User blog comment:King2218/Rdc(e1,2) Part 1/@comment-10429372-20140220153747/@comment-10429372-20140220193014

I believe the following analysis is correct:

1. ε0^ε0

2. ε0^ω^ω

3. ε0^ω^2

4. ε0^ω2

5. ε0^ω+2

6. (ε0^ω+1)ω^ω

7. (ε0^ω+1)ω^2

8. (ε0^ω+1)ω2

9. (ε0^ω+1)ω+(ε0^ω+1)2

10. (ε0^ω+1)ω+(ε0^ω+1)+(ε0^ω)ω^ω

Then the following shorthands should be made:

Reducing ε0 takes 9 steps.

Reducing ε0*2 takes 18 steps.

Reducing ε0*ω takes 19 steps.

Reducing ε0*ω2 takes 38 steps.

Reducing ε0*ω^2 takes 39 steps.

Reducing ε0*ω^ω takes 40 steps.

Reducing ε0^2 takes 41 steps.

Reducing ε0^ω takes 42 steps.

Reducing (ε0^ω)2 takes 84 steps.

Reducing (ε0^ω)ω takes 85 steps.

Reducing (ε0^ω)ω2 takes 170 steps.

Reducing (ε0^ω)ω^2 takes 171 steps.

Reducing (ε0^ω)ω^ω takes 172 steps.

Therefore:

10. (ε0^ω+1)ω+(ε0^ω+1)+(ε0^ω)ω^ω

182. (ε0^ω+1)ω+(ε0^ω+1)

183. (ε0^ω+1)ω+(ε0^ω)ω^ω

355. (ε0^ω+1)ω

356. (ε0^ω+1)2

357. (ε0^ω+1)+(ε0^ω)ω^ω

529. ε0^ω+1

530. (ε0^ω)ω^ω

702. 0