times2+2}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)\times\Omega)\\&f_{\psi(\Omega)\times3}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)\times\psi_1(\Omega_2))\\&f_{\psi(\Omega)\times3+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^2)\\&f_{\psi(\Omega)\times\omega+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^\Omega)\\&f_{\psi(\Omega)\times\omega+\psi(\Omega)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^{\Omega+1})\\&f_{\psi(\Omega)\times\psi(0)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^{\psi_1(0)})\\&f_{\psi(\Omega)^2}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^{\psi_1(\Omega_2)})\\&f_{\psi(\Omega)^2+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^{\psi_1(\Omega_2\times\Omega)})\\&f_{\psi(\Omega)^{\psi(\Omega)}+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^{\psi_1(\Omega_2\times\Omega)^{\psi_1(\Omega_2\times\Omega)}})\\&f_{\psi(\Omega+1)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+1))\\&f_{\psi(\Omega+1)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\Omega))\\&f_{\psi(\Omega+2)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\Omega+1))\\&f_{\psi(\Omega+2)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\Omega\times2))\\&f_{\psi(\Omega+\omega)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\Omega^2))\\&f_{\psi(\Omega+\psi(0))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(0)))\\&f_{\psi(\Omega+\psi(0))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega)))\\&f_{\psi(\Omega+\psi(\Omega))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2)))\\&f_{\psi(\Omega+\psi(\Omega))[n\times2]}(f_{\psi(\Omega+\psi(\Omega))}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times2)))\\&f_{\psi(\Omega+\psi(\Omega))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times\Omega)))\\&f_{\psi(\Omega+\psi(\Omega)+1)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times\Omega)+1))\\&f_{\psi(\Omega+\psi(\Omega+1))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times\Omega+1)))\\&f_{\psi(\Omega+\psi(\Omega+\psi(\Omega)))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times\Omega))))\\&f_{\psi(\Omega\times2)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\Omega_2))\\&f_{\psi(\Omega\times2)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2))\\&f_{\psi(\Omega\times2)\times2+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2)^2)\\&f_{\psi(\Omega\times2+1)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2+1))\\&f_{\psi(\Omega\times2+1)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2+\Omega))\\&f_{\psi(\Omega\times2+\psi(\Omega\times2))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2+\psi_1(\Omega_2\times\Omega\times2)))\\&f_{\psi(\Omega\times3)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2+\Omega_2))\\&f_{\psi(\Omega\times3)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times3))\\&f_{\psi(\Omega\times\omega)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times\omega))\\&f_{\psi(\Omega\times\omega)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^2))\\&f_{\psi(\Omega\times\omega+1)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^2+1))\\&f_{\psi(\Omega\times\omega+\Omega)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^2+\Omega_2\times\Omega))\\&f_{\psi(\Omega\times\omega\times2)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^2\times2))\\&f_{\psi(\Omega\times\omega^2)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^3))\\&f_{\psi(\Omega\times\omega^\omega)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^\Omega))\\&f_{\psi(\Omega\times\psi(0))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(0)))\\&f_{\psi(\Omega\times\psi(0))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega)))\\&f_{\psi(\Omega\times\psi(1))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega+1)))\\&f_{\psi(\Omega\times\psi(\Omega))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2)))\\&f_{\psi(\Omega\times\psi(\Omega))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2\times\Omega)))\\&f_{\psi(\Omega\times\psi(\Omega+1))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2\times\Omega+1)))\\&f_{\psi(\Omega\times\psi(\Omega\times2))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2)))\\&f_{\psi(\Omega\times\psi(\Omega\times\psi(0)))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2\times\psi_1(0))))\\&f_{\psi(\Omega\times\psi(\Omega\times\psi(\Omega)))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2))))\\&f_{\psi(\Omega^2)}(n)\sim\psi(\Omega_2^2)\\&f_{\psi(\Omega^2)[n]}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\psi_1(\Omega^2_2))\\&f_{\psi(\Omega\times\psi(\Omega^2)[n-1]+1)}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\psi_1(\Omega^2_2+1))\\&\psi(\Omega^2)[n]=\psi(\Omega\times\psi(\Omega^2)[n-1]) \\&f_{\psi(\Omega\times\psi(\Omega^2)[n-1]+\Omega)[n]}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\Omega_2)\\&f_{\psi(\Omega\times\psi(\Omega^2)[n-1]+\Omega)}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\Omega_2\times\Omega)\\&f_{\psi(\Omega\times\psi(\Omega^2)[n-1]+\Omega\times\psi(\Omega))}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\Omega_2\times\psi_1(\Omega_2))\\&f_{\psi(\Omega^2)[n+1]}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\Omega_2\times\psi_1(\Omega_2^2))\\&f_{\psi(\Omega^2)[n\times2]}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2\times2)\\&f_{\psi(\Omega^2)+1}(n)\sim\psi(\Omega^2_2\times\Omega)\\&f_{\psi(\Omega^2)+2}(n)\sim\psi(\Omega^2_2\times\Omega^2)\\&f_{\psi(\Omega^2)+\psi(0)}(n)\sim\psi(\Omega^2_2\times\psi_1(0))\\&f_{\psi(\Omega^2)+\psi(\Omega)}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2))\\&f_{\psi(\Omega^2)+\psi(\Omega\times\psi(\Omega))}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2)))\\&f_{\psi(\Omega^2)\times2}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2))\\&f_{\psi(\Omega^2)\times2+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega))\\&f_{\psi(\Omega^2)^2+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega)^{\psi_1(\Omega^2_2\times\Omega)})\\&f_{\psi(\Omega^2+1)}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+1))\\&f_{\psi(\Omega^2+1)+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega))\\&f_{\psi(\Omega^2+\psi(\Omega^2))+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\psi_1(\Omega^2_2\times\Omega)))\\&f_{\psi(\Omega^2+\Omega)}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega_2))\\&f_{\psi(\Omega^2+\Omega)+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega_2\times\Omega))\\&f_{\psi(\Omega^2+\Omega\times2)+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega_2\times\Omega\times2))\\&f_{\psi(\Omega^2+\Omega\times\psi(0))+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega_2\times\psi_1(\Omega)))\\&f_{\psi(\Omega^2+\Omega\times\psi(\Omega^2))+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega_2\times\psi_1(\Omega_2^2\times\Omega)))\\&f_{\psi(\Omega^2\times2)}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega\times2))\\&f_{\psi(\Omega^2\times\omega)+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega^2))\\&f_{\psi(\Omega^2\times\psi(0))+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\psi_1(0)))\\&f_{\psi(\Omega^2\times\psi(\Omega^2))}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\psi_1(\Omega_2^2)))\\&f_{\psi(\Omega^2\times\psi(\Omega^2))+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\psi_1(\Omega_2^2\times\Omega)))\\&f_{\psi(\Omega^3)}(n)\sim\psi(\Omega_2^3)\\&f_{\psi(\Omega^4)}(n)\sim\psi(\Omega_2^4)\\&f_{\psi(\Omega^\omega)}(n)\sim\psi(\Omega_2^\omega)\\&f_{\psi(\Omega^\omega)+1}(n)\sim\psi(\Omega_2^\Omega)\\&f_{\psi(\Omega^\omega)+2}(n)\sim\psi(\Omega_2^\Omega\times\Omega)\\&f_{\psi(\Omega^\omega)\times2}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\omega))\\&f_{\psi(\Omega^\omega)\times2+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega))\\&f_{\psi(\Omega^\omega)\times2+2}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times\Omega)\\&f_{\psi(\Omega^\omega)^2+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)^{\psi_1(\Omega_2^\Omega)})\\&f_{\psi(\Omega^\omega+1)}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+1))\\&f_{\psi(\Omega^\omega+\psi(\Omega^\omega))+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)))\\&f_{\psi(\Omega^\omega+\Omega)+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\Omega_2\times\Omega))\\&f_{\psi(\Omega^\omega\times2)}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\Omega_2^\omega))\\&f_{\psi(\Omega^\omega\times2)+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times2))\\&f_{\psi(\Omega^\omega\times\psi(0))+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega)))\\&f_{\psi(\Omega^\omega\times\psi(\Omega^\omega))+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega^\Omega)))\\&f_{\psi(\Omega^{\omega+1})}(n)\sim\psi(\Omega_2^{\Omega+1})\\&f_{\psi(\Omega^{\omega\times2})+1}(n)\sim\psi(\Omega_2^{\Omega\times2})\\&f_{\psi(\Omega^{\omega^2})+1}(n)\sim\psi(\Omega_2^{\Omega^2})\\&f_{\psi(\Omega^{\omega^\omega})+1}(n)\sim\psi(\Omega_2^{\Omega^\Omega})\\&f_{\psi(\Omega^{\psi(0)})}(n)\sim\psi(\Omega_2^{\psi_1(0)})\\&f_{\psi(\Omega^{\psi(0)})+1}(n)\sim\psi(\Omega_2^{\psi_1(\Omega)})\\&f_{\psi(\Omega^{\psi(\Omega)})}(n)\sim\psi(\Omega_2^{\psi_1(\Omega_2)})\\&f_{\psi(\Omega^{\psi(\Omega^2)})}(n)\sim\psi(\Omega_2^{\psi_1(\Omega_2^2)})\\&f_{\psi(\Omega^{\psi(\Omega^{\psi(\Omega)})})}(n)\sim\psi(\Omega_2^{\psi_1(\Omega_2^{\psi_1(\Omega_2)})})\\&f_{\psi(\Omega^{\Omega})}(n)\sim\psi(\Omega_2^{\Omega_2})\\&f_{\psi(\Omega^{\Omega})+1}(n)\sim\psi(\Omega_2^{\Omega_2}\times\Omega)\\&f_{\psi(\Omega^{\Omega})\times2}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}))\\&f_{\psi(\Omega^{\Omega}+1)+1}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times\Omega+\Omega))\\&f_{\psi(\Omega^{\Omega}+\Omega)+1}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times\Omega+\Omega_2\times\Omega))\\&f_{\psi(\Omega^{\Omega}+\Omega^{\psi(\Omega^\Omega)})}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times\Omega+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}))\\&f_{\psi(\Omega^{\Omega}\times2)}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times\Omega\times2))\\&f_{\psi(\Omega^{\Omega}\times\psi(0))}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times\psi_1(0)))\\&f_{\psi(\Omega^{\Omega+1})}(n)\sim\psi(\Omega_2^{\Omega_2+1})\\&f_{\psi(\Omega^{\Omega+2})}(n)\sim\psi(\Omega_2^{\Omega_2+2})\\&f_{\psi(\Omega^{\Omega+\omega})+1}(n)\sim\psi(\Omega_2^{\Omega_2+\Omega})\\&f_{\psi(\Omega^{\Omega+\psi(\Omega^\Omega)})}(n)\sim\psi(\Omega_2^{\Omega_2+\psi_1(\Omega_2^{\Omega_2})})\\&f_{\psi(\Omega^{\Omega\times2})}(n)\sim\psi(\Omega_2^{\Omega_2\times2})\\&f_{\psi(\Omega^{\Omega^2})}(n)\sim\psi(\Omega_2^{\Omega_2^2})\\&f_{\psi(\Omega^{\Omega^\omega})}(n)\sim\psi(\Omega_2^{\Omega_2^\omega})\\&f_{\psi(\Omega^{\Omega^\omega})+1}(n)\sim\psi(\Omega_2^{\Omega_2^\Omega})\\&f_{\psi(\Omega^{\Omega^\Omega})}(n)\sim\psi(\Omega_2^{\Omega_2^{\Omega_2}})\\&f_{\psi(\psi_1(0))}(n)\sim\psi(\psi_2(0))\\&f_{\psi(\psi_1(0)\times\Omega)}(n)\sim\psi(\psi_2(0)\times\Omega_2)\\&f_{\psi(\psi_1(0)^2)}(n)\sim\psi(\psi_2(0)^2)\\&f_{\psi(\psi_1(0)^\Omega)}(n)\sim\psi(\psi_2(0)^{\Omega_2})\\&f_{\psi(\psi_1(0)^{\psi_1(0)})}(n)\sim\psi(\psi_2(0)^{\psi_2(0)})\\&f_{\psi(\psi_1(1))}(n)\sim\psi(\psi_2(1))\\&f_{\psi(\psi_1(\omega))+1}(n)\sim\psi(\psi_2(\Omega))\\&f_{\psi(\psi_1(\psi(0)))}(n)\sim\psi(\psi_2(\psi_1(0)))\\&f_{\psi(\psi_1(\psi(\Omega)))}(n)\sim\psi(\psi_2(\psi_1(\Omega_2)))\\&f_{\psi(\psi_1(\psi(\Omega^\Omega)))}(n)\sim\psi(\psi_2(\psi_1(\Omega_2^{\Omega_2})))\\&f_{\psi(\psi_1(\psi(\psi_1(0))))}(n)\sim\psi(\psi_2(\psi_1(\psi_2(0))))\\&f_{\psi(\psi_1(\Omega))}(n)\sim\psi(\psi_2(\Omega_2))\\&f_{\psi(\psi_1(\psi_1(0)))}(n)\sim\psi(\psi_2(\psi_2(0)))\\&f_{\psi(\Omega_2)}(n)\sim\psi(\Omega_3)\\&f_{\psi(\Omega_2)[n]}(f_{\psi(\Omega_2)}(n))\sim\psi(\Omega_3+\psi_2(\Omega_3))\\&f_{\psi(\Omega_2)[n+1]}(f_{\psi(\Omega_2)}(n))\sim\psi(\Omega_3+\psi_2(\Omega_3+\psi_2(\Omega_3)))\\&f_{\psi(\Omega_2)[n\times2]}(f_{\psi(\Omega_2)}(n))\sim\psi(\Omega_3\times2)\\&f_{\psi(\Omega_2)+1}(n)\sim\psi(\Omega_3\times\Omega)\\&f_{\psi(\Omega_2)+\psi(0)}(n)\sim\psi(\Omega_3\times\psi_1(0))\\&f_{\psi(\Omega_2)+\psi(\Omega)}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_2))\\&f_{\psi(\Omega_2)\times2}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3))\\&f_{\psi(\Omega_2)\times2+1}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega))\\&f_{\psi(\Omega_2)\times3+1}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega)^2)\\&f_{\psi(\Omega_2)^2+1}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega)^{\psi_1(\Omega_3\times\Omega)})\\&f_{\psi(\Omega_2+1)}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+1))\\&f_{\psi(\Omega_2+\Omega)}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+\Omega_2))\\&f_{\psi(\Omega_2+\psi_1(\Omega_2))}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+\psi_2(\Omega_3)))\\&f_{\psi(\Omega_2+\psi_1(\Omega_2))+1}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+\psi_2(\Omega_3\times\Omega)))\\&f_{\psi(\Omega_2+\psi_1(\Omega_2+1))}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+\psi_2(\Omega_3\times\Omega+1)))\\&f_{\psi(\Omega_2\times2)}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+\Omega_3))\\&f_{\psi(\Omega_2\times2)+1}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega\times2))\\&f_{\psi(\Omega_2\times\psi(\Omega_2))}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\psi_1(\Omega_3)))\\&f_{\psi(\Omega_2\times\Omega)}(n)\sim\psi(\Omega_3\times\Omega_2)\\&f_{\psi(\Omega_2\times\psi_1(0))}(n)\sim\psi(\Omega_3\times\psi_2(0))\\&f_{\psi(\Omega_2\times\psi_1(\Omega_2))}(n)\sim\psi(\Omega_3\times\psi_2(\Omega_3))\\&f_{\psi(\Omega_2^2)}(n)\sim\psi(\Omega_3^2)\\&f_{\psi(\Omega_2^{\Omega_2})}(n)\sim\psi(\Omega_3^{\Omega_3})\\&f_{\psi(\psi_2(0))}(n)\sim\psi(\psi_3(0))\\&f_{\psi(\Omega_3)}(n)\sim\psi(\Omega_4)\\&f_{\psi(\Omega_4)}(n)\sim\psi(\Omega_5)\\&\dots \\ \end{align}</nowiki> | ||
[[分类:分析]] | |||
2025年8月21日 (四) 09:32的版本
本条目展示SGH与FGH的对照.本文使用Veblen函数和MOCF
\begin{align} & g_{\varepsilon_0\times\omega}(n)=g_{\varepsilon_0\times n}(n)=(n\uparrow\uparrow n)\times n\\ &g_{\varepsilon_0\times\omega^2}(n)=g_{\varepsilon_0\times\omega\times n}(n)=(n\uparrow\uparrow n)\times n^2\\ &g_{\varepsilon_0\times\omega^\omega}(n)=g_{\varepsilon_0\times\omega^n}(n)=(n\uparrow\uparrow n)\times n^n\\ &g_{\varepsilon_0\times\omega^{\omega^\omega}}(n)=(n\uparrow\uparrow n)\times (n\uparrow\uparrow3)\\ &g_{\varepsilon_0^2}(n)=g_{\varepsilon_0\times\varepsilon_0[n]}(n)=(n\uparrow\uparrow n)^2\\ &g_{\varepsilon_0^3}(n)=(n\uparrow\uparrow n)^3\\ &g_{\varepsilon_0^\omega}(n)=g_{\varepsilon_0^n}(n)=(n\uparrow\uparrow n)^n\\ &g_{\varepsilon_0^{\omega^\omega}}(n)=(n\uparrow\uparrow n)^{n^n}\\ &g_{\varepsilon_0^{\varepsilon_0}}(n)=(n\uparrow\uparrow n)^{n\uparrow\uparrow n}=(n\uparrow\uparrow n)\uparrow\uparrow2\\ &g_{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}(n)=(n\uparrow\uparrow n)\uparrow\uparrow3\\ &g_{\varepsilon_1}(n)=(n\uparrow\uparrow n)\uparrow\uparrow n\approx n\uparrow\uparrow(n\times2)\\ &g_{\varepsilon_2}(n)=((n\uparrow\uparrow n)\uparrow\uparrow n)\uparrow\uparrow n\approx n\uparrow\uparrow(n\times3)\\ &n\uparrow\uparrow(n\times3)\sim\varepsilon_2\\ &n\uparrow\uparrow(n\times3+1)\sim\varepsilon_2^{\varepsilon_2}\\ &n\uparrow\uparrow(n\times3+2)\sim\varepsilon_2^{\varepsilon_2^{\varepsilon_2}}\\ &n\uparrow\uparrow(n\times4)\sim\varepsilon_3\\ &n\uparrow\uparrow(n\times5)\sim\varepsilon_4\\ &n\uparrow\uparrow(n^2)\sim\varepsilon_\omega\\ &n\uparrow\uparrow(n^2+1)\sim\varepsilon_\omega^{\varepsilon_\omega}\\&n\uparrow\uparrow(n^2+n)\sim\varepsilon_{\omega+1}\\&n\uparrow\uparrow(n^2\times2)\sim\varepsilon_{\omega\times2}\\&n\uparrow\uparrow(n^3)\sim\varepsilon_{\omega^2}\\&n\uparrow\uparrow(n^n)=n\uparrow\uparrow n\uparrow\uparrow2\sim\varepsilon_{\omega^\omega}\\&n\uparrow\uparrow(n^n+n)\sim\varepsilon_{\omega^\omega+1}\\&n\uparrow\uparrow(n^{n+1})\sim\varepsilon_{\omega^{\omega+1}}\\&n\uparrow\uparrow(n^{n^2})\sim\varepsilon_{\omega^{\omega^2}}\\&n\uparrow\uparrow n\uparrow\uparrow3\sim\varepsilon_{\omega^{\omega^\omega}}\\&n\uparrow\uparrow n\uparrow\uparrow n=n\uparrow\uparrow\uparrow 3\sim\varepsilon_{\varepsilon_0}\\&n\uparrow\uparrow (n\uparrow\uparrow n+n)\sim\varepsilon_{\varepsilon_0+1}\\&n\uparrow\uparrow ((n\uparrow\uparrow n)\times2)\sim\varepsilon_{\varepsilon_0\times2}\\&n\uparrow\uparrow ((n\uparrow\uparrow n)\uparrow\uparrow 2)\approx n\uparrow\uparrow n\uparrow\uparrow(n+1)\sim\varepsilon_{\varepsilon_0^{\varepsilon_0}}\\&n\uparrow\uparrow n\uparrow\uparrow(n\times2)\sim\varepsilon_{\varepsilon_1}\\&n\uparrow\uparrow n\uparrow\uparrow(n^2)\sim\varepsilon_{\varepsilon_\omega}\\&n\uparrow\uparrow n\uparrow\uparrow n\uparrow\uparrow n=n\uparrow\uparrow\uparrow4\sim\varepsilon_{\varepsilon_{\varepsilon_0}}\\&n\uparrow\uparrow\uparrow n\sim\zeta_0\\&(n\uparrow\uparrow\uparrow n)\uparrow\uparrow n\sim\varepsilon_{\zeta_0+1}\\&(n\uparrow\uparrow\uparrow n)\uparrow\uparrow (n\times2)\sim\varepsilon_{\zeta_0+2}\\&(n\uparrow\uparrow\uparrow n)\uparrow\uparrow (n\uparrow\uparrow n)\sim\varepsilon_{\zeta_0+\varepsilon_0}\\&(n\uparrow\uparrow\uparrow n)\uparrow\uparrow (n\uparrow\uparrow\uparrow n)\approx n\uparrow\uparrow\uparrow(n+1)\sim\varepsilon_{\zeta_0\times2}\\&(n\uparrow\uparrow\uparrow n)\uparrow\uparrow (n\uparrow\uparrow\uparrow n)\uparrow\uparrow n\sim\varepsilon_{\varepsilon_{\zeta_0+1}}\\&(n\uparrow\uparrow\uparrow n)\uparrow\uparrow (n\uparrow\uparrow\uparrow n)\uparrow\uparrow (n\uparrow\uparrow\uparrow n)\sim\varepsilon_{\varepsilon_{\zeta_0\times2}}\\&(n\uparrow\uparrow\uparrow n)\uparrow\uparrow \uparrow n\approx n\uparrow\uparrow\uparrow(n\times2)\sim\zeta_1\\&(n\uparrow\uparrow\uparrow(n\times2))\uparrow\uparrow n\sim\varepsilon_{\zeta_1+1}\\&(n\uparrow\uparrow\uparrow(n\times2))\uparrow\uparrow (n\uparrow\uparrow\uparrow n)\sim\varepsilon_{\zeta_1+\zeta_0}\\&(n\uparrow\uparrow\uparrow(n\times2))\uparrow\uparrow (n\uparrow\uparrow\uparrow(n\times2))\sim\varepsilon_{\zeta_1\times2}\\&(n\uparrow\uparrow\uparrow(n\times2))\uparrow\uparrow \uparrow n\approx n\uparrow\uparrow\uparrow(n\times3)\sim\zeta_2\\&n\uparrow\uparrow\uparrow(n^2)\sim\zeta_\omega\\&n\uparrow\uparrow\uparrow(n^n)\sim\zeta_{\omega^\omega}\\&n\uparrow\uparrow\uparrow(n\uparrow\uparrow n)\sim\zeta_{\varepsilon_0}\\&n\uparrow\uparrow\uparrow n\uparrow\uparrow\uparrow n \sim\zeta_{\zeta_0}\\&n\uparrow\uparrow\uparrow\uparrow n \sim\eta_0\\&(n\uparrow\uparrow\uparrow\uparrow n)\uparrow\uparrow\uparrow n \sim\zeta_{\eta_0+1}\\&n\uparrow\uparrow\uparrow\uparrow (n\times2) \sim\eta_1\\&n\uparrow^53 \sim\eta_{\eta_0}\\&n\uparrow^5n \sim\varphi(4,0)\\&n\uparrow^5(n\times2) \sim\varphi(4,1)\\&n\uparrow^6 n \sim\varphi(5,0)\\&n\uparrow^n n \sim\varphi(\omega,0)\\ \end{align}
\begin{align} &f_3(f_\omega(n))\approx (n\uparrow^nn)\uparrow\uparrow n\sim\psi(\Omega^\omega+1)\\&f_3^2(f_\omega(n))\approx (n\uparrow^nn)\uparrow\uparrow (n\times2)\sim\psi(\Omega^\omega+2)\\&f_3^n(f_\omega(n))\approx (n\uparrow^nn)\uparrow\uparrow (n^2)\sim\psi(\Omega^\omega+\omega)\\&f_3^{f_3(n)}(f_\omega(n))\approx (n\uparrow^nn)\uparrow\uparrow (n\uparrow\uparrow n)\sim\psi(\Omega^\omega+\psi(0))\\&f_4(f_\omega(n))=f_3^{f_\omega(n)}(f_\omega(n))\approx (n\uparrow^nn)\uparrow\uparrow\uparrow2\sim\psi(\Omega^\omega+\psi(\Omega^\omega))\\&f_3(f_4(f_\omega(n)))\approx ((n\uparrow^nn)\uparrow\uparrow\uparrow2)\uparrow\uparrow n\sim\psi(\Omega^\omega+\psi(\Omega^\omega)+1)\\&f_3^{f_{\omega}(n)}(f_4(f_\omega(n)))\approx ((n\uparrow^nn)\uparrow\uparrow\uparrow2)\uparrow\uparrow (n\uparrow^nn)\sim\psi(\Omega^\omega+\psi(\Omega^\omega)\times2)\\&f_3^{f_{\omega}(n)\times2}(f_4(f_\omega(n)))\sim\psi(\Omega^\omega+\psi(\Omega^\omega)\times3)\\&f_3^{f_3(f_{\omega}(n))}(f_4(f_\omega(n)))\sim\psi(\Omega^\omega+\psi(\Omega^\omega+1))\\&f_3^{f_3^2(f_{\omega}(n))}(f_4(f_\omega(n)))\sim\psi(\Omega^\omega+\psi(\Omega^\omega+2))\\&f_4^2(f_\omega(n))=f_3^{f_3^{f_\omega(n)}(f_{\omega}(n))}(f_4(f_\omega(n)))\sim\psi(\Omega^\omega+\psi(\Omega^\omega+\psi(\Omega^\omega)))\\&f_3(f_4^2(f_\omega(n)))\sim\psi(\Omega^\omega+\psi(\Omega^\omega+\psi(\Omega^\omega))+1)\\&f_3^{f_4(f_\omega(n))}(f_4^2(f_\omega(n)))\sim\psi(\Omega^\omega+\psi(\Omega^\omega+\psi(\Omega^\omega))\times2)\\&f_3^{f_3(f_4(f_\omega(n)))}(f_4^2(f_\omega(n)))\sim\psi(\Omega^\omega+\psi(\Omega^\omega+\psi(\Omega^\omega)+1))\\&f_3^{f_3^{f_\omega(n)}(f_4(f_\omega(n)))}(f_4^2(f_\omega(n)))\sim\psi(\Omega^\omega+\psi(\Omega^\omega+\psi(\Omega^\omega)\times2))\\&f_4^3(f_\omega(n))\sim\psi(\Omega^\omega+\psi(\Omega^\omega+\psi(\Omega^\omega+\psi(\Omega^\omega))))\\&f_4^n(f_\omega(n))\approx (n\uparrow^nn)\uparrow\uparrow\uparrow n\sim\psi(\Omega^\omega+\Omega)\\&f_4^{n+1}(f_\omega(n))\sim\psi(\Omega^\omega+\Omega+\psi(\Omega^\omega+\Omega))\\&f_4^{n+2}(f_\omega(n))\sim\psi(\Omega^\omega+\Omega+\psi(\Omega^\omega+\Omega+\psi(\Omega^\omega+\Omega)))\\&f_4^{n\times2}(f_\omega(n))\sim\psi(\Omega^\omega+\Omega\times2)\\&f_4^{n^2}(f_\omega(n))\sim\psi(\Omega^\omega+\Omega\times\omega)\\&f_4^{f_3(n)}(f_\omega(n))\sim\psi(\Omega^\omega+\Omega\times\psi(0))\\&f_5(f_\omega(n))=f_4^{f_\omega(n)}(f_\omega(n))\sim\psi(\Omega^\omega+\Omega\times\psi(\Omega^\omega))\\&f_3(f_5(f_\omega(n)))\sim\psi(\Omega^\omega+\Omega\times\psi(\Omega^\omega)+1)\\&f_3^{f_\omega(n)}(f_5(f_\omega(n)))\sim\psi(\Omega^\omega+\Omega\times\psi(\Omega^\omega)+\psi(\Omega^\omega))\\&f_4(f_5(f_\omega(n)))\sim\psi(\Omega^\omega+\Omega\times\psi(\Omega^\omega)+\psi(\Omega^\omega+\Omega\times\psi(\Omega^\omega)))\\&f_4^n(f_5(f_\omega(n)))\sim\psi(\Omega^\omega+\Omega\times\psi(\Omega^\omega)+\Omega)\\&f_4^{f_\omega(n)}(f_5(f_\omega(n)))\sim\psi(\Omega^\omega+\Omega\times\psi(\Omega^\omega)\times2)\\&f_4^{f_\omega(n)\times2}(f_5(f_\omega(n)))\sim\psi(\Omega^\omega+\Omega\times\psi(\Omega^\omega)\times3)\\&f_4^{f_3(f_\omega(n))}(f_5(f_\omega(n)))\sim\psi(\Omega^\omega+\Omega\times\psi(\Omega^\omega+1))\\&f_4^{f_4(f_\omega(n))}(f_5(f_\omega(n)))\sim\psi(\Omega^\omega+\Omega\times\psi(\Omega^\omega+\Omega))\\&f_5^2(f_\omega(n))=f_4^{f_5(f_\omega(n))}(f_5(f_\omega(n)))\sim\psi(\Omega^\omega+\Omega\times\psi(\Omega^\omega+\Omega\times\psi(\Omega^\omega)))\\&f_5^n(f_\omega(n))\approx (n\uparrow^nn)\uparrow\uparrow\uparrow\uparrow n\sim\psi(\Omega^\omega+\Omega^2)\\&f_5^{n\times2}(f_\omega(n))\sim\psi(\Omega^\omega+\Omega^2\times2)\\&f_6(f_\omega(n))\sim\psi(\Omega^\omega+\Omega^2\times\psi(\Omega^\omega))\\&f_6^n(f_\omega(n))\sim\psi(\Omega^\omega+\Omega^3)\\&f_7^n(f_\omega(n))\sim\psi(\Omega^\omega+\Omega^4)\\&f_n(f_\omega(n))\approx (n\uparrow^nn)\uparrow^nn\approx n\uparrow^n(2n)\sim\psi(\Omega^\omega\times2)\\&f_n^2(f_\omega(n))\approx n\uparrow^n(3n)\sim\psi(\Omega^\omega\times3)\\&f_n^n(f_\omega(n))\approx n\uparrow^n(n^2)\sim\psi(\Omega^\omega\times\omega)\\&f_n^{f_3(n)}(f_\omega(n))\approx n\uparrow^nn\uparrow\uparrow n\sim\psi(\Omega^\omega\times\psi(0))\\&f_{n+1}(f_\omega(n))=f_n^{f_\omega(n)}(f_\omega(n))\approx n\uparrow^nn\uparrow^nn\sim\psi(\Omega^\omega\times\psi(\Omega^\omega))\\&f_n(f_{n+1}(f_\omega(n)))\sim\psi(\Omega^\omega\times\psi(\Omega^\omega)+\Omega^\omega)\\&f_n^{f_\omega(n)}(f_{n+1}(f_\omega(n)))\sim\psi(\Omega^\omega\times\psi(\Omega^\omega)\times2)\\&f_n^{f_3(f_\omega(n))}(f_{n+1}(f_\omega(n)))\sim\psi(\Omega^\omega\times\psi(\Omega^\omega+1))\\&f_n^{f_n(f_\omega(n))}(f_{n+1}(f_\omega(n)))\sim\psi(\Omega^\omega\times\psi(\Omega^\omega\times2))\\&f_{n+1}^2(f_\omega(n))\approx n\uparrow^nn\uparrow^nn\uparrow^nn\sim\psi(\Omega^\omega\times\psi(\Omega^\omega\times\psi(\Omega^\omega)))\\&f_{n+1}^n(f_\omega(n))\approx n\uparrow^{n+1}n\sim\psi(\Omega^{\omega+1})\\&f_n(f_{n+1}^n(f_\omega(n)))\sim\psi(\Omega^{\omega+1}+\Omega^\omega)\\&f_{n+1}^{n+1}(f_\omega(n))=f_n^{f_{n+1}^n(f_\omega(n))}(f_{n+1}^n(f_\omega(n)))\sim\psi(\Omega^{\omega+1}+\Omega^\omega\times\psi(\Omega^{\omega+1}))\\&f_{n+1}^{n\times2}(f_\omega(n))\approx n\uparrow^{n+1}(2n)\sim\psi(\Omega^{\omega+1}\times2)\\&f_{n+2}(f_\omega(n))\sim\psi(\Omega^{\omega+1}\times\psi(\Omega^\omega))\\&f_n(f_{n+2}(f_\omega(n)))\sim\psi(\Omega^{\omega+1}\times\psi(\Omega^\omega)+\Omega^\omega)\\&f_n^{f_{n+1}^n(f_\omega(n))}(f_{n+2}(f_\omega(n)))\sim\psi(\Omega^{\omega+1}\times\psi(\Omega^\omega)+\Omega^\omega\times\psi(\Omega^{\omega+1}))\\&f_{n+1}(f_{n+2}(f_\omega(n)))\sim\psi(\Omega^{\omega+1}\times\psi(\Omega^\omega)+\Omega^\omega\times\psi(\Omega^{\omega+1}\times\psi(\Omega^\omega)))\\&f_{n+1}^n(f_{n+2}(f_\omega(n)))\sim\psi(\Omega^{\omega+1}\times\psi(\Omega^\omega)+\Omega^{\omega+1})\\&f_{n+1}^{f_\omega(n)}(f_{n+2}(f_\omega(n)))\sim\psi(\Omega^{\omega+1}\times\psi(\Omega^\omega)\times2)\\&f_{n+1}^{f_{n+1}(f_\omega(n))}(f_{n+2}(f_\omega(n)))\sim\psi(\Omega^{\omega+1}\times\psi(\Omega^\omega\times\psi(\Omega^\omega)))\\&f_{n+1}^{f_{n+1}^n(f_\omega(n))}(f_{n+2}(f_\omega(n)))\sim\psi(\Omega^{\omega+1}\times\psi(\Omega^{\omega+1}))\\&f_{n+2}^2(f_\omega(n))\sim\psi(\Omega^{\omega+1}\times\psi(\Omega^{\omega+1}\times\psi(\Omega^\omega)))\\&f_{n+2}^n(f_\omega(n))\sim\psi(\Omega^{\omega+2})\\&f_{n+2}^{n+1}(f_\omega(n))\sim\psi(\Omega^{\omega+2}+\Omega^{\omega+1}\times\psi(\Omega^\omega))\\&f_{n+2}^{n\times2}(f_\omega(n))\sim\psi(\Omega^{\omega+2}\times2)\\&f_{n+3}(f_\omega(n))\sim\psi(\Omega^{\omega+2}\times\psi(\Omega^\omega))\\&f_{n+3}^2(f_\omega(n))\sim\psi(\Omega^{\omega+2}\times\psi(\Omega^{\omega+2}\times\psi(\Omega^\omega)))\\&f_{n+3}^n(f_\omega(n))\sim\psi(\Omega^{\omega+3})\\&f_{n\times2}(f_\omega(n))\sim\psi(\Omega^{\omega\times2})\\&f_{n\times2+1}(f_\omega(n))\sim\psi(\Omega^{\omega\times2}\times\psi(\Omega^{\omega}))\\&f_{n\times2+1}^n(f_\omega(n))\sim\psi(\Omega^{\omega\times2+1})\\&f_{n\times3}(f_\omega(n))\sim\psi(\Omega^{\omega\times3})\\&f_{n^2}(f_\omega(n))\sim\psi(\Omega^{\omega^2})\\&f_{f_3(n)}(f_\omega(n))\approx n\uparrow^{n\uparrow\uparrow n}n\sim\psi(\Omega^{\psi(0)})\\&f_{f_4(n)}(f_\omega(n))\approx n\uparrow^{n\uparrow\uparrow\uparrow n}n\sim\psi(\Omega^{\psi(\Omega)})\\&f_\omega^2(n)=f_{f_\omega(n)}(f_\omega(n))\approx n\uparrow^{n\uparrow^n n}n\sim\psi(\Omega^{\psi(\Omega^\omega)})\\&f_n(f_\omega^2(n))\sim\psi(\Omega^{\psi(\Omega^\omega)}+\Omega^\omega)\\&f_{n+1}^n(f_\omega^2(n))\sim\psi(\Omega^{\psi(\Omega^\omega)}+\Omega^{\omega+1})\\&f_{f_\omega(n)}(f_\omega^2(n))\sim\psi(\Omega^{\psi(\Omega^\omega)}\times2)\\&f_{f_\omega(n)}^n(f_\omega^2(n))\sim\psi(\Omega^{\psi(\Omega^\omega)}\times\omega)\\&f_{f_\omega(n)+1}(f_\omega^2(n))\sim\psi(\Omega^{\psi(\Omega^\omega)}\times\psi(\Omega^{\psi(\Omega^\omega)}))\\&f_{f_\omega(n)+1}^n(f_\omega^2(n))\sim\psi(\Omega^{\psi(\Omega^\omega)+1})\\&f_{f_\omega(n)+n}(f_\omega^2(n))\sim\psi(\Omega^{\psi(\Omega^\omega)+\omega})\\&f_{f_\omega(n)\times2}(f_\omega^2(n))\sim\psi(\Omega^{\psi(\Omega^\omega)\times2})\\&f_{f_3(f_\omega(n))}(f_\omega^2(n))\sim\psi(\Omega^{\psi(\Omega^\omega+1)})\\&f_{f_{n+1}^n(f_\omega(n))}(f_\omega^2(n))\sim\psi(\Omega^{\psi(\Omega^{\omega+1})})\\&f_\omega^3(n)=f_{f_{f_\omega(n)}(f_\omega(n))}(f_\omega^2(n))\sim\psi(\Omega^{\psi(\Omega^{\psi(\Omega^\omega)})})\\&f_{\omega+1}(n)=f_\omega^n(n)\sim\psi(\Omega^\Omega)=\varphi(1,0,0)\\ \end{align}
\begin{align} & f_3(f_{\omega+1}(n))\sim\psi(\Omega^\Omega+1)\\&f_4(f_{\omega+1}(n))=f_3^{f_{\omega+1}(n)}(f_{\omega+1}(n))\sim\psi(\Omega^\Omega+\psi(\Omega^\Omega))\\&f_4^n(f_{\omega+1}(n))\sim\psi(\Omega^\Omega+\Omega)\\&f_5^n(f_{\omega+1}(n))\sim\psi(\Omega^\Omega+\Omega^2)\\&f_n(f_{\omega+1}(n))\sim\psi(\Omega^\Omega+\Omega^\omega)\\&f_{n+1}^n(f_{\omega+1}(n))\sim\psi(\Omega^\Omega+\Omega^{\omega+1})\\&f_{f_3(n)}(f_{\omega+1}(n))\sim\psi(\Omega^\Omega+\Omega^{\psi(0)})\\&f_{f_\omega(n)}(f_{\omega+1}(n))\sim\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\omega)})\\&f_\omega(f_{\omega+1}(n))=f_{f_{\omega+1}(n)}(f_{\omega+1}(n))\sim\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)})=\varphi(\varphi(1,0,0),1)\\&f_{f_{\omega+1}(n)}(f_{\omega}(f_{\omega+1}(n)))\sim\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times2)\\&f_{f_{\omega+1}(n)+1}^n(f_{\omega}(f_{\omega+1}(n)))\sim\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)+1})\\&f_{f_3(f_{\omega+1}(n))}(f_{\omega}(f_{\omega+1}(n)))\sim\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega+1)})\\&f_{f_n(f_{\omega+1}(n))}(f_{\omega}(f_{\omega+1}(n)))\sim\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega+\Omega^\omega)})\\&f_\omega^2(f_{\omega+1}(n))=f_{f_\omega(f_{\omega+1}(n))}(f_{\omega}(f_{\omega+1}(n)))\sim\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)})})\\&f_\omega^n(f_{\omega+1}(n))\sim\psi(\Omega^\Omega\times2)=\varphi(1,0,1)\\&f_\omega^{n\times2}(f_{\omega+1}(n))\sim\psi(\Omega^\Omega\times3)\\&f_{\omega+1}^2(n)=f_\omega^{f_{\omega+1}(n)}(f_{\omega+1}(n))\sim\psi(\Omega^\Omega\times\psi(\Omega^\Omega))\\&f_\omega^n(f_{\omega+1}^2(n))\sim\psi(\Omega^\Omega\times\psi(\Omega^\Omega)+\Omega^\Omega)\\&f_\omega^{f_{\omega+1}(n)}(f_{\omega+1}^2(n))\sim\psi(\Omega^\Omega\times\psi(\Omega^\Omega)\times2)\\&f_\omega^{f_n(f_{\omega+1}(n))}(f_{\omega+1}^2(n))\sim\psi(\Omega^\Omega\times\psi(\Omega^\Omega+\Omega^\omega))\\&f_\omega^{f_\omega(f_{\omega+1}(n))}(f_{\omega+1}^2(n))\sim\psi(\Omega^\Omega\times\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}))\\&f_\omega^{f_\omega^n(f_{\omega+1}(n))}(f_{\omega+1}^2(n))\sim\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times2))\\&f_{\omega+1}^3(n)\sim\psi(\Omega^\Omega\times\psi(\Omega^\Omega\times\psi(\Omega^\Omega)))\\&f_{\omega+2}(n)=f_{\omega+1}^n(n)\sim\psi(\Omega^{\Omega+1})=\varphi(1,1,0)\\&f_\omega(f_{\omega+2}(n))\sim\psi(\Omega^{\Omega+1}+\Omega^{\psi(\Omega^{\Omega+1})})\\&f_\omega^n(f_{\omega+2}(n))\sim\psi(\Omega^{\Omega+1}+\Omega^{\Omega})\\&f_\omega^{n\times2}(f_{\omega+2}(n))\sim\psi(\Omega^{\Omega+1}+\Omega^{\Omega}\times2)\\&f_{\omega+1}(f_{\omega+2}(n))=f_\omega^{f_{\omega+2}(n)}(f_{\omega+2}(n))\sim\psi(\Omega^{\Omega+1}+\Omega^{\Omega}\times\psi(\Omega^{\Omega+1}))\\&f_\omega^{f_{\omega+2}(n)}(f_{\omega+1}(f_{\omega+2}(n)))\sim\psi(\Omega^{\Omega+1}+\Omega^{\Omega}\times\psi(\Omega^{\Omega+1})\times2)\\&f_\omega^{f_\omega^n(f_{\omega+2}(n))}(f_{\omega+1}(f_{\omega+2}(n)))\sim\psi(\Omega^{\Omega+1}+\Omega^{\Omega}\times\psi(\Omega^{\Omega+1}+\Omega^\Omega))\\&f_{\omega+1}^2(f_{\omega+2}(n))\sim\psi(\Omega^{\Omega+1}+\Omega^{\Omega}\times\psi(\Omega^{\Omega+1}+\Omega^\Omega\times\psi(\Omega^{\Omega+1})))\\&f_{\omega+1}^n(f_{\omega+2}(n))\sim\psi(\Omega^{\Omega+1}\times2)\\&f_{\omega+2}^2(n)\sim\psi(\Omega^{\Omega+1}\times\psi(\Omega^{\Omega+1}))\\&f_{\omega+3}(n)=f_{\omega+2}^n(n)\sim\psi(\Omega^{\Omega+2})\\&f_{\omega+4}(n)\sim\psi(\Omega^{\Omega+3})\\&f_{\omega\times2}(n)=f_{\omega+n}(n)\sim\psi(\Omega^{\Omega+\omega})\\&f_\omega(f_{\omega\times2}(n))\sim\psi(\Omega^{\Omega+\omega}+\Omega^{\psi(\Omega^{\Omega+\omega})})\\&f_\omega^n(f_{\omega\times2}(n))\sim\psi(\Omega^{\Omega+\omega}+\Omega^\Omega)\\&f_{\omega+1}(f_{\omega\times2}(n))\sim\psi(\Omega^{\Omega+\omega}+\Omega^\Omega\times\psi(\Omega^{\Omega+\omega}))\\&f_{\omega+1}^n(f_{\omega\times2}(n))\sim\psi(\Omega^{\Omega+\omega}+\Omega^{\Omega+1})\\&f_{\omega+2}^n(f_{\omega\times2}(n))\sim\psi(\Omega^{\Omega+\omega}+\Omega^{\Omega+2})\\&f_{\omega+n}(f_{\omega\times2}(n))\sim\psi(\Omega^{\Omega+\omega}\times2)\\&f_{\omega+n+1}(f_{\omega\times2}(n))\sim\psi(\Omega^{\Omega+\omega}\times\psi(\Omega^{\Omega+\omega}))\\&f_{\omega+n+1}^n(f_{\omega\times2}(n))\sim\psi(\Omega^{\Omega+\omega+1})\\&f_{\omega+n\times2}(f_{\omega\times2}(n))\sim\psi(\Omega^{\Omega+\omega\times2})\\&f_{\omega+f_{\omega+1}(n)}(f_{\omega\times2}(n))\sim\psi(\Omega^{\Omega+\psi(\Omega^\Omega)})\\&f_{\omega+f_{\omega+2}(n)}(f_{\omega\times2}(n))\sim\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+1})})\\&f_{\omega\times2}^2(n)=f_{\omega+f_{\omega+n}(n)}(f_{\omega\times2}(n))\sim\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega})})\\&f_{\omega\times2}^3(n)\sim\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\psi(\Omega^{\Omega+\omega})})})\\&f_{\omega\times2+1}(n)\sim\psi(\Omega^{\Omega\times2})\\&f_\omega^{n}(f_{\omega\times2+1}(n))\sim\psi(\Omega^{\Omega\times2}+\Omega^\Omega)\\&f_{\omega\times2}^{n}(f_{\omega\times2+1}(n))\sim\psi(\Omega^{\Omega\times2}\times2)\\&f_{\omega\times2+1}^2(n)\sim\psi(\Omega^{\Omega\times2}\times\psi(\Omega^{\Omega\times2}))\\&f_{\omega\times2+2}(n)\sim\psi(\Omega^{\Omega\times2+1})\\&f_{\omega\times3}(n)\sim\psi(\Omega^{\Omega\times2+\omega})\\&f_{\omega\times3}^2(n)\sim\psi(\Omega^{\Omega\times2+\psi(\Omega^{\Omega\times2+\omega})})\\&f_{\omega\times3+1}(n)\sim\psi(\Omega^{\Omega\times3})\\&f_{\omega\times4}(n)\sim\psi(\Omega^{\Omega\times3+\omega})\\&f_{\omega\times4+1}(n)\sim\psi(\Omega^{\Omega\times4})\\&f_{\omega^2}(n)\sim\psi(\Omega^{\Omega\times\omega})=\varphi(\omega,0,0)\\&f_{\omega}^n(f_{\omega^2}(n))\sim\psi(\Omega^{\Omega\times\omega}+\Omega^\Omega)\\&f_{\omega\times2}^n(f_{\omega^2}(n))\sim\psi(\Omega^{\Omega\times\omega}+\Omega^{\Omega\times2})\\&f_{\omega\times n}(f_{\omega^2}(n))\sim\psi(\Omega^{\Omega\times\omega}\times2)\\&f_{\omega\times n+1}(f_{\omega^2}(n))\sim\psi(\Omega^{\Omega\times\omega}\times\psi(\Omega^{\Omega\times\omega}))\\&f_{\omega\times n+1}^n(f_{\omega^2}(n))\sim\psi(\Omega^{\Omega\times\omega+1})\\&f_{\omega\times n+2}^n(f_{\omega^2}(n))\sim\psi(\Omega^{\Omega\times\omega+2})\\&f_{\omega\times n+n}(f_{\omega^2}(n))\sim\psi(\Omega^{\Omega\times\omega+\omega})\\&f_{\omega\times n+f_{\omega^2}(n)}(f_{\omega^2}(n))\sim\psi(\Omega^{\Omega\times\omega+\psi(\Omega^{\Omega\times\omega})})\\&f_{\omega\times n+\omega}(f_{\omega^2}(n))\sim\psi(\Omega^{\Omega\times\omega+\Omega})\\&f_{\omega\times n+\omega\times2}(f_{\omega^2}(n))\sim\psi(\Omega^{\Omega\times\omega+\Omega\times2})\\&f_{\omega\times n\times2}(f_{\omega^2}(n))\sim\psi(\Omega^{\Omega\times\omega\times2})\\&f_{\omega^2}^2(n)=f_{\omega\times f_{\omega^2}(n)}(f_{\omega^2}(n))\sim\psi(\Omega^{\Omega\times\psi(\Omega^{\Omega\times\omega})})\\&f_{\omega^2}^3(n)\sim\psi(\Omega^{\Omega\times\psi(\Omega^{\Omega\times\psi(\Omega^{\Omega\times\omega})})})\\&f_{\omega^2+1}(n)\sim\psi(\Omega^{\Omega^2})=\varphi(1,0,0,0)\\&f_\omega^n(f_{\omega^2+1}(n))\sim\psi(\Omega^{\Omega^2}+\Omega^\Omega)\\&f_{\omega\times2}^n(f_{\omega^2+1}(n))\sim\psi(\Omega^{\Omega^2}+\Omega^{\Omega\times2})\\&f_{\omega\times n}(f_{\omega^2+1}(n))\sim\psi(\Omega^{\Omega^2}+\Omega^{\Omega\times\omega})\\&f_{\omega^2}(f_{\omega^2+1}(n))=f_{\omega\times f_{\omega^2+1}(n)}(f_{\omega^2+1}(n))\sim\psi(\Omega^{\Omega^2}+\Omega^{\Omega\times{\psi(\Omega^{\Omega^2})}})=\varphi(\varphi(1,0,0,0),0,1)\\&f_{\omega^2}^2(f_{\omega^2+1}(n))\sim\psi(\Omega^{\Omega^2}+\Omega^{\Omega\times\psi(\Omega^{\Omega^2}+\Omega^{\Omega\times\psi(\Omega^{\Omega^2})})})\\&f_{\omega^2}^n(f_{\omega^2+1}(n))\sim\psi(\Omega^{\Omega^2}\times2)\\&f_{\omega^2+1}^2(n)\sim\psi(\Omega^{\Omega^2}\times\psi(\Omega^{\Omega^2}))\\&f_{\omega^2+2}(n)\sim\psi(\Omega^{\Omega^2+1})\\&f_{\omega^2+\omega}(n)\sim\psi(\Omega^{\Omega^2+\omega})\\&f_{\omega^2+\omega+1}(n)\sim\psi(\Omega^{\Omega^2+\Omega})\\&f_{\omega^2+\omega+2}(n)\sim\psi(\Omega^{\Omega^2+\Omega+1})\\&f_{\omega^2+\omega\times2+1}(n)\sim\psi(\Omega^{\Omega^2+\Omega\times2})\\&f_{\omega^2\times2}(n)\sim\psi(\Omega^{\Omega^2+\Omega\times\omega})\\&f_{\omega^2\times2+1}(n)\sim\psi(\Omega^{\Omega^2\times2})\\&f_{\omega^2\times3+1}(n)\sim\psi(\Omega^{\Omega^2\times3})\\&f_{\omega^3}(n)\sim\psi(\Omega^{\Omega^2\times\omega})\\&f_{\omega^2\times n}(f_{\omega^3}(n))\sim\psi(\Omega^{\Omega^2\times\omega}\times2)\\&f_{\omega^2\times n+1}^n(f_{\omega^3}(n))\sim\psi(\Omega^{\Omega^2\times\omega+1})\\&f_{\omega^2\times n+n}(f_{\omega^3}(n))\sim\psi(\Omega^{\Omega^2\times\omega+\omega})\\&f_{\omega^2\times n+\omega}(f_{\omega^3}(n))\sim\psi(\Omega^{\Omega^2\times\omega+\psi(\Omega^{\Omega^2\times\omega})})\\&f_{\omega^2\times n+\omega}^n(f_{\omega^3}(n))\sim\psi(\Omega^{\Omega^2\times\omega+\Omega})\\&f_{\omega^2\times n+\omega\times n}(f_{\omega^3}(n))\sim\psi(\Omega^{\Omega^2\times\omega+\Omega\times\omega})\\&f_{\omega^2\times n+\omega^2}^n(f_{\omega^3}(n))\sim\psi(\Omega^{\Omega^2\times\omega+\Omega^2})\\&f_{\omega^2\times n\times2}(f_{\omega^3}(n))\sim\psi(\Omega^{\Omega^2\times\omega\times2})\\&f_{\omega^3}^2(n)\sim\psi(\Omega^{\Omega^2\times\psi(\Omega^{\Omega^2})})\\&f_{\omega^3+1}(n)\sim\psi(\Omega^{\Omega^3})\\&f_{\omega^3+2}(n)\sim\psi(\Omega^{\Omega^3+1})\\&f_{\omega^3+\omega+1}(n)\sim\psi(\Omega^{\Omega^3+\Omega})\\&f_{\omega^3+\omega^2+1}(n)\sim\psi(\Omega^{\Omega^3+\Omega^2})\\&f_{\omega^3\times2+1}(n)\sim\psi(\Omega^{\Omega^3\times2})\\&f_{\omega^4}(n)\sim\psi(\Omega^{\Omega^3\times\omega})\\&f_{\omega^4+1}(n)\sim\psi(\Omega^{\Omega^4})\\&f_{\omega^\omega}(n)\sim\psi(\Omega^{\Omega^\omega})=\varphi(1@\omega)\\ \end{align}
\begin{align} & f_{\omega^\omega}(n)\sim\psi(\Omega^{\Omega^\omega})\\&f_3(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+1)\\&f_4^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega)\\&f_5^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^2)\\&f_n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^\omega)\\&f_{\omega}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\psi(\Omega^{\Omega^\omega})})\\&f_{\omega}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega})\\&f_{\omega+1}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega+1})\\&f_{\omega+n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega+\omega})\\&f_{\omega\times2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega\times2})\\&f_{\omega\times n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega\times\omega})\\&f_{\omega^2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega^2})\\&f_{\omega^3}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}+\Omega^{\Omega^3})\\&f_{\omega^n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}\times2)\\&f_{\omega^n}^2(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}\times3)\\&f_{\omega^n}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}\times\omega)\\&f_{\omega^n+1}(f_{\omega^\omega}(n))=f_{\omega^n}^{f_{\omega^\omega}(n)}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega}\times\psi(\Omega^{\Omega^\omega}))\\&f_{\omega^n+1}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+1})\\&f_{\omega^n+2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+2})\\&f_{\omega^n+n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+\omega})\\&f_{\omega^n+\omega}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+\Omega})\\&f_{\omega^n+\omega\times2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+\Omega\times2})\\&f_{\omega^n+\omega^2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega+\Omega^2})\\&f_{\omega^n\times2}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega\times2})\\&f_{\omega^n\times3}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega\times3})\\&f_{\omega^n\times n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^\omega\times\omega})\\&f_{\omega^{n+1}}(f_{\omega^\omega}(n))=f_{\omega^n\times f_{\omega^\omega}(n)}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}})\\&f_{\omega^n}(f_{\omega^{n+1}}(f_{\omega^\omega}(n)))\sim\psi(\Omega^{\Omega^{\omega+1}}+\Omega^{\Omega^\omega})\\&f_{\omega^n+1}^n(f_{\omega^{n+1}}(f_{\omega^\omega}(n)))\sim\psi(\Omega^{\Omega^{\omega+1}}+\Omega^{\Omega^\omega+1})\\&f_{\omega^n\times n}(f_{\omega^{n+1}}(f_{\omega^\omega}(n)))\sim\psi(\Omega^{\Omega^{\omega+1}}+\Omega^{\Omega^\omega\times\omega})\\&f_{\omega^{n+1}}^2(f_{\omega^\omega}(n))=f_{\omega^n\times f_{\omega^{n+1}}(f_{\omega^\omega}(n))}(f_{\omega^{n+1}}(f_{\omega^\omega}(n)))\sim\psi(\Omega^{\Omega^{\omega+1}}\times2)\\&f_{\omega^{n+1}}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}}\times\omega)\\&f_{\omega^{n+1}+1}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}+1})\\&f_{\omega^{n+1}+\omega^n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}+\Omega^\omega})\\&f_{\omega^{n+1}\times2}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}\times2})\\&f_{\omega^{n+1}\times n}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+1}\times\omega})\\&f_{\omega^{n+2}}^n(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega+2}})\\&f_{\omega^{n\times2}}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega\times2}})\\&f_{\omega^{n^2}}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\omega^2}})\\&f_{\omega^{f_3(n)}}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\psi(0)}})\\&f_{\omega^\omega}^2(n)=f_{\omega^{f_{\omega^\omega}(n)}}(f_{\omega^\omega}(n))\sim\psi(\Omega^{\Omega^{\psi(\Omega^{\Omega^\omega})}})\\&f_{\omega^\omega}^3(n)\sim\psi(\Omega^{\Omega^{\psi(\Omega^{\Omega^{\psi(\Omega^{\Omega^\omega})}})}})\\&f_{\omega^\omega+1}(n)=f_{\omega^\omega}^n(n)\sim\psi(\Omega^{\Omega^{\Omega}})\\&f_{\omega^\omega+2}(n)\sim\psi(\Omega^{\Omega^\Omega+1})\\&f_{\omega^\omega+3}(n)\sim\psi(\Omega^{\Omega^\Omega+2})\\&f_{\omega^\omega+\omega}(n)\sim\psi(\Omega^{\Omega^\Omega+\omega})\\&f_{\omega^\omega+\omega+1}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega})\\&f_{\omega^\omega+\omega\times2}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega+\omega})\\&f_{\omega^\omega+\omega\times2+1}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega\times2})\\&f_{\omega^\omega+\omega^2}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega\times\omega})\\&f_{\omega^\omega+\omega^2+1}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega^2})\\&f_{\omega^\omega+\omega^3+1}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega^3})\\&f_{\omega^\omega\times2}(n)\sim\psi(\Omega^{\Omega^\Omega+\Omega^\omega})\\&f_{\omega^\omega\times2+1}(n)\sim\psi(\Omega^{\Omega^\Omega\times2})\\&f_{\omega^\omega\times3+1}(n)\sim\psi(\Omega^{\Omega^\Omega\times3})\\&f_{\omega^{\omega+1}}(n)\sim\psi(\Omega^{\Omega^\Omega\times\omega})\\&f_{\omega^{\omega+1}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega+1}})\\&f_{\omega^{\omega+1}+\omega+1}(n)\sim\psi(\Omega^{\Omega^{\Omega+1}+\Omega})\\&f_{\omega^{\omega+1}+\omega^\omega+1}(n)\sim\psi(\Omega^{\Omega^{\Omega+1}+\Omega^\Omega})\\&f_{\omega^{\omega+1}\times2+1}(n)\sim\psi(\Omega^{\Omega^{\Omega+1}\times2})\\&f_{\omega^{\omega+2}}(n)\sim\psi(\Omega^{\Omega^{\Omega+1}\times\omega})\\&f_{\omega^{\omega+2}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega+2}})\\&f_{\omega^{\omega\times2}}(n)\sim\psi(\Omega^{\Omega^{\Omega+\omega}})\\&f_{\omega^{\omega\times2}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega\times2}})\\&f_{\omega^{\omega\times3}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega\times3}})\\&f_{\omega^{\omega^2}}(n)\sim\psi(\Omega^{\Omega^{\Omega\times\omega}})\\&f_{\omega^{\omega^2}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^2}})\\&f_{\omega^{\omega^2}\times2+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^2}\times2})\\&f_{\omega^{\omega^2+1}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^2+1}})\\&f_{\omega^{\omega^2+\omega}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^2+\Omega}})\\&f_{\omega^{\omega^2\times2}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^2\times2}})\\&f_{\omega^{\omega^3}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^3}})\\&f_{\omega^{\omega^\omega}}(n)\sim\psi(\Omega^{\Omega^{\Omega^\omega}})\\&f_{\omega^{\omega^\omega}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^\Omega}})\\&f_{\omega^{\omega^{\omega^\omega}}+1}(n)\sim\psi(\Omega^{\Omega^{\Omega^{\Omega^\Omega}}})\\&f_{\psi(0)}(n)\sim\psi(\psi_1(0))\\&f_3(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+1)\\&f_4^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega)\\&f_n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^\omega)\\&f_\omega(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\psi(\psi_1(0))})\\&f_\omega^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega})\\&f_{\omega+1}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega+1})\\&f_{\omega\times2}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega\times2})\\&f_{\omega^\omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega^\Omega})\\&f_{\omega^\omega+1}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega^\Omega+1})\\&f_{\omega^{\omega^\omega}}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega^{\Omega^\Omega}})\\&f_{\omega^{\omega^{\omega^\omega}}}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)+\Omega^{\Omega^{\Omega^{\Omega^\Omega}}})\\&f_{\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times2)\\&f_{\psi(0)[n]}^2(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times3)\\&f_{\psi(0)[n]}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\omega)\\&f_{\psi(0)[n]+1}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\psi(\psi_1(0)))\\&f_{\psi(0)[n]+1}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega)\\&f_{\psi(0)[n]}(f_{\psi(0)[n]+1}^n(f_{\psi(0)}(n)))\sim\psi(\psi_1(0)\times\Omega+\psi_1(0))\\&f_{\psi(0)[n]+1}^{n+1}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega+\psi_1(0)\times\psi(\psi_1(0)\times\Omega))\\&f_{\psi(0)[n]+1}^{n\times2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega\times2)\\&f_{\psi(0)[n]+2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega\times\psi(\psi_1(0)))\\&f_{\psi(0)[n]+2}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega^2)\\&f_{\psi(0)[n]+n}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega^\omega)\\&f_{\psi(0)[n]+\omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)\times\Omega^\Omega)\\&f_{\psi(0)[n]\times2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^2)\\&f_{\psi(0)[n]\times n}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^\omega)\\&f_{\psi(0)[n]\times \omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^\Omega)\\&f_{\psi(0)[n]\times \omega^2}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\Omega^2})\\&f_{\psi(0)[n]\times \omega^\omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\Omega^\Omega})\\&f_{\psi(0)[n]^2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)})\\&f_{\psi(0)[n]^2+\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)+1})\\&f_{\psi(0)[n]^2\times2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)\times2})\\&f_{\psi(0)[n]^2\times n}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)\times\omega})\\&f_{\psi(0)[n]^2\times \omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)\times\Omega})\\&f_{\psi(0)[n]^3}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^2})\\&f_{\psi(0)[n]^n}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^\omega})\\&f_{\psi(0)[n]^\omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^\Omega})\\&f_{\psi(0)[n]^{\psi(0)[n]}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}})\\&f_{\psi(0)[n+1]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}})\\&f_{\psi(0)[n+1]+\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}+1})\\&f_{\psi(0)[n+1]+\psi(0)[n]^2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}+\psi_1(0)})\\&f_{\psi(0)[n+1]+\psi(0)[n]^\omega}^n(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}+\psi_1(0)^\Omega})\\&f_{\psi(0)[n+1]\times2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)}\times2})\\&f_{\psi(0)[n+1]\times\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)+1}})\\&f_{\psi(0)[n+1]\times\psi(0)[n]^2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)+2}})\\&f_{\psi(0)[n+1]^2}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)\times2}})\\&f_{\psi(0)[n+1]^{\psi(0)[n]}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^2}})\\&f_{\psi(0)[n+1]^{\psi(0)[n]+1}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^2+\psi_1(0)}})\\&f_{\psi(0)[n+1]^{\psi(0)[n]\times2}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^2\times2}})\\&f_{\psi(0)[n+1]^{\psi(0)[n]^2}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^3}})\\&f_{\psi(0)[n+2]}(f_{\psi(0)}(n))=f_{\psi(0)[n+1]^{\psi(0)[n+1]}}(f_{\psi(0)}(n))=f_{\psi(0)[n+1]^{\psi(0)[n]^{\psi(0)[n]}}}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^{\psi_1(0)}}})\\&f_{\psi(0)[n+3]}(f_{\psi(0)}(n))\sim\psi(\psi_1(0)^{\psi_1(0)^{\psi_1(0)^{\psi_1(0)^{\psi_1(0)}}}})\\&f_{\psi(0)[n\times2]}(f_{\psi(0)}(n))\sim\psi(\psi_1(1))\\&f_{\psi(0)[n]}(f_{\psi(0)[n\times2]}(f_{\psi(0)}(n)))\sim\psi(\psi_1(1)+\psi_1(0))\\&f_{\psi(0)[n\times2]}^2(f_{\psi(0)}(n))\sim\psi(\psi_1(1)\times2)\\&f_{\psi(0)[n\times2]+\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)\times\psi_1(0))\\&f_{\psi(0)[n\times2]+\psi(0)[n+1]}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)\times\psi_1(0)^{\psi_1(0)^{\psi_1(0)}})\\&f_{\psi(0)[n\times2]\times2}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)^2)\\&f_{\psi(0)[n\times2]\times\psi(0)[n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)^{\psi_1(0)})\\&f_{\psi(0)[n\times2]^2}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)^{\psi_1(1)})\\&f_{\psi(0)[n\times2]^3}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)^{\psi_1(1)^2})\\&f_{\psi(0)[n\times2+1]}(f_{\psi(0)}(n))=f_{\psi(0)[n\times2]^{\psi(0)[n\times2]}}(f_{\psi(0)}(n))\sim\psi(\psi_1(1)^{\psi_1(1)^{\psi_1(1)}})\\&f_{\psi(0)[n\times3]}(f_{\psi(0)}(n))\sim\psi(\psi_1(2))\\&f_{\psi(0)[n^2]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\omega))\\&f_{\psi(0)[n^2+n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\omega+1))\\&f_{\psi(0)[n^3]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\omega^2))\\&f_{\psi(0)[n^n]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\omega^\omega))\\&f_{\psi(0)[f_3(n)]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\psi(0)))\\&f_{\psi(0)}^2(n)=f_{\psi(0)[f_{\psi(0)}(n)]}(f_{\psi(0)}(n))\sim\psi(\psi_1(\psi(\psi_1(0))))\\&f_{\psi(0)[n]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)))\times\psi_1(0))\\&f_{\psi(0)[n\times2]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)))\times\psi_1(1))\\&f_{\psi(0)[f_{\psi(0)}(n)]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)))^2)\\&f_{\psi(0)[f_{\psi(0)}(n)+1]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)))^{\psi_1(\psi(\psi_1(0)))^{\psi_1(\psi(\psi_1(0)))}})\\&f_{\psi(0)[f_{\psi(0)}(n)+n]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0))+1))\\&f_{\psi(0)[f_{\psi(0)}(n)\times2]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0))\times2))\\&f_{\psi(0)[f_3(f_{\psi(0)}(n))]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)+1)))\\&f_{\psi(0)[f_{\psi(0)[n]}(f_{\psi(0)}(n))]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(0)\times2)))\\&f_{\psi(0)[f_{\psi(0)[n\times2]}(f_{\psi(0)}(n))]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(1))))\\&f_{\psi(0)[f_{\psi(0)[n^2]}(f_{\psi(0)}(n))]}(f_{\psi(0)}^2(n))\sim\psi(\psi_1(\psi(\psi_1(\omega))))\\&f_{\psi(0)}^3(n)\sim\psi(\psi_1(\psi(\psi_1(\psi(\psi_1(0))))))\\&f_{\psi(0)+1}(n)\sim\psi(\psi_1(\Omega))\\&f_{\psi(0)[n]}(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)+\psi_1(0))\\&f_{\psi(0)[n\times2]}(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)+\psi_1(1))\\&f_{\psi(0)[f_{\psi(0)}(n)]}(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)+\psi_1(\psi(\psi_1(0))))\\&f_{\psi(0)}(f_{\psi(0)+1}(n))=f_{\psi(0)[f_{\psi(0)+1}(n)]}(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)+\psi_1(\psi(\psi_1(\Omega))))\\&f_{\psi(0)}^2(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)+\psi_1(\psi(\psi_1(\Omega)+\psi_1(\psi(\psi_1(\Omega))))))\\&f_{\psi(0)}^n(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)\times2)\\&f_{\psi(0)}^{n^2}(f_{\psi(0)+1}(n))\sim\psi(\psi_1(\Omega)\times\omega)\\&f_{\psi(0)+1}^2(n)\sim\psi(\psi_1(\Omega)\times\psi(\psi_1(\Omega)))\\&f_{\psi(0)+2}(n)\sim\psi(\psi_1(\Omega)\times\Omega)\\&f_{\psi(0)+3}(n)\sim\psi(\psi_1(\Omega)\times\Omega^2)\\&f_{\psi(0)+\omega}(n)\sim\psi(\psi_1(\Omega)\times\Omega^\omega)\\&f_{\psi(0)+\omega+1}(n)\sim\psi(\psi_1(\Omega)\times\Omega^\Omega)\\&f_{\psi(0)+\omega^\omega+1}(n)\sim\psi(\psi_1(\Omega)\times\Omega^{\Omega^\Omega})\\&f_{\psi(0)\times2}(n)\sim\psi(\psi_1(\Omega)\times\psi_1(0))\\&f_{\psi(0)\times2+1}(n)\sim\psi(\psi_1(\Omega)^2)\\&f_{\psi(0)\times3+1}(n)\sim\psi(\psi_1(\Omega)^3)\\&f_{\psi(0)\times\omega}(n)\sim\psi(\psi_1(\Omega)^\omega)\\&f_{\psi(0)\times\omega+1}(n)\sim\psi(\psi_1(\Omega)^\Omega)\\&f_{\psi(0)^2}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(0)})\\&f_{\psi(0)^2+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)})\\&f_{\psi(0)^2+\psi(0)+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)+1})\\&f_{\psi(0)^2\times2+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)\times2})\\&f_{\psi(0)^3+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)^2})\\&f_{\psi(0)^\omega+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)^\Omega})\\&f_{\psi(0)^{\psi(0)}}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)^{\psi_1(0)}})\\&f_{\psi(0)^{\psi(0)}+1}(n)\sim\psi(\psi_1(\Omega)^{\psi_1(\Omega)^{\psi_1(\Omega)}})\\&f_{\psi(1)}(n)\sim\psi(\psi_1(\Omega+1))\\&f_{\psi(0)[n]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)+\psi_1(0))\\&f_{\psi(0)}^n(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)+\psi_1(\Omega))\\&f_{\psi(0)^{\psi(0)}}^n(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)+\psi_1(\Omega)^{\psi_1(\Omega)^{\psi_1(\Omega)}})\\&f_{\psi(1)[n]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times2)\\&f_{\psi(1)[n]}^2(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times3)\\&f_{\psi(1)[n]+1}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times\psi(\psi_1(\Omega+1)))\\&f_{\psi(1)[n]+1}^n(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times\Omega)\\&f_{\psi(1)[n]+\psi(0)[n]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times\psi_1(0))\\&f_{\psi(1)[n]+\psi(0)}^n(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)\times\psi_1(\Omega))\\&f_{\psi(1)[n]\times2}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)^2)\\&f_{\psi(1)[n]\times\psi(0)[n]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)^{\psi_1(0)})\\&f_{\psi(1)[n]^2}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)^{\psi_1(\Omega+1)})\\&f_{\psi(1)[n+1]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+1)^{\psi_1(\Omega+1)^{\psi_1(\Omega+1)}})\\&f_{\psi(1)[n\times2]}(f_{\psi(1)}(n))\sim\psi(\psi_1(\Omega+2))\\&f_{\psi(1)}^2(n)\sim\psi(\psi_1(\Omega+\psi(\psi_1(\Omega))))\\&f_{\psi(1)+1}(n)\sim\psi(\psi_1(\Omega\times2))\\&f_{\psi(1)+2}(n)\sim\psi(\psi_1(\Omega\times2)\times\Omega)\\&f_{\psi(1)+\psi(0)+1}(n)\sim\psi(\psi_1(\Omega\times2)\times\psi_1(\Omega))\\&f_{\psi(1)\times2+1}(n)\sim\psi(\psi_1(\Omega\times2)^2)\\&f_{\psi(1)\times{\psi(0)}+1}(n)\sim\psi(\psi_1(\Omega\times2)^{\psi_1(\Omega)})\\&f_{\psi(1)^{2}+1}(n)\sim\psi(\psi_1(\Omega\times2)^{\psi_1(\Omega\times2)})\\&f_{\psi(1)^{\psi(1)}+1}(n)\sim\psi(\psi_1(\Omega\times2)^{\psi_1(\Omega\times2)^{\psi_1(\Omega\times2)}})\\&f_{\psi(2)}(n)\sim\psi(\psi_1(\Omega\times2+1))\\&f_{\psi(2)+1}(n)\sim\psi(\psi_1(\Omega\times3))\\&f_{\psi(3)}(n)\sim\psi(\psi_1(\Omega\times3+1))\\&f_{\psi(4)}(n)\sim\psi(\psi_1(\Omega\times4+1))\\&f_{\psi(\omega)}(n)\sim\psi(\psi_1(\Omega\times\omega))\\&f_{\psi(\omega)+1}(n)\sim\psi(\psi_1(\Omega^2))\\&f_{\psi(\omega)+2}(n)\sim\psi(\psi_1(\Omega^2)\times\Omega)\\&f_{\psi(\omega)\times2+1}(n)\sim\psi(\psi_1(\Omega^2)^2)\\&f_{\psi(\omega)^2+1}(n)\sim\psi(\psi_1(\Omega^2)^{\psi_1(\Omega^2)})\\&f_{\psi(\omega+1)}(n)\sim\psi(\psi_1(\Omega^2+1))\\&f_{\psi(\omega+1)+1}(n)\sim\psi(\psi_1(\Omega^2+\Omega))\\&f_{\psi(\omega+2)+1}(n)\sim\psi(\psi_1(\Omega^2+\Omega\times2))\\&f_{\psi(\omega\times2)+1}(n)\sim\psi(\psi_1(\Omega^2\times2))\\&f_{\psi(\omega^2)+1}(n)\sim\psi(\psi_1(\Omega^3))\\&f_{\psi(\omega^\omega)}(n)\sim\psi(\psi_1(\Omega^\omega))\\&f_{\psi(\omega^\omega)+1}(n)\sim\psi(\psi_1(\Omega^\Omega))\\&f_{\psi(\omega^{\omega^\omega})+1}(n)\sim\psi(\psi_1(\Omega^{\Omega^\Omega}))\\&f_{\psi(\psi(0))}(n)\sim\psi(\psi_1(\psi_1(0)))\\&f_{\psi(\psi(0))+1}(n)\sim\psi(\psi_1(\psi_1(\Omega)))\\&f_{\psi(\psi(1))+1}(n)\sim\psi(\psi_1(\psi_1(\Omega\times2)))\\&f_{\psi(\psi(\psi(0)))+1}(n)\sim\psi(\psi_1(\psi_1(\psi_1(\Omega))))\\&f_{\psi(\Omega)}(n)\sim\psi(\Omega_2)\\&f_{3}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+1)\\&f_{\omega}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\Omega^\Omega)\\&f_{\psi(0)[n]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(0))\\&f_{\psi(0)}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega))\\&f_{\psi(1)[n]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega+1))\\&f_{\psi(1)}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega\times2))\\&f_{\psi(\omega)}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega^2))\\&f_{\psi(\psi(0))}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\psi_1(\Omega)))\\&f_{\psi(\psi(\psi(0)))}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\psi_1(\psi_1(\Omega))))\\&f_{\psi(\Omega)[n]}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)\times\omega)\\&f_{\psi(\Omega)[n]+1}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)\times\Omega)\\&f_{\psi(\Omega)[n]\times2}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)^2)\\&f_{\psi(\Omega)[n]\times \omega}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)^\Omega)\\&f_{\psi(\Omega)[n]\times \psi(0)+1}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)^{\psi_1(\Omega)})\\&f_{\psi(\Omega)[n]^2}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)^{\psi_1(\Omega_2)})\\&f_{\psi(\Omega)[n]^{\psi(\Omega)[n]}}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2)^{\psi_1(\Omega_2)^{\psi_1(\Omega_2)}})\\&f_{\psi(\psi(\Omega)[n-1]+1)[n]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+1))\\&f_{\psi(\psi(\Omega)[n-1]+1)}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\Omega))\\&f_{\psi(\psi(\Omega)[n-1]+n)}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\Omega\times\omega))\\&f_{\psi(\psi(\Omega)[n-1]+\omega)}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\Omega^2))\\&f_{\psi(\psi(\Omega)[n-1]+\psi(0))}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega)))\\&f_{\psi(\psi(\Omega)[n-1]+\psi(\psi(0)))}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\psi_1(\Omega))))\\&f_{\psi(\Omega)[n+1]}(f_{\psi(\Omega)}(n))=f_{\psi(\psi(\Omega)[n])}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)))\\&f_{\psi(\psi(\Omega)[n]+1)}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)+1))\\&f_{\psi(\psi(\Omega)[n]\times2)}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)\times2))\\&f_{\psi(\psi(\Omega)[n]^2)}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)^2))\\&f_{\psi(\psi(\psi(\Omega)[n-1]+1))}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2+1)))\\&f_{\psi(\Omega)[n+2]}(f_{\psi(\Omega)}(n))=f_{\psi(\psi(\psi(\Omega)[n]))}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2))))\\&f_{\psi(\Omega)[n\times2]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2)\\&f_{\psi(\Omega)[n]}(f_{\psi(\Omega)[n\times2]}(f_{\psi(\Omega)}(n)))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2))\\&f_{\psi(\Omega)[n\times2]}^2(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2))\\&f_{\psi(\Omega)[n\times2]+1}^n(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2)\times\Omega)\\&f_{\psi(\Omega)[n\times2]\times2}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2)^2)\\&f_{\psi(\Omega)[n\times2]^2}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2)^{\psi_!(\Omega_2\times2)})\\&f_{\psi(\psi(\Omega)[n\times2-1]+1)}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2+1))\\&f_{\psi(\Omega)[n\times2+1]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times2+\psi_1(\Omega_2\times2+\psi_1(\Omega_2\times2)))\\&f_{\psi(\Omega)[n\times3]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times3)\\&f_{\psi(\Omega)[n^2]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\omega)\\&f_{\psi(\Omega)[n^2+1]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\omega+\psi_1(\Omega_2\times\omega+\psi_1(\Omega_2\times\omega)))\\&f_{\psi(\Omega)[n^2+n]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\omega+\Omega_2)\\&f_{\psi(\Omega)[n^3]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\omega^2)\\&f_{\psi(\Omega)[f_3(n)]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\psi(0))\\&f_{\psi(\Omega)}^2(n)=f_{\psi(\Omega)[f_{\psi(\Omega)}(n)]}(f_{\psi(\Omega)}(n))\sim\psi(\Omega_2\times\psi(\Omega_2))\\&f_{\psi(\Omega)}^3(n)\sim\psi(\Omega_2\times\psi(\Omega_2\times\psi(\Omega_2)))\\&f_{\psi(\Omega)+1}(n)=f_{\psi(\Omega)}^n(n)\sim\psi(\Omega_2\times\Omega)\\&f_{\psi(\Omega)}(f_{\psi(\Omega)+1}(n))\sim\psi(\Omega_2\times\Omega+\Omega_2\times\psi(\Omega_2\times\Omega))\\&f_{\psi(\Omega)}^n(f_{\psi(\Omega)+1}(n))\sim\psi(\Omega_2\times\Omega\times2)\\&f_{\psi(\Omega)+1}^2(n)\sim\psi(\Omega_2\times\Omega\times\psi(\Omega_2\times\Omega))\\&f_{\psi(\Omega)+2}(n)\sim\psi(\Omega_2\times\Omega^2)\\&f_{\psi(\Omega)+\omega}(n)\sim\psi(\Omega_2\times\Omega^\omega)\\&f_{\psi(\Omega)+\omega+1}(n)\sim\psi(\Omega_2\times\Omega^\Omega)\\&f_{\psi(\Omega)+\omega^\omega+1}(n)\sim\psi(\Omega_2\times\Omega^{\Omega^\Omega})\\&f_{\psi(\Omega)+\psi(0)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega))\\&f_{\psi(\Omega)+\psi(1)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega\times2))\\&f_{\psi(\Omega)+\psi(\psi(0))+1}(n)\sim\psi(\Omega_2\times\psi_1(\psi_1(\Omega)))\\&f_{\psi(\Omega)\times2}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2))\\&f_{\psi(\Omega)}^n(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)+\Omega_2\times\Omega)\\&f_{\psi(\Omega)+\psi(0)}^n(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)+\Omega_2\times\psi_1(\Omega))\\&f_{\psi(\Omega)+\psi(\Omega)[n]}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)\times2)\\&f_{\psi(\Omega)+\psi(\Omega)[n]}^2(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)\times3)\\&f_{\psi(\Omega)+\psi(\Omega)[n]+1}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)\times\psi(\Omega_2\times\psi_1(\Omega_2)))\\&f_{\psi(\Omega)+\psi(\Omega)[n]+1}^n(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)\times\Omega)\\&f_{\psi(\Omega)+\psi(\Omega)[n]\times2}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2)^2)\\&f_{\psi(\Omega)+\psi(\psi(\Omega)[n-1]+1)[n]}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2+1))\\&f_{\psi(\Omega)+\psi(\Omega)[n+1]}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2+\psi_1(\Omega_2)))\\&f_{\psi(\Omega)+\psi(\Omega)[n\times2]}(f_{\psi(\Omega)\times2}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2\times2))\\&f_{\psi(\Omega)\times2}^2(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi(\Omega_2\times\psi_1(\Omega_2))))\\&f_{\psi(\Omega)\times2+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega))\\&f_{\psi(\Omega)\times2}(f_{\psi(\Omega)\times2+1}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)+\Omega_2\times\psi_1(\Omega_2\times\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega))))\\&f_{\psi(\Omega)\times2}^n(f_{\psi(\Omega)\times2+1}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)\times2)\\&f_{\psi(\Omega)\times2+1}^2(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)\times\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)))\\&f_{\psi(\Omega)\times2+2}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)\times\Omega)\\&f_{\psi(\Omega)\times3}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)\times\psi_1(\Omega_2))\\&f_{\psi(\Omega)\times3+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^2)\\&f_{\psi(\Omega)\times\omega+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^\Omega)\\&f_{\psi(\Omega)\times\omega+\psi(\Omega)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^{\Omega+1})\\&f_{\psi(\Omega)\times\psi(0)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^{\psi_1(0)})\\&f_{\psi(\Omega)^2}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^{\psi_1(\Omega_2)})\\&f_{\psi(\Omega)^2+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^{\psi_1(\Omega_2\times\Omega)})\\&f_{\psi(\Omega)^{\psi(\Omega)}+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega)^{\psi_1(\Omega_2\times\Omega)^{\psi_1(\Omega_2\times\Omega)}})\\&f_{\psi(\Omega+1)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+1))\\&f_{\psi(\Omega+1)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\Omega))\\&f_{\psi(\Omega+2)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\Omega+1))\\&f_{\psi(\Omega+2)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\Omega\times2))\\&f_{\psi(\Omega+\omega)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\Omega^2))\\&f_{\psi(\Omega+\psi(0))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(0)))\\&f_{\psi(\Omega+\psi(0))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega)))\\&f_{\psi(\Omega+\psi(\Omega))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2)))\\&f_{\psi(\Omega+\psi(\Omega))[n\times2]}(f_{\psi(\Omega+\psi(\Omega))}(n))\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times2)))\\&f_{\psi(\Omega+\psi(\Omega))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times\Omega)))\\&f_{\psi(\Omega+\psi(\Omega)+1)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times\Omega)+1))\\&f_{\psi(\Omega+\psi(\Omega+1))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times\Omega+1)))\\&f_{\psi(\Omega+\psi(\Omega+\psi(\Omega)))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times\Omega+\psi_1(\Omega_2\times\Omega))))\\&f_{\psi(\Omega\times2)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega+\Omega_2))\\&f_{\psi(\Omega\times2)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2))\\&f_{\psi(\Omega\times2)\times2+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2)^2)\\&f_{\psi(\Omega\times2+1)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2+1))\\&f_{\psi(\Omega\times2+1)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2+\Omega))\\&f_{\psi(\Omega\times2+\psi(\Omega\times2))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2+\psi_1(\Omega_2\times\Omega\times2)))\\&f_{\psi(\Omega\times3)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2+\Omega_2))\\&f_{\psi(\Omega\times3)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times3))\\&f_{\psi(\Omega\times\omega)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega\times\omega))\\&f_{\psi(\Omega\times\omega)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^2))\\&f_{\psi(\Omega\times\omega+1)}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^2+1))\\&f_{\psi(\Omega\times\omega+\Omega)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^2+\Omega_2\times\Omega))\\&f_{\psi(\Omega\times\omega\times2)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^2\times2))\\&f_{\psi(\Omega\times\omega^2)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^3))\\&f_{\psi(\Omega\times\omega^\omega)+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\Omega^\Omega))\\&f_{\psi(\Omega\times\psi(0))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(0)))\\&f_{\psi(\Omega\times\psi(0))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega)))\\&f_{\psi(\Omega\times\psi(1))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega+1)))\\&f_{\psi(\Omega\times\psi(\Omega))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2)))\\&f_{\psi(\Omega\times\psi(\Omega))+1}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2\times\Omega)))\\&f_{\psi(\Omega\times\psi(\Omega+1))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2\times\Omega+1)))\\&f_{\psi(\Omega\times\psi(\Omega\times2))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2\times\Omega\times2)))\\&f_{\psi(\Omega\times\psi(\Omega\times\psi(0)))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2\times\psi_1(0))))\\&f_{\psi(\Omega\times\psi(\Omega\times\psi(\Omega)))}(n)\sim\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2))))\\&f_{\psi(\Omega^2)}(n)\sim\psi(\Omega_2^2)\\&f_{\psi(\Omega^2)[n]}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\psi_1(\Omega^2_2))\\&f_{\psi(\Omega\times\psi(\Omega^2)[n-1]+1)}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\psi_1(\Omega^2_2+1))\\&\psi(\Omega^2)[n]=\psi(\Omega\times\psi(\Omega^2)[n-1]) \\&f_{\psi(\Omega\times\psi(\Omega^2)[n-1]+\Omega)[n]}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\Omega_2)\\&f_{\psi(\Omega\times\psi(\Omega^2)[n-1]+\Omega)}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\Omega_2\times\Omega)\\&f_{\psi(\Omega\times\psi(\Omega^2)[n-1]+\Omega\times\psi(\Omega))}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\Omega_2\times\psi_1(\Omega_2))\\&f_{\psi(\Omega^2)[n+1]}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2+\Omega_2\times\psi_1(\Omega_2^2))\\&f_{\psi(\Omega^2)[n\times2]}(f_{\psi(\Omega^2)}(n))\sim\psi(\Omega^2_2\times2)\\&f_{\psi(\Omega^2)+1}(n)\sim\psi(\Omega^2_2\times\Omega)\\&f_{\psi(\Omega^2)+2}(n)\sim\psi(\Omega^2_2\times\Omega^2)\\&f_{\psi(\Omega^2)+\psi(0)}(n)\sim\psi(\Omega^2_2\times\psi_1(0))\\&f_{\psi(\Omega^2)+\psi(\Omega)}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2))\\&f_{\psi(\Omega^2)+\psi(\Omega\times\psi(\Omega))}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2)))\\&f_{\psi(\Omega^2)\times2}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2))\\&f_{\psi(\Omega^2)\times2+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega))\\&f_{\psi(\Omega^2)^2+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega)^{\psi_1(\Omega^2_2\times\Omega)})\\&f_{\psi(\Omega^2+1)}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+1))\\&f_{\psi(\Omega^2+1)+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega))\\&f_{\psi(\Omega^2+\psi(\Omega^2))+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\psi_1(\Omega^2_2\times\Omega)))\\&f_{\psi(\Omega^2+\Omega)}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega_2))\\&f_{\psi(\Omega^2+\Omega)+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega_2\times\Omega))\\&f_{\psi(\Omega^2+\Omega\times2)+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega_2\times\Omega\times2))\\&f_{\psi(\Omega^2+\Omega\times\psi(0))+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega_2\times\psi_1(\Omega)))\\&f_{\psi(\Omega^2+\Omega\times\psi(\Omega^2))+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega+\Omega_2\times\psi_1(\Omega_2^2\times\Omega)))\\&f_{\psi(\Omega^2\times2)}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega\times2))\\&f_{\psi(\Omega^2\times\omega)+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\Omega^2))\\&f_{\psi(\Omega^2\times\psi(0))+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\psi_1(0)))\\&f_{\psi(\Omega^2\times\psi(\Omega^2))}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\psi_1(\Omega_2^2)))\\&f_{\psi(\Omega^2\times\psi(\Omega^2))+1}(n)\sim\psi(\Omega^2_2\times\psi_1(\Omega_2^2\times\psi_1(\Omega_2^2\times\Omega)))\\&f_{\psi(\Omega^3)}(n)\sim\psi(\Omega_2^3)\\&f_{\psi(\Omega^4)}(n)\sim\psi(\Omega_2^4)\\&f_{\psi(\Omega^\omega)}(n)\sim\psi(\Omega_2^\omega)\\&f_{\psi(\Omega^\omega)+1}(n)\sim\psi(\Omega_2^\Omega)\\&f_{\psi(\Omega^\omega)+2}(n)\sim\psi(\Omega_2^\Omega\times\Omega)\\&f_{\psi(\Omega^\omega)\times2}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\omega))\\&f_{\psi(\Omega^\omega)\times2+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega))\\&f_{\psi(\Omega^\omega)\times2+2}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)\times\Omega)\\&f_{\psi(\Omega^\omega)^2+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega)^{\psi_1(\Omega_2^\Omega)})\\&f_{\psi(\Omega^\omega+1)}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+1))\\&f_{\psi(\Omega^\omega+\psi(\Omega^\omega))+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\psi_1(\Omega_2^\Omega)))\\&f_{\psi(\Omega^\omega+\Omega)+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\Omega_2\times\Omega))\\&f_{\psi(\Omega^\omega\times2)}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega+\Omega_2^\omega))\\&f_{\psi(\Omega^\omega\times2)+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times2))\\&f_{\psi(\Omega^\omega\times\psi(0))+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega)))\\&f_{\psi(\Omega^\omega\times\psi(\Omega^\omega))+1}(n)\sim\psi(\Omega_2^\Omega\times\psi_1(\Omega_2^\Omega\times\psi_1(\Omega^\Omega)))\\&f_{\psi(\Omega^{\omega+1})}(n)\sim\psi(\Omega_2^{\Omega+1})\\&f_{\psi(\Omega^{\omega\times2})+1}(n)\sim\psi(\Omega_2^{\Omega\times2})\\&f_{\psi(\Omega^{\omega^2})+1}(n)\sim\psi(\Omega_2^{\Omega^2})\\&f_{\psi(\Omega^{\omega^\omega})+1}(n)\sim\psi(\Omega_2^{\Omega^\Omega})\\&f_{\psi(\Omega^{\psi(0)})}(n)\sim\psi(\Omega_2^{\psi_1(0)})\\&f_{\psi(\Omega^{\psi(0)})+1}(n)\sim\psi(\Omega_2^{\psi_1(\Omega)})\\&f_{\psi(\Omega^{\psi(\Omega)})}(n)\sim\psi(\Omega_2^{\psi_1(\Omega_2)})\\&f_{\psi(\Omega^{\psi(\Omega^2)})}(n)\sim\psi(\Omega_2^{\psi_1(\Omega_2^2)})\\&f_{\psi(\Omega^{\psi(\Omega^{\psi(\Omega)})})}(n)\sim\psi(\Omega_2^{\psi_1(\Omega_2^{\psi_1(\Omega_2)})})\\&f_{\psi(\Omega^{\Omega})}(n)\sim\psi(\Omega_2^{\Omega_2})\\&f_{\psi(\Omega^{\Omega})+1}(n)\sim\psi(\Omega_2^{\Omega_2}\times\Omega)\\&f_{\psi(\Omega^{\Omega})\times2}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}))\\&f_{\psi(\Omega^{\Omega}+1)+1}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times\Omega+\Omega))\\&f_{\psi(\Omega^{\Omega}+\Omega)+1}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times\Omega+\Omega_2\times\Omega))\\&f_{\psi(\Omega^{\Omega}+\Omega^{\psi(\Omega^\Omega)})}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times\Omega+\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}))\\&f_{\psi(\Omega^{\Omega}\times2)}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times\Omega\times2))\\&f_{\psi(\Omega^{\Omega}\times\psi(0))}(n)\sim\psi(\Omega_2^{\Omega_2}\times\psi_1(\Omega_2^{\Omega_2}\times\psi_1(0)))\\&f_{\psi(\Omega^{\Omega+1})}(n)\sim\psi(\Omega_2^{\Omega_2+1})\\&f_{\psi(\Omega^{\Omega+2})}(n)\sim\psi(\Omega_2^{\Omega_2+2})\\&f_{\psi(\Omega^{\Omega+\omega})+1}(n)\sim\psi(\Omega_2^{\Omega_2+\Omega})\\&f_{\psi(\Omega^{\Omega+\psi(\Omega^\Omega)})}(n)\sim\psi(\Omega_2^{\Omega_2+\psi_1(\Omega_2^{\Omega_2})})\\&f_{\psi(\Omega^{\Omega\times2})}(n)\sim\psi(\Omega_2^{\Omega_2\times2})\\&f_{\psi(\Omega^{\Omega^2})}(n)\sim\psi(\Omega_2^{\Omega_2^2})\\&f_{\psi(\Omega^{\Omega^\omega})}(n)\sim\psi(\Omega_2^{\Omega_2^\omega})\\&f_{\psi(\Omega^{\Omega^\omega})+1}(n)\sim\psi(\Omega_2^{\Omega_2^\Omega})\\&f_{\psi(\Omega^{\Omega^\Omega})}(n)\sim\psi(\Omega_2^{\Omega_2^{\Omega_2}})\\&f_{\psi(\psi_1(0))}(n)\sim\psi(\psi_2(0))\\&f_{\psi(\psi_1(0)\times\Omega)}(n)\sim\psi(\psi_2(0)\times\Omega_2)\\&f_{\psi(\psi_1(0)^2)}(n)\sim\psi(\psi_2(0)^2)\\&f_{\psi(\psi_1(0)^\Omega)}(n)\sim\psi(\psi_2(0)^{\Omega_2})\\&f_{\psi(\psi_1(0)^{\psi_1(0)})}(n)\sim\psi(\psi_2(0)^{\psi_2(0)})\\&f_{\psi(\psi_1(1))}(n)\sim\psi(\psi_2(1))\\&f_{\psi(\psi_1(\omega))+1}(n)\sim\psi(\psi_2(\Omega))\\&f_{\psi(\psi_1(\psi(0)))}(n)\sim\psi(\psi_2(\psi_1(0)))\\&f_{\psi(\psi_1(\psi(\Omega)))}(n)\sim\psi(\psi_2(\psi_1(\Omega_2)))\\&f_{\psi(\psi_1(\psi(\Omega^\Omega)))}(n)\sim\psi(\psi_2(\psi_1(\Omega_2^{\Omega_2})))\\&f_{\psi(\psi_1(\psi(\psi_1(0))))}(n)\sim\psi(\psi_2(\psi_1(\psi_2(0))))\\&f_{\psi(\psi_1(\Omega))}(n)\sim\psi(\psi_2(\Omega_2))\\&f_{\psi(\psi_1(\psi_1(0)))}(n)\sim\psi(\psi_2(\psi_2(0)))\\&f_{\psi(\Omega_2)}(n)\sim\psi(\Omega_3)\\&f_{\psi(\Omega_2)[n]}(f_{\psi(\Omega_2)}(n))\sim\psi(\Omega_3+\psi_2(\Omega_3))\\&f_{\psi(\Omega_2)[n+1]}(f_{\psi(\Omega_2)}(n))\sim\psi(\Omega_3+\psi_2(\Omega_3+\psi_2(\Omega_3)))\\&f_{\psi(\Omega_2)[n\times2]}(f_{\psi(\Omega_2)}(n))\sim\psi(\Omega_3\times2)\\&f_{\psi(\Omega_2)+1}(n)\sim\psi(\Omega_3\times\Omega)\\&f_{\psi(\Omega_2)+\psi(0)}(n)\sim\psi(\Omega_3\times\psi_1(0))\\&f_{\psi(\Omega_2)+\psi(\Omega)}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_2))\\&f_{\psi(\Omega_2)\times2}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3))\\&f_{\psi(\Omega_2)\times2+1}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega))\\&f_{\psi(\Omega_2)\times3+1}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega)^2)\\&f_{\psi(\Omega_2)^2+1}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega)^{\psi_1(\Omega_3\times\Omega)})\\&f_{\psi(\Omega_2+1)}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+1))\\&f_{\psi(\Omega_2+\Omega)}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+\Omega_2))\\&f_{\psi(\Omega_2+\psi_1(\Omega_2))}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+\psi_2(\Omega_3)))\\&f_{\psi(\Omega_2+\psi_1(\Omega_2))+1}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+\psi_2(\Omega_3\times\Omega)))\\&f_{\psi(\Omega_2+\psi_1(\Omega_2+1))}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+\psi_2(\Omega_3\times\Omega+1)))\\&f_{\psi(\Omega_2\times2)}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega+\Omega_3))\\&f_{\psi(\Omega_2\times2)+1}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\Omega\times2))\\&f_{\psi(\Omega_2\times\psi(\Omega_2))}(n)\sim\psi(\Omega_3\times\psi_1(\Omega_3\times\psi_1(\Omega_3)))\\&f_{\psi(\Omega_2\times\Omega)}(n)\sim\psi(\Omega_3\times\Omega_2)\\&f_{\psi(\Omega_2\times\psi_1(0))}(n)\sim\psi(\Omega_3\times\psi_2(0))\\&f_{\psi(\Omega_2\times\psi_1(\Omega_2))}(n)\sim\psi(\Omega_3\times\psi_2(\Omega_3))\\&f_{\psi(\Omega_2^2)}(n)\sim\psi(\Omega_3^2)\\&f_{\psi(\Omega_2^{\Omega_2})}(n)\sim\psi(\Omega_3^{\Omega_3})\\&f_{\psi(\psi_2(0))}(n)\sim\psi(\psi_3(0))\\&f_{\psi(\Omega_3)}(n)\sim\psi(\Omega_4)\\&f_{\psi(\Omega_4)}(n)\sim\psi(\Omega_5)\\&\dots \\ \end{align}