User blog comment:Hyp cos/Fundamental Sequences in Taranovsky's Notation/@comment-32697988-20190204142752/@comment-11227630-20190206080627

Let \(\alpha=C(C(\Omega_2,C(\Omega_2,0)),0)\).

In the processes to get α[0], α[1] and α[2], \(\gamma=0\land m=1\) do not happen.

To get α[3], C(C(Ω2,C(Ω2,0)),0) where \(\gamma=0\land m=1\) happens 3 times.
 * (step 2)-> C(C(0,C(Ω2,0)),0)
 * (step 3)-> C(C(C(C(C(Ω2,Ω2),Ω2),0),C(Ω2,0)),0)
 * (step 2)-> C(C(C(C(C(0,Ω2),Ω2),0),C(Ω2,0)),0)
 * (step 2)-> C(C(C(C(Ω2,C(Ω2,Ω2)),0),C(Ω2,0)),0)
 * (step 2)-> C(C(C(C(0,C(Ω2,Ω2)),0),C(Ω2,0)),0)
 * (step 2)-> C(C(C(Ω2,C(C(Ω2,Ω2),0)),C(Ω2,0)),0)
 * (step 2)-> C(C(C(0,C(C(Ω2,Ω2),0)),C(Ω2,0)),0)
 * (step 2)-> C(C(Ω2,C(C(C(Ω2,Ω2),0),C(Ω2,0))),0)
 * (step 2)-> C(C(0,C(C(C(Ω2,Ω2),0),C(Ω2,0))),0)
 * (step 2)-> C(Ω2,C(C(C(C(Ω2,Ω2),0),C(Ω2,0)),0))
 * (step 2)-> C(0,C(C(C(C(Ω2,Ω2),0),C(Ω2,0)),0))
 * (step 2, then back to step 1)-> C(C(C(C(Ω2,Ω2),0),C(Ω2,0)),0)
 * (step 2)-> C(C(C(C(0,Ω2),0),C(Ω2,0)),0)
 * (step 3)-> C(C(C(C(C(Ω2,0),Ω2),0),C(Ω2,0)),0)
 * (step 2)-> C(C(C(C(C(0,0),Ω2),0),C(Ω2,0)),0)
 * (many step 2's)-> C(0,C(C(C(C(0,Ω2),0),C(Ω2,0)),0))
 * (step 2, then back to step 1)-> C(C(C(C(0,Ω2),0),C(Ω2,0)),0)
 * (step 2)-> C(C(C(Ω2,C(Ω2,0)),C(Ω2,0)),0)
 * (step 3)-> C(C(C(C(Ω2,Ω2),C(Ω2,0)),C(Ω2,0)),0)
 * (step 2)-> C(C(C(C(0,Ω2),C(Ω2,0)),C(Ω2,0)),0)
 * (many step 2's)-> C(0,C(C(C(Ω2,C(Ω2,0)),C(Ω2,0)),0))
 * (step 2, then back to step 1)-> C(C(C(Ω2,C(Ω2,0)),C(Ω2,0)),0)
 * (step 2)-> C(C(C(0,C(Ω2,0)),C(Ω2,0)),0)
 * (step 3)-> C(C(C(C(Ω2,0),C(Ω2,0)),C(Ω2,0)),0)

To get α[4], \(\gamma=0\land m=1\) happen 31 times, where \(\beta\)'s are
 * C(0,C(C(C(C(C(Ω2,Ω2),Ω2),0),C(Ω2,0)),0))
 * C(0,C(C(C(C(C(0,Ω2),Ω2),0),C(Ω2,0)),0))
 * C(0,C(C(C(C(Ω2,C(Ω2,Ω2)),0),C(Ω2,0)),0))
 * C(0,C(C(C(C(0,C(Ω2,Ω2)),0),C(Ω2,0)),0))
 * C(0,C(C(C(Ω2,C(C(Ω2,Ω2),0)),C(Ω2,0)),0))
 * C(0,C(C(C(0,C(C(Ω2,Ω2),0)),C(Ω2,0)),0))
 * C(0,C(C(Ω2,C(C(C(Ω2,Ω2),0),C(Ω2,0))),0))
 * C(0,C(C(0,C(C(C(Ω2,Ω2),0),C(Ω2,0))),0))
 * C(0,C(Ω2,C(C(C(C(Ω2,Ω2),0),C(Ω2,0)),0)))
 * C(0,C(0,C(C(C(C(Ω2,Ω2),0),C(Ω2,0)),0)))
 * C(0,C(C(C(C(Ω2,Ω2),0),C(Ω2,0)),0))
 * C(0,C(C(C(C(C(Ω2,0),Ω2),0),C(Ω2,0)),0))
 * C(0,C(C(C(C(C(0,0),Ω2),0),C(Ω2,0)),0))
 * C(0,C(C(C(C(Ω2,C(0,Ω2)),0),C(Ω2,0)),0))
 * C(0,C(C(C(C(0,C(0,Ω2)),0),C(Ω2,0)),0))
 * C(0,C(C(C(Ω2,C(C(0,Ω2),0)),C(Ω2,0)),0))
 * C(0,C(C(C(0,C(C(0,Ω2),0)),C(Ω2,0)),0))
 * C(0,C(C(Ω2,C(C(C(0,Ω2),0),C(Ω2,0))),0))
 * C(0,C(C(0,C(C(C(0,Ω2),0),C(Ω2,0))),0))
 * C(0,C(Ω2,C(C(C(C(0,Ω2),0),C(Ω2,0)),0)))
 * C(0,C(0,C(C(C(C(0,Ω2),0),C(Ω2,0)),0)))
 * C(0,C(C(C(C(0,Ω2),0),C(Ω2,0)),0))
 * C(0,C(C(C(C(Ω2,Ω2),C(Ω2,0)),C(Ω2,0)),0))
 * C(0,C(C(C(C(0,Ω2),C(Ω2,0)),C(Ω2,0)),0))
 * C(0,C(C(C(Ω2,C(Ω2,C(Ω2,0))),C(Ω2,0)),0))
 * C(0,C(C(C(0,C(Ω2,C(Ω2,0))),C(Ω2,0)),0))
 * C(0,C(C(Ω2,C(C(Ω2,C(Ω2,0)),C(Ω2,0))),0))
 * C(0,C(C(0,C(C(Ω2,C(Ω2,0)),C(Ω2,0))),0))
 * C(0,C(Ω2,C(C(C(Ω2,C(Ω2,0)),C(Ω2,0)),0)))
 * C(0,C(0,C(C(C(Ω2,C(Ω2,0)),C(Ω2,0)),0)))
 * C(0,C(C(C(Ω2,C(Ω2,0)),C(Ω2,0)),0))