(f[3,1,2]^2 ++ f[2,1,2]^2 ++ f[3,3]^2 ++ f[2,3]^2)(3)
=(f[3,1,2]^2 ++ f[2,1,2]^2 ++ f[3,3]^2 ++ f[2,3] ++ f[3,2]^3)(3)
=(f[3,1,2]^2 ++ f[2,1,2]^2 ++ f[3,3]^2 ++ f[2,3] ++ f[3,2]^2 ++ f[2,2]^3)(3)
=(f[3,1,2]^2 ++ f[2,1,2]^2 ++ f[3,3]^2 ++ f[2,3] ++ f[3,2]^2 ++ f[2,2]^2 ++ f[3]^3)(3)
≒(f[3,1,2]^2 ++ f[2,1,2]^2 ++ f[3,3]^2 ++ f[2,3] ++ f[3,2]^2 ++ f[2,2]^2)(10^10^8)
=(f[3,1,2]^2 ++ f[2,1,2]^2 ++ f[3,3]^2 ++ f[2,3] ++ f[3,2]^2 ++ f[2,2] ++ f[3]^3)(10^10^8)
=(f[3,1,2]^2 ++ f[2,1,2]^2 ++ f[3,3]^2 ++ f[2,3] ++ f[3,2]^2 ++ f[2,2] ++ f[3]^2 ++ f[2]^10^10^8)(10^10^8)
.........

あ、ルール2訂正
ルール2: f[1,1,1,...,e+1, ...](n)=f[n,n,n,...,e,...](n)

それとルール2はnが何か分からなくても使えます

ついでに
f[2,2,2](2) = f[1,2,2]^2(2)=f[2,1,2]^2(2)=(f[2,1,2] ++ f[2,2]^2)(2)=(f[2,1,2] ++ f[2,2] ++ f[2]²)(2)=(f[2,1,2] ++ f[2,2])(8)
=(f[2,1,2] ++ f[2]^8)(8)=f[2,1,2](2048)=f[1,1,2](2048)=f[2048,2048](2048)=f[2047,2048]^2048(2048)
=(f[2047,2048]^2047 ++ f[2046,2048]^2048)(2048)
・・・

f[2,2,2](1) = f[1,2,2](1) = f[1,1,2](1) = f[1,1](1) = f[1](1) = f(1) = 2