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tt rt r - PowerPoint PPT Presentation

Oct 23, 2022 •201 likes •2.06k views

tt rt r sr Prt r r t trt

  1. ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛✉t♩♠❛t✐❝ ❛♥❛❧②s✐s ♊❢ ❚❘❙s ❝♊♥st✐t✉t❡s t❀❡♊r❡♠ ♣r♊✈✐♥❣ ◮ r❡✇r✐t✐♥❣ ✐s ❛t ❀❡❛rt ♊❢ ❡q✉❛t✐♊♥❛❧ r❡❛s♊♥✐♥❣ ◮ ❚❡❛❝❀✐♥❣ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛♥♥✉❛❧ ❝♩✉rs❡ ❛t ❯♥✐✈❡rs✐t② ♊❢ ■♥♥s❜r✉❝❩ t❛✉❣❀t ❜② ❆❛rt ▌✐❞❞❡❧❞♊r♣ ◮ s✐♥❝❡ ✷✵✵✻✿ ■♥t❡r♥❛t✐♊♥❛❧ ❙✉♠♠❡r ❙❝❀♊♊❧ ♊♥ ❘❡✇r✐t✐♥❣ ◮ ℓ → r ♠♩t✐✈❛t❡s ❀ t❡❛❝❀✐♥❣ ❡ ❧ ♣ st✉❞❡♥ts ✇r✐t❡ t♩♩❧s ❘❡✇r✐t❡ ❚♩♩❧s ❉❡✈❡❧♊♣❡❞ ❅ ❈♊♠♣✉t❛t✐♊♥❛❧ ▲♊❣✐❝ ●r♊✉♣ ❚❚❚✷✱ ❚❈❚✱ ❈❙■✱ ❈❛t✱ ♠❩❜tt✱ ❑❇❈❱✱ ♠Ê❞♠❛①✱ ❋❖❘❚✱ Pr♊❚❡▌✱ ❈❡ ❚ ❆✱ ❈♊♥❈♊♥✱ ▌✐♥✐❙♠t✱ ❆✉t♩❙tr❛t✱ ❈tr❧ ❀tt♣✿✎✎❝❧✲✐♥❢♊r♠❛t✐❊✳✉✐❜❊✳❛❝✳❛t✮r❡s❡❛r❝❀✎s♊❢t✇❛r❡ ✷

  2. ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛✉t♩♠❛t✐❝ ❛♥❛❧②s✐s ♊❢ ❚❘❙s ❝♊♥st✐t✉t❡s t❀❡♊r❡♠ ♣r♊✈✐♥❣ ◮ r❡✇r✐t✐♥❣ ✐s ❛t ❀❡❛rt ♊❢ ❡q✉❛t✐♊♥❛❧ r❡❛s♊♥✐♥❣ ◮ ❚❡❛❝❀✐♥❣ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛♥♥✉❛❧ ❝♩✉rs❡ ❛t ❯♥✐✈❡rs✐t② ♊❢ ■♥♥s❜r✉❝❩ t❛✉❣❀t ❜② ❆❛rt ▌✐❞❞❡❧❞♊r♣ ◮ s✐♥❝❡ ✷✵✵✻✿ ■♥t❡r♥❛t✐♊♥❛❧ ❙✉♠♠❡r ❙❝❀♊♊❧ ♊♥ ❘❡✇r✐t✐♥❣ ◮ ℓ → r ♠♩t✐✈❛t❡s ❀ t❡❛❝❀✐♥❣ ❡ ❧ ♣ st✉❞❡♥ts ✇r✐t❡ t♩♩❧s ❘❡✇r✐t❡ ❚♩♩❧s ❉❡✈❡❧♊♣❡❞ ❅ ❈♊♠♣✉t❛t✐♊♥❛❧ ▲♊❣✐❝ ●r♊✉♣ ❚❚❚✷✱ ❚❈❚✱ ❈❙■✱ ❈❛t✱ ♠❩❜tt✱ ❑❇❈❱✱ ♠Ê❞♠❛①✱ ❋❖❘❚✱ Pr♊❚❡▌✱ ❈❡ ❚ ❆✱ ❈♊♥❈♊♥✱ ▌✐♥✐❙♠t✱ ❆✉t♩❙tr❛t✱ ❈tr❧ ❀tt♣✿✎✎❝❧✲✐♥❢♊r♠❛t✐❊✳✉✐❜❊✳❛❝✳❛t✮r❡s❡❛r❝❀✎s♊❢t✇❛r❡ ✷

  3. ❖✉t❧✐♥❡ ▌♊t✐✈❛t✐♥❣ ❊①❛♠♣❧❡s ❚❡r♠ ❘❡✇r✐t✐♥❣ ❚♩♩❧s ❋♩r♠❛❧✐③❛t✐♊♥ ❛♥❞ ❈❡rt✐✜❝❛t✐♊♥ ❈♊♥❝❧✉s✐♊♥ ✾

  4. ❚❡❝❀♥✐q✉❡s ❡①✐st t♩ ♣❡r❢♊r♠ t❀❡ ❢♊❧❧♊✇✐♥❣ ❉◆❆ tr❛♥s❢♊r♠❛t✐♊♥s✿ ❚❈❆❚ ❚ ●❆● ❆● ❈❚❈ ❚❈ ❆●❚❆ ❆ ❚❆❚ ❈❚ ❘❡❝❡♥t❧② ✐t ❀❛s ❜❡❡♥ ❞✐s❝♊✈❡r❡❞ t❀❛t t❀❡ ♠❛❞ ❝♩✇ ❞✐s❡❛s❡ ✐s ❝❛✉s❡❞ ❜② ❛ r❡tr♩✈✐r✉s ✇✐t❀ t❀❡ ❢♊❧❧♊✇✐♥❣ ❉◆❆ s❡q✉❡♥❝❡ ❈❚●❈❚❆❈❚●❆❈❚ ❲❀❛t ♥♊✇✱ ✐❢ ❛❝❝✐❞❡♥t❛❧❧② ❝♩✇s ✇✐t❀ t❀✐s ✈✐r✉s ❛r❡ ❝r❡❛t❡❞❄ ❆❝❝♩r❞✐♥❣ t♩ t❀❡ ❡♥❣✐♥❡❡rs t❀❡r❡ ✐s ❧✐tt❧❡ r✐s❊ ❜❡❝❛✉s❡ t❀✐s ♥❡✈❡r ❀❛♣♣❡♥❡❞ ✐♥ t❀❡✐r ❡①♣❡r✐♠❡♥ts✱ ❜✉t ✈❛r✐♩✉s ❛❝t✐♊♥ ❣r♊✉♣s ❞❡♠❛♥❞ ❛❜s♩❧✉t❡ ❛ss✉r❛♥❝❡✳ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✶✿ ❈♩❧❛ ●❡♥❡ P✉③③❧❡ ●❡♥❡t✐❝ ❡♥❣✐♥❡❡rs ✇❛♥t t♩ ❝r❡❛t❡ ❝♩✇s t❀❛t ♣r♊❞✉❝❡ ❝♩❧❛ ✐♥st❡❛❞ ♊❢ ♠✐❧❊✳ ❚♩ t❀❛t ❡♥❞ t❀❡② ❀❛✈❡ t♩ tr❛♥s❢♊r♠ t❀❡ ❉◆❆ ♊❢ t❀❡ ♠✐❧❩ ❣❡♥❡ ❚❆●❈❚❆●❈❚❆●❈❚ ✐♥ ❡✈❡r② ❢❡rt✐❧✐③❡❞ ❡❣❣ ✐♥t♩ t❀❡ ❝♩❧❛ ❣❡♥❡ ❈❚●❆❈❚●❆❈❚ ✹

  5. ❘❡❝❡♥t❧② ✐t ❀❛s ❜❡❡♥ ❞✐s❝♊✈❡r❡❞ t❀❛t t❀❡ ♠❛❞ ❝♩✇ ❞✐s❡❛s❡ ✐s ❝❛✉s❡❞ ❜② ❛ r❡tr♩✈✐r✉s ✇✐t❀ t❀❡ ❢♊❧❧♊✇✐♥❣ ❉◆❆ s❡q✉❡♥❝❡ ❈❚●❈❚❆❈❚●❆❈❚ ❲❀❛t ♥♊✇✱ ✐❢ ❛❝❝✐❞❡♥t❛❧❧② ❝♩✇s ✇✐t❀ t❀✐s ✈✐r✉s ❛r❡ ❝r❡❛t❡❞❄ ❆❝❝♩r❞✐♥❣ t♩ t❀❡ ❡♥❣✐♥❡❡rs t❀❡r❡ ✐s ❧✐tt❧❡ r✐s❊ ❜❡❝❛✉s❡ t❀✐s ♥❡✈❡r ❀❛♣♣❡♥❡❞ ✐♥ t❀❡✐r ❡①♣❡r✐♠❡♥ts✱ ❜✉t ✈❛r✐♩✉s ❛❝t✐♊♥ ❣r♊✉♣s ❞❡♠❛♥❞ ❛❜s♩❧✉t❡ ❛ss✉r❛♥❝❡✳ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✶✿ ❈♩❧❛ ●❡♥❡ P✉③③❧❡ ●❡♥❡t✐❝ ❡♥❣✐♥❡❡rs ✇❛♥t t♩ ❝r❡❛t❡ ❝♩✇s t❀❛t ♣r♊❞✉❝❡ ❝♩❧❛ ✐♥st❡❛❞ ♊❢ ♠✐❧❊✳ ❚♩ t❀❛t ❡♥❞ t❀❡② ❀❛✈❡ t♩ tr❛♥s❢♊r♠ t❀❡ ❉◆❆ ♊❢ t❀❡ ♠✐❧❩ ❣❡♥❡ ❚❆●❈❚❆●❈❚❆●❈❚ ✐♥ ❡✈❡r② ❢❡rt✐❧✐③❡❞ ❡❣❣ ✐♥t♩ t❀❡ ❝♩❧❛ ❣❡♥❡ ❈❚●❆❈❚●❆❈❚ ❚❡❝❀♥✐q✉❡s ❡①✐st t♩ ♣❡r❢♊r♠ t❀❡ ❢♊❧❧♊✇✐♥❣ ❉◆❆ tr❛♥s❢♊r♠❛t✐♊♥s✿ ❚❈❆❚ ↔ ❚ ●❆● ↔ ❆● ❈❚❈ ↔ ❚❈ ❆●❚❆ ↔ ❆ ❚❆❚ ↔ ❈❚ ✹

  6. ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✶✿ ❈♩❧❛ ●❡♥❡ P✉③③❧❡ ●❡♥❡t✐❝ ❡♥❣✐♥❡❡rs ✇❛♥t t♩ ❝r❡❛t❡ ❝♩✇s t❀❛t ♣r♊❞✉❝❡ ❝♩❧❛ ✐♥st❡❛❞ ♊❢ ♠✐❧❊✳ ❚♩ t❀❛t ❡♥❞ t❀❡② ❀❛✈❡ t♩ tr❛♥s❢♊r♠ t❀❡ ❉◆❆ ♊❢ t❀❡ ♠✐❧❩ ❣❡♥❡ ❚❆●❈❚❆●❈❚❆●❈❚ ✐♥ ❡✈❡r② ❢❡rt✐❧✐③❡❞ ❡❣❣ ✐♥t♩ t❀❡ ❝♩❧❛ ❣❡♥❡ ❈❚●❆❈❚●❆❈❚ ❚❡❝❀♥✐q✉❡s ❡①✐st t♩ ♣❡r❢♊r♠ t❀❡ ❢♊❧❧♊✇✐♥❣ ❉◆❆ tr❛♥s❢♊r♠❛t✐♊♥s✿ ❚❈❆❚ ↔ ❚ ●❆● ↔ ❆● ❈❚❈ ↔ ❚❈ ❆●❚❆ ↔ ❆ ❚❆❚ ↔ ❈❚ ❘❡❝❡♥t❧② ✐t ❀❛s ❜❡❡♥ ❞✐s❝♊✈❡r❡❞ t❀❛t t❀❡ ♠❛❞ ❝♩✇ ❞✐s❡❛s❡ ✐s ❝❛✉s❡❞ ❜② ❛ r❡tr♩✈✐r✉s ✇✐t❀ t❀❡ ❢♊❧❧♊✇✐♥❣ ❉◆❆ s❡q✉❡♥❝❡ ❈❚●❈❚❆❈❚●❆❈❚ ❲❀❛t ♥♊✇✱ ✐❢ ❛❝❝✐❞❡♥t❛❧❧② ❝♩✇s ✇✐t❀ t❀✐s ✈✐r✉s ❛r❡ ❝r❡❛t❡❞❄ ❆❝❝♩r❞✐♥❣ t♩ t❀❡ ❡♥❣✐♥❡❡rs t❀❡r❡ ✐s ❧✐tt❧❡ r✐s❊ ❜❡❝❛✉s❡ t❀✐s ♥❡✈❡r ❀❛♣♣❡♥❡❞ ✐♥ t❀❡✐r ❡①♣❡r✐♠❡♥ts✱ ❜✉t ✈❛r✐♩✉s ❛❝t✐♊♥ ❣r♊✉♣s ❞❡♠❛♥❞ ❛❜s♩❧✉t❡ ❛ss✉r❛♥❝❡✳ ✹

  7. ■s ✐t ♣♊ss✐❜❧❡ t❀❛t ❛❧❧ ✺✹ ❝❀❛♠❡❧❡♊♥s ❜❡❝♊♠❡ t❀❡ s❛♠❡ ❝♩❧♩r❄ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✷✿ ❈❀❛♠❡❧❡♊♥ P✉③③❧❡ ❆ ❝♊❧♊♥② ♊❢ ❇r❛③✐❧✐❛♥ ❝❀❛♠❡❧❡♊♥s ❝♊♥s✐sts ♊❢ ✷✵ r❡❞✱ ✶✜ ❜❧✉❡✱ ❛♥❞ ✶✻ ❣r❡❡♥ ❛♥✐♠❛❧s✳ ❲❀❡♥❡✈❡r t✇♩ ♊❢ ❞✐✛❡r❡♥t ❝♩❧♩r ♠❡❡t✱ ❜♩t❀ ❝❀❛♥❣❡ t♩ t❀❡ t❀✐r❞ ❝♩❧♩r✳ ❙♊♠❡ t✐♠❡ ♣❛ss❡s ❞✉r✐♥❣ ✇❀✐❝❀ ♥♊ ❝❀❛♠❡❧❡♊♥s ❛r❡ ❜♩r♥ ♩r ❞✐❡ ♥♊r ❞♩ ❛♥② ❡♥t❡r ♩r ❧❡❛✈❡ t❀❡ ❝♊❧♊♥②✳ ✺

  8. ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✷✿ ❈❀❛♠❡❧❡♊♥ P✉③③❧❡ ❆ ❝♊❧♊♥② ♊❢ ❇r❛③✐❧✐❛♥ ❝❀❛♠❡❧❡♊♥s ❝♊♥s✐sts ♊❢ ✷✵ r❡❞✱ ✶✜ ❜❧✉❡✱ ❛♥❞ ✶✻ ❣r❡❡♥ ❛♥✐♠❛❧s✳ ❲❀❡♥❡✈❡r t✇♩ ♊❢ ❞✐✛❡r❡♥t ❝♩❧♩r ♠❡❡t✱ ❜♩t❀ ❝❀❛♥❣❡ t♩ t❀❡ t❀✐r❞ ❝♩❧♩r✳ ❙♊♠❡ t✐♠❡ ♣❛ss❡s ❞✉r✐♥❣ ✇❀✐❝❀ ♥♊ ❝❀❛♠❡❧❡♊♥s ❛r❡ ❜♩r♥ ♩r ❞✐❡ ♥♊r ❞♩ ❛♥② ❡♥t❡r ♩r ❧❡❛✈❡ t❀❡ ❝♊❧♊♥②✳ ■s ✐t ♣♊ss✐❜❧❡ t❀❛t ❛❧❧ ✺✹ ❝❀❛♠❡❧❡♊♥s ❜❡❝♊♠❡ t❀❡ s❛♠❡ ❝♩❧♩r❄ ✺

  9. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ q✉❡st✐♊♥s ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ✐♥✐t✐❛❧ st❛t❡ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ✻

  10. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ q✉❡st✐♊♥s ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ✐♥✐t✐❛❧ st❛t❡ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ✻

  11. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ q✉❡st✐♊♥s ✐♥✐t✐❛❧ st❛t❡ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✻

  12. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ✻

  13. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ ✻

  14. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ ✻

  15. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✷ ✻

  16. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✷ ✻

  17. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✷ • ◩ • ◩ • • ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✶ ✻

  18. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✷ • ◩ • ◩ • • ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✶ ✻

  19. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✷ • ◩ • ◩ • • ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✷ ✻

  20. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✷ • ◩ • ◩ • • ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✷ ✻

  21. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✷ • ◩ • ◩ • • ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✷ • • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✶ ✻

  22. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✷ • ◩ • ◩ • • ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✷ • • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✶ • • ◩ • • ◩ • ◩ • ♣❧❛②❡r ✷ ✻

  23. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✷ • ◩ • ◩ • • ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✷ • • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✶ • • ◩ • • ◩ • ◩ • ♣❧❛②❡r ✷ • • ◩ • • ◩ • • ♣❧❛②❡r ✶ ✻

  24. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✷ • ◩ • ◩ • • ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✷ • • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✶ • • ◩ • • ◩ • ◩ • ♣❧❛②❡r ✷ • • ◩ • • ◩ • • ♣❧❛②❡r ✶ • • ◩ • • ◩ ◩ ♣❧❛②❡r ✷ ✻

  25. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✷ • ◩ • ◩ • • ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✷ • • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✶ • • ◩ • • ◩ • ◩ • ♣❧❛②❡r ✷ • • ◩ • • ◩ • • ♣❧❛②❡r ✶ • • ◩ • • ◩ ◩ ♣❧❛②❡r ✷ • • ◩ • • ◩ ♣❧❛②❡r ✶ ✻

  26. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✷ • ◩ • ◩ • • ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✷ • • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✶ • • ◩ • • ◩ • ◩ • ♣❧❛②❡r ✷ • • ◩ • • ◩ • • ♣❧❛②❡r ✶ • • ◩ • • ◩ ◩ ♣❧❛②❡r ✷ • • ◩ • • ◩ ♣❧❛②❡r ✶ • • ◩ • • ♣❧❛②❡r ✷ ✻

  27. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✷ ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✷ • ◩ • ◩ • • ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✷ • • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✶ • • ◩ • • ◩ • ◩ • ♣❧❛②❡r ✷ • • ◩ • • ◩ • • ♣❧❛②❡r ✶ • • ◩ • • ◩ ◩ ♣❧❛②❡r ✷ • • ◩ • • ◩ ♣❧❛②❡r ✶ • • ◩ • • ♣❧❛②❡r ✷ • • ◩ ◩ ♣❧❛②❡r ✶ ✻

  28. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✶ ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✷ • ◩ • ◩ • • ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✷ • • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✶ • • ◩ • • ◩ • ◩ • ♣❧❛②❡r ✷ • • ◩ • • ◩ • • ♣❧❛②❡r ✶ • • ◩ • • ◩ ◩ ♣❧❛②❡r ✷ • • ◩ • • ◩ ♣❧❛②❡r ✶ • • ◩ • • ♣❧❛②❡r ✷ • • ◩ ◩ ♣❧❛②❡r ✶ • • ◩ ♣❧❛②❡r ✷ ✻

  29. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ♣❧❛②❡r ✷ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✷ • ◩ • ◩ • • ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✷ • • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✶ • • ◩ • • ◩ • ◩ • ♣❧❛②❡r ✷ • • ◩ • • ◩ • • ♣❧❛②❡r ✶ • • ◩ • • ◩ ◩ ♣❧❛②❡r ✷ • • ◩ • • ◩ ♣❧❛②❡r ✶ • • ◩ • • ♣❧❛②❡r ✷ • • ◩ ◩ ♣❧❛②❡r ✶ • • ◩ ♣❧❛②❡r ✷ • • ♣❧❛②❡r ✶ ✻

  30. ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ q✉❡st✐♊♥s ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ◩ ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✷ • ◩ • ◩ • • ◩ • ◩ ◩ • ◩ ♣❧❛②❡r ✶ • ◩ • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✷ • • ◩ • • ◩ • ◩ • ◩ ♣❧❛②❡r ✶ • • ◩ • • ◩ • ◩ • ♣❧❛②❡r ✷ • • ◩ • • ◩ • • ♣❧❛②❡r ✶ • • ◩ • • ◩ ◩ ♣❧❛②❡r ✷ • • ◩ • • ◩ ♣❧❛②❡r ✶ • • ◩ • • ♣❧❛②❡r ✷ • • ◩ ◩ ♣❧❛②❡r ✶ • • ◩ ♣❧❛②❡r ✷ • • ♣❧❛②❡r ✶ ◩ ♣❧❛②❡r ✷ ✻

  31. ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ q✉❡st✐♊♥s ◮ ◮ ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ✻

  32. ❚❡❛❝❀✐♥❣ ❊①❛♠♣❧❡ ✞✿ ❙✐♠♣❧❡ ●❛♠❡ t✇♊✲♣❧❛②❡r ❣❛♠❡ ✇❀❡r❡ st❛t❡ ✐s s❡q✉❡♥❝❡ ♊❢ ❜❧❛❝❩ ❛♥❞ ✇❀✐t❡ st♊♥❡s ◮ ❛❧❧♊✇❡❞ ♠♊✈❡s ❛r❡ ◮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ♣❧❛②❡r ✇❀♊ ♣✉ts ❧❛st ✇❀✐t❡ ✇✐♥s ◮ ✐♥✐t✐❛❧ st❛t❡ ◮ • • ◩ • ◩ • • ◩ ◩ • ◩ ◩ • • ◩ q✉❡st✐♊♥s ◮ ◮ ❞♊❡s t❀❡ ❣❛♠❡ t❡r♠✐♥❛t❡❄ ◮ ✇❀✐❝❀ str❛t❡❣✐❡s ❛r❡ ✇✐♥♥✐♥❣ str❛t❡❣✐❡s ❢♊r ♣❧❛②❡r ✷❄ ✻

  33. ✐s t❀❡ ❣✐✈❡♥ ♣r♊❣r❛♠ t❡r♠✐♥❛t✐♥❣❄ ❛r❡ r❡s✉❧ts✱ ✐❢ ❡①✐st❡♥t✱ ✉♥✐q✉❡❄ ✇❀❛t ✐s t❀❡ ♣r♊❣r❛♠✬s ❝♊♠♣✉t❛t✐♊♥❛❧ ❝♊♠♣❧❡①✐t②✱ ✐❢ ✐t t❡r♠✐♥❛t❡s❄ ◗✉❡st✐♊♥s ❆❜♩✉t ✭❋✉♥❝t✐♊♥❛❧✮ Pr♊❣r❛♠s ❊①❛♠♣❧❡ ✹✿ ❙✐❡✈❡ ♊❢ ❊r❛t♩st❀❡♥❡s ❚❘❙ R ♠♊❞❡❧s s✐❡✈❡ ♊❢ ❊r❛t♩st❀❡♥❡s t♩ ❡♥✉♠❡r❛t❡ ♣r✐♠❡ ♥✉♠❜❡rs✿ ♣r✐♠❡s → s✐❡✈❡ ( ❢r♩♠ ( s ( s ( ✵ )))) s✐❡✈❡ ( ✵ : y ) → s✐❡✈❡ ( y ) ❢r♩♠ ( x ) → x : ❢r♩♠ ( s ( x )) s✐❡✈❡ ( s ( x ): y ) → s ( x ): s✐❡✈❡ ( ✜❧t❡r ( x , y , x )) ❀❞ ( x : y ) → x ✜❧t❡r ( ✵ , y : z , w ) → ✵ : ✜❧t❡r ( w , z , w ) t❧ ( x : y ) → y ✜❧t❡r ( s ( x ) , y : z , w ) → y : ✜❧t❡r ( x , z , w ) ✌

  34. ❛r❡ r❡s✉❧ts✱ ✐❢ ❡①✐st❡♥t✱ ✉♥✐q✉❡❄ ✇❀❛t ✐s t❀❡ ♣r♊❣r❛♠✬s ❝♊♠♣✉t❛t✐♊♥❛❧ ❝♊♠♣❧❡①✐t②✱ ✐❢ ✐t t❡r♠✐♥❛t❡s❄ ❊①❛♠♣❧❡ ✹✿ ❙✐❡✈❡ ♊❢ ❊r❛t♩st❀❡♥❡s ❚❘❙ R ♠♊❞❡❧s s✐❡✈❡ ♊❢ ❊r❛t♩st❀❡♥❡s t♩ ❡♥✉♠❡r❛t❡ ♣r✐♠❡ ♥✉♠❜❡rs✿ ♣r✐♠❡s → s✐❡✈❡ ( ❢r♩♠ ( s ( s ( ✵ )))) s✐❡✈❡ ( ✵ : y ) → s✐❡✈❡ ( y ) ❢r♩♠ ( x ) → x : ❢r♩♠ ( s ( x )) s✐❡✈❡ ( s ( x ): y ) → s ( x ): s✐❡✈❡ ( ✜❧t❡r ( x , y , x )) ❀❞ ( x : y ) → x ✜❧t❡r ( ✵ , y : z , w ) → ✵ : ✜❧t❡r ( w , z , w ) t❧ ( x : y ) → y ✜❧t❡r ( s ( x ) , y : z , w ) → y : ✜❧t❡r ( x , z , w ) ◗✉❡st✐♊♥s ❆❜♩✉t ✭❋✉♥❝t✐♊♥❛❧✮ Pr♊❣r❛♠s ✐s t❀❡ ❣✐✈❡♥ ♣r♊❣r❛♠ t❡r♠✐♥❛t✐♥❣❄ ◮ ✌

  35. ✇❀❛t ✐s t❀❡ ♣r♊❣r❛♠✬s ❝♊♠♣✉t❛t✐♊♥❛❧ ❝♊♠♣❧❡①✐t②✱ ✐❢ ✐t t❡r♠✐♥❛t❡s❄ ❊①❛♠♣❧❡ ✹✿ ❙✐❡✈❡ ♊❢ ❊r❛t♩st❀❡♥❡s ❚❘❙ R ♠♊❞❡❧s s✐❡✈❡ ♊❢ ❊r❛t♩st❀❡♥❡s t♩ ❡♥✉♠❡r❛t❡ ♣r✐♠❡ ♥✉♠❜❡rs✿ ♣r✐♠❡s → s✐❡✈❡ ( ❢r♩♠ ( s ( s ( ✵ )))) s✐❡✈❡ ( ✵ : y ) → s✐❡✈❡ ( y ) ❢r♩♠ ( x ) → x : ❢r♩♠ ( s ( x )) s✐❡✈❡ ( s ( x ): y ) → s ( x ): s✐❡✈❡ ( ✜❧t❡r ( x , y , x )) ❀❞ ( x : y ) → x ✜❧t❡r ( ✵ , y : z , w ) → ✵ : ✜❧t❡r ( w , z , w ) t❧ ( x : y ) → y ✜❧t❡r ( s ( x ) , y : z , w ) → y : ✜❧t❡r ( x , z , w ) ◗✉❡st✐♊♥s ❆❜♩✉t ✭❋✉♥❝t✐♊♥❛❧✮ Pr♊❣r❛♠s ✐s t❀❡ ❣✐✈❡♥ ♣r♊❣r❛♠ t❡r♠✐♥❛t✐♥❣❄ ◮ ❛r❡ r❡s✉❧ts✱ ✐❢ ❡①✐st❡♥t✱ ✉♥✐q✉❡❄ ◮ ✌

  36. ❊①❛♠♣❧❡ ✹✿ ❙✐❡✈❡ ♊❢ ❊r❛t♩st❀❡♥❡s ❚❘❙ R ♠♊❞❡❧s s✐❡✈❡ ♊❢ ❊r❛t♩st❀❡♥❡s t♩ ❡♥✉♠❡r❛t❡ ♣r✐♠❡ ♥✉♠❜❡rs✿ ♣r✐♠❡s → s✐❡✈❡ ( ❢r♩♠ ( s ( s ( ✵ )))) s✐❡✈❡ ( ✵ : y ) → s✐❡✈❡ ( y ) ❢r♩♠ ( x ) → x : ❢r♩♠ ( s ( x )) s✐❡✈❡ ( s ( x ): y ) → s ( x ): s✐❡✈❡ ( ✜❧t❡r ( x , y , x )) ❀❞ ( x : y ) → x ✜❧t❡r ( ✵ , y : z , w ) → ✵ : ✜❧t❡r ( w , z , w ) t❧ ( x : y ) → y ✜❧t❡r ( s ( x ) , y : z , w ) → y : ✜❧t❡r ( x , z , w ) ◗✉❡st✐♊♥s ❆❜♩✉t ✭❋✉♥❝t✐♊♥❛❧✮ Pr♊❣r❛♠s ✐s t❀❡ ❣✐✈❡♥ ♣r♊❣r❛♠ t❡r♠✐♥❛t✐♥❣❄ ◮ ❛r❡ r❡s✉❧ts✱ ✐❢ ❡①✐st❡♥t✱ ✉♥✐q✉❡❄ ◮ ✇❀❛t ✐s t❀❡ ♣r♊❣r❛♠✬s ❝♊♠♣✉t❛t✐♊♥❛❧ ❝♊♠♣❧❡①✐t②✱ ✐❢ ✐t t❡r♠✐♥❛t❡s❄ ◮ ✌

  37. ❖✉t❧✐♥❡ ▌♊t✐✈❛t✐♥❣ ❊①❛♠♣❧❡s ❚❡r♠ ❘❡✇r✐t✐♥❣ ❚♩♩❧s ❋♩r♠❛❧✐③❛t✐♊♥ ❛♥❞ ❈❡rt✐✜❝❛t✐♊♥ ❈♊♥❝❧✉s✐♊♥ ✜

  38. ❜✉t ❛❧s♩ ❛♥❞ ✳ ✳ ✳ ✐s t❡r♠✐♥❛t✐♥❣ ✐❢ t❀❡r❡ ❛r❡ ♥♊ ✐♥✜♥✐t❡ r❡✇r✐t❡ s❡q✉❡♥❝❡s ✳ ✳ ✳ ✐s ❝♊♥✢✉❡♥t ✐❢ ✳ ✳ ✳ ✐s ❝♊♠♣❧❡t❡ ✐❢ t❡r♠✐♥❛t✐♥❣ ❛♥❞ ❝♊♥✢✉❡♥t r❡✇r✐t❡ s❡q✉❡♥❝❡✿ ✐s t❡r♠✐♥❛t✐♥❣ ✐s ❝♊♥✢✉❡♥t ❡✳❣✳ ❛♥❞ ❆❜str❛❝t ❘❡✇r✐t✐♥❣ ❛❜str❛❝t r❡✇r✐t❡ s②st❡♠ ✐s ❝❛rr✐❡r s❡t ✇✐t❀ ❜✐♥❛r② r❡❧❛t✐♊♥ ◮ ❊①❛♠♣❧❡ r❡✇r✐t❡ s②st❡♠ R ✟

  39. ❜✉t ❛❧s♩ ❛♥❞ ✳ ✳ ✳ ✐s t❡r♠✐♥❛t✐♥❣ ✐❢ t❀❡r❡ ❛r❡ ♥♊ ✐♥✜♥✐t❡ r❡✇r✐t❡ s❡q✉❡♥❝❡s ✳ ✳ ✳ ✐s ❝♊♥✢✉❡♥t ✐❢ ✳ ✳ ✳ ✐s ❝♊♠♣❧❡t❡ ✐❢ t❡r♠✐♥❛t✐♥❣ ❛♥❞ ❝♊♥✢✉❡♥t ✐s t❡r♠✐♥❛t✐♥❣ ✐s ❝♊♥✢✉❡♥t ❡✳❣✳ ❛♥❞ ❆❜str❛❝t ❘❡✇r✐t✐♥❣ ❛❜str❛❝t r❡✇r✐t❡ s②st❡♠ ✐s ❝❛rr✐❡r s❡t ✇✐t❀ ❜✐♥❛r② r❡❧❛t✐♊♥ ◮ ❊①❛♠♣❧❡ r❡✇r✐t❡ s②st❡♠ R r❡✇r✐t❡ st❡♣✿ ◮ R ✟

  40. ❜✉t ❛❧s♩ ❛♥❞ ✳ ✳ ✳ ✐s t❡r♠✐♥❛t✐♥❣ ✐❢ t❀❡r❡ ❛r❡ ♥♊ ✐♥✜♥✐t❡ r❡✇r✐t❡ s❡q✉❡♥❝❡s ✳ ✳ ✳ ✐s ❝♊♥✢✉❡♥t ✐❢ ✳ ✳ ✳ ✐s ❝♊♠♣❧❡t❡ ✐❢ t❡r♠✐♥❛t✐♥❣ ❛♥❞ ❝♊♥✢✉❡♥t ✐s t❡r♠✐♥❛t✐♥❣ ✐s ❝♊♥✢✉❡♥t ❡✳❣✳ ❛♥❞ ❆❜str❛❝t ❘❡✇r✐t✐♥❣ ❛❜str❛❝t r❡✇r✐t❡ s②st❡♠ ✐s ❝❛rr✐❡r s❡t ✇✐t❀ ❜✐♥❛r② r❡❧❛t✐♊♥ ◮ ❊①❛♠♣❧❡ r❡✇r✐t❡ s②st❡♠ R r❡✇r✐t❡ s❡q✉❡♥❝❡✿ ◮ R R R ✟

  41. ❜✉t ❛❧s♩ ❛♥❞ ✳ ✳ ✳ ✐s t❡r♠✐♥❛t✐♥❣ ✐❢ t❀❡r❡ ❛r❡ ♥♊ ✐♥✜♥✐t❡ r❡✇r✐t❡ s❡q✉❡♥❝❡s ✳ ✳ ✳ ✐s ❝♊♥✢✉❡♥t ✐❢ ✳ ✳ ✳ ✐s ❝♊♠♣❧❡t❡ ✐❢ t❡r♠✐♥❛t✐♥❣ ❛♥❞ ❝♊♥✢✉❡♥t ✐s t❡r♠✐♥❛t✐♥❣ ✐s ❝♊♥✢✉❡♥t ❡✳❣✳ ❛♥❞ ❆❜str❛❝t ❘❡✇r✐t✐♥❣ ❛❜str❛❝t r❡✇r✐t❡ s②st❡♠ ✐s ❝❛rr✐❡r s❡t ✇✐t❀ ❜✐♥❛r② r❡❧❛t✐♊♥ ◮ ❊①❛♠♣❧❡ r❡✇r✐t❡ s②st❡♠ R r❡✇r✐t❡ s❡q✉❡♥❝❡✿ ◮ ∗ R R R R ✟

  42. ❜✉t ❛❧s♩ ❛♥❞ ✳ ✳ ✳ ✐s ❝♊♥✢✉❡♥t ✐❢ ✳ ✳ ✳ ✐s ❝♊♠♣❧❡t❡ ✐❢ t❡r♠✐♥❛t✐♥❣ ❛♥❞ ❝♊♥✢✉❡♥t ✐s t❡r♠✐♥❛t✐♥❣ ✐s ❝♊♥✢✉❡♥t ❡✳❣✳ ❛♥❞ ❆❜str❛❝t ❘❡✇r✐t✐♥❣ ❛❜str❛❝t r❡✇r✐t❡ s②st❡♠ ✐s ❝❛rr✐❡r s❡t ✇✐t❀ ❜✐♥❛r② r❡❧❛t✐♊♥ ◮ ✳ ✳ ✳ ✐s t❡r♠✐♥❛t✐♥❣ ✐❢ t❀❡r❡ ❛r❡ ♥♊ ✐♥✜♥✐t❡ r❡✇r✐t❡ s❡q✉❡♥❝❡s ◮ ❊①❛♠♣❧❡ r❡✇r✐t❡ s②st❡♠ R r❡✇r✐t❡ s❡q✉❡♥❝❡✿ ◮ ∗ R R R R ✟

  43. ❜✉t ❛❧s♩ ❛♥❞ ✳ ✳ ✳ ✐s ❝♊♥✢✉❡♥t ✐❢ ✳ ✳ ✳ ✐s ❝♊♠♣❧❡t❡ ✐❢ t❡r♠✐♥❛t✐♥❣ ❛♥❞ ❝♊♥✢✉❡♥t ✐s ❝♊♥✢✉❡♥t ❡✳❣✳ ❛♥❞ ❆❜str❛❝t ❘❡✇r✐t✐♥❣ ❛❜str❛❝t r❡✇r✐t❡ s②st❡♠ ✐s ❝❛rr✐❡r s❡t ✇✐t❀ ❜✐♥❛r② r❡❧❛t✐♊♥ ◮ ✳ ✳ ✳ ✐s t❡r♠✐♥❛t✐♥❣ ✐❢ t❀❡r❡ ❛r❡ ♥♊ ✐♥✜♥✐t❡ r❡✇r✐t❡ s❡q✉❡♥❝❡s ◮ ❊①❛♠♣❧❡ r❡✇r✐t❡ s②st❡♠ R r❡✇r✐t❡ s❡q✉❡♥❝❡✿ ◮ ∗ R R R R R ✐s ♥♊t t❡r♠✐♥❛t✐♥❣✿ ◮ · · · R R R R R ✟

  44. ❜✉t ❛❧s♩ ❛♥❞ ✳ ✳ ✳ ✐s ❝♊♥✢✉❡♥t ✐❢ ✳ ✳ ✳ ✐s ❝♊♠♣❧❡t❡ ✐❢ t❡r♠✐♥❛t✐♥❣ ❛♥❞ ❝♊♥✢✉❡♥t ✐s ❝♊♥✢✉❡♥t ❡✳❣✳ ❛♥❞ ❆❜str❛❝t ❘❡✇r✐t✐♥❣ ❛❜str❛❝t r❡✇r✐t❡ s②st❡♠ ✐s ❝❛rr✐❡r s❡t ✇✐t❀ ❜✐♥❛r② r❡❧❛t✐♊♥ ◮ ✳ ✳ ✳ ✐s t❡r♠✐♥❛t✐♥❣ ✐❢ t❀❡r❡ ❛r❡ ♥♊ ✐♥✜♥✐t❡ r❡✇r✐t❡ s❡q✉❡♥❝❡s ◮ ❊①❛♠♣❧❡ r❡✇r✐t❡ s②st❡♠ R r❡✇r✐t❡ s❡q✉❡♥❝❡✿ ◮ ∗ R R R R R ✐s t❡r♠✐♥❛t✐♥❣ ◮ ✟

  45. ❜✉t ❛❧s♩ ❛♥❞ ✳ ✳ ✳ ✐s ❝♊♠♣❧❡t❡ ✐❢ t❡r♠✐♥❛t✐♥❣ ❛♥❞ ❝♊♥✢✉❡♥t ✐s ❝♊♥✢✉❡♥t ❡✳❣✳ ❛♥❞ ❆❜str❛❝t ❘❡✇r✐t✐♥❣ ❛❜str❛❝t r❡✇r✐t❡ s②st❡♠ ✐s ❝❛rr✐❡r s❡t ✇✐t❀ ❜✐♥❛r② r❡❧❛t✐♊♥ ◮ ✳ ✳ ✳ ✐s t❡r♠✐♥❛t✐♥❣ ✐❢ t❀❡r❡ ❛r❡ ♥♊ ✐♥✜♥✐t❡ r❡✇r✐t❡ s❡q✉❡♥❝❡s ◮ R ← · → ∗ ∗ R ⊆ → ∗ ∗ ✳ ✳ ✳ ✐s ❝♊♥✢✉❡♥t ✐❢ R · R ← ◮ ❊①❛♠♣❧❡ r❡✇r✐t❡ s②st❡♠ R r❡✇r✐t❡ s❡q✉❡♥❝❡✿ ◮ ∗ R R R R R ✐s t❡r♠✐♥❛t✐♥❣ ◮ ✟

  46. ❜✉t ❛❧s♩ ❛♥❞ ✳ ✳ ✳ ✐s ❝♊♠♣❧❡t❡ ✐❢ t❡r♠✐♥❛t✐♥❣ ❛♥❞ ❝♊♥✢✉❡♥t ✐s ❝♊♥✢✉❡♥t ❡✳❣✳ ❛♥❞ ❆❜str❛❝t ❘❡✇r✐t✐♥❣ ❛❜str❛❝t r❡✇r✐t❡ s②st❡♠ ✐s ❝❛rr✐❡r s❡t ✇✐t❀ ❜✐♥❛r② r❡❧❛t✐♊♥ ◮ ✳ ✳ ✳ ✐s t❡r♠✐♥❛t✐♥❣ ✐❢ t❀❡r❡ ❛r❡ ♥♊ ✐♥✜♥✐t❡ r❡✇r✐t❡ s❡q✉❡♥❝❡s ◮ R ← · → ∗ ∗ ✳ ✳ ✳ ✐s ❝♊♥✢✉❡♥t ✐❢ R ⊆ ↓ R ◮ ❊①❛♠♣❧❡ r❡✇r✐t❡ s②st❡♠ R r❡✇r✐t❡ s❡q✉❡♥❝❡✿ ◮ ∗ R R R R R ✐s t❡r♠✐♥❛t✐♥❣ ◮ ✟

  47. ✳ ✳ ✳ ✐s ❝♊♠♣❧❡t❡ ✐❢ t❡r♠✐♥❛t✐♥❣ ❛♥❞ ❝♊♥✢✉❡♥t ❜✉t ❛❧s♩ ❛♥❞ ❆❜str❛❝t ❘❡✇r✐t✐♥❣ ❛❜str❛❝t r❡✇r✐t❡ s②st❡♠ ✐s ❝❛rr✐❡r s❡t ✇✐t❀ ❜✐♥❛r② r❡❧❛t✐♊♥ ◮ ✳ ✳ ✳ ✐s t❡r♠✐♥❛t✐♥❣ ✐❢ t❀❡r❡ ❛r❡ ♥♊ ✐♥✜♥✐t❡ r❡✇r✐t❡ s❡q✉❡♥❝❡s ◮ R ← · → ∗ ∗ ✳ ✳ ✳ ✐s ❝♊♥✢✉❡♥t ✐❢ R ⊆ ↓ R ◮ ❊①❛♠♣❧❡ r❡✇r✐t❡ s②st❡♠ R r❡✇r✐t❡ s❡q✉❡♥❝❡✿ ◮ ∗ R R R R R ✐s t❡r♠✐♥❛t✐♥❣ ◮ R ✐s ❝♊♥✢✉❡♥t ◮ ∗ ∗ ❡✳❣✳ ❛♥❞ R R ✟

  48. ✳ ✳ ✳ ✐s ❝♊♠♣❧❡t❡ ✐❢ t❡r♠✐♥❛t✐♥❣ ❛♥❞ ❝♊♥✢✉❡♥t ❆❜str❛❝t ❘❡✇r✐t✐♥❣ ❛❜str❛❝t r❡✇r✐t❡ s②st❡♠ ✐s ❝❛rr✐❡r s❡t ✇✐t❀ ❜✐♥❛r② r❡❧❛t✐♊♥ ◮ ✳ ✳ ✳ ✐s t❡r♠✐♥❛t✐♥❣ ✐❢ t❀❡r❡ ❛r❡ ♥♊ ✐♥✜♥✐t❡ r❡✇r✐t❡ s❡q✉❡♥❝❡s ◮ R ← · → ∗ ∗ ✳ ✳ ✳ ✐s ❝♊♥✢✉❡♥t ✐❢ R ⊆ ↓ R ◮ ❊①❛♠♣❧❡ r❡✇r✐t❡ s②st❡♠ R r❡✇r✐t❡ s❡q✉❡♥❝❡✿ ◮ ∗ R R R R R ✐s t❡r♠✐♥❛t✐♥❣ ◮ R ✐s ❝♊♥✢✉❡♥t ◮ ∗ ∗ ∗ ∗ ❡✳❣✳ ❛♥❞ ❜✉t ❛❧s♩ ❛♥❞ R R R R ✟

  49. ❆❜str❛❝t ❘❡✇r✐t✐♥❣ ❛❜str❛❝t r❡✇r✐t❡ s②st❡♠ ✐s ❝❛rr✐❡r s❡t ✇✐t❀ ❜✐♥❛r② r❡❧❛t✐♊♥ ◮ ✳ ✳ ✳ ✐s t❡r♠✐♥❛t✐♥❣ ✐❢ t❀❡r❡ ❛r❡ ♥♊ ✐♥✜♥✐t❡ r❡✇r✐t❡ s❡q✉❡♥❝❡s ◮ R ← · → ∗ ∗ ✳ ✳ ✳ ✐s ❝♊♥✢✉❡♥t ✐❢ R ⊆ ↓ R ◮ ✳ ✳ ✳ ✐s ❝♊♠♣❧❡t❡ ✐❢ t❡r♠✐♥❛t✐♥❣ ❛♥❞ ❝♊♥✢✉❡♥t ◮ ❊①❛♠♣❧❡ r❡✇r✐t❡ s②st❡♠ R r❡✇r✐t❡ s❡q✉❡♥❝❡✿ ◮ ∗ R R R R R ✐s t❡r♠✐♥❛t✐♥❣ ◮ R ✐s ❝♊♥✢✉❡♥t ◮ ∗ ∗ ∗ ∗ ❡✳❣✳ ❛♥❞ ❜✉t ❛❧s♩ ❛♥❞ R R R R ✟

  50. ❛♥❞ ✈❛r✐❛❜❧❡s✿ ① ✱ ② ✱ ③ ✱ ✳ ✳ ✳ ① s s ① ✵ ② s s ✵ s s s ✵ s s ✵ s s s ✵ s s s s s ✵ ❢✉♥❝t✐♊♥ s②♠❜♊❧s ✵✱ s✱ ✳ ✳ ✳ t❡r♠s ✵ s ✵ s s ✵ s s s ✵ r❡✇r✐t❡ r✉❧❡s ✿ ✵ ① ① s ① ② s ① ② r❡✇r✐t❡ st❡♣ s s ✵ s s s ✵ ♥♊r♠❛❧ ❢♊r♠ ❋❛❝t t❡r♠ r❡✇r✐t✐♥❣ ✐s ❚✉r✐♥❣ ❝♊♠♣❧❡t❡ ♠♊❞❡❧ ♊❢ ❝♊♠♣✉t❛t✐♊♥ r❡✇r✐t❡ r✉❧❡ ✐s ♣❛✐r ♊❢ t❡r♠s t❡r♠ r❡✇r✐t❡ s②st❡♠ ✭❚❘❙✮ ✐s s❡t ♊❢ r❡✇r✐t❡ r✉❧❡s r❡✇r✐t❡ st❡♣ ❛♣♣❧✐❡s r❡✇r✐t❡ r✉❧❡ ✉s✐♥❣ s✉❜st✐t✉t✐♊♥ ❛♥❞ ✐♥ ❝♊♥t❡①t ❊①❛♠♣❧❡ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛ss✉♠❡ t❡r♠ str✉❝t✉r❡ ♊♥ ♊❜❥❡❝ts t♩ r❡✇r✐t❡ ◮ ✶✵

  51. ① s s ① ✵ ② s s ✵ s s s ✵ s s ✵ s s s ✵ s s s s s ✵ r❡✇r✐t❡ r✉❧❡ ✐s ♣❛✐r ♊❢ t❡r♠s t❡r♠ r❡✇r✐t❡ s②st❡♠ ✭❚❘❙✮ ✐s s❡t ♊❢ r❡✇r✐t❡ r✉❧❡s r❡✇r✐t❡ st❡♣ ❛♣♣❧✐❡s r❡✇r✐t❡ r✉❧❡ ✉s✐♥❣ s✉❜st✐t✉t✐♊♥ ❛♥❞ ✐♥ ❝♊♥t❡①t ❛♥❞ ✈❛r✐❛❜❧❡s✿ ① ✱ ② ✱ ③ ✱ ✳ ✳ ✳ t❡r♠s ✵ s ✵ s s ✵ s s s ✵ r❡✇r✐t❡ r✉❧❡s ✿ ✵ ① ① s ① ② s ① ② r❡✇r✐t❡ st❡♣ s s ✵ s s s ✵ ♥♊r♠❛❧ ❢♊r♠ ❋❛❝t t❡r♠ r❡✇r✐t✐♥❣ ✐s ❚✉r✐♥❣ ❝♊♠♣❧❡t❡ ♠♊❞❡❧ ♊❢ ❝♊♠♣✉t❛t✐♊♥ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛ss✉♠❡ t❡r♠ str✉❝t✉r❡ ♊♥ ♊❜❥❡❝ts t♩ r❡✇r✐t❡ ◮ ❊①❛♠♣❧❡ ❢✉♥❝t✐♊♥ s②♠❜♊❧s ✵✱ s✱ + ✳ ✳ ✳ ◮ ✶✵

  52. ① s s ① ✵ ② s s ✵ s s s ✵ s s ✵ s s s ✵ s s s s s ✵ r❡✇r✐t❡ r✉❧❡ ✐s ♣❛✐r ♊❢ t❡r♠s t❡r♠ r❡✇r✐t❡ s②st❡♠ ✭❚❘❙✮ ✐s s❡t ♊❢ r❡✇r✐t❡ r✉❧❡s r❡✇r✐t❡ st❡♣ ❛♣♣❧✐❡s r❡✇r✐t❡ r✉❧❡ ✉s✐♥❣ s✉❜st✐t✉t✐♊♥ ❛♥❞ ✐♥ ❝♊♥t❡①t t❡r♠s ✵ s ✵ s s ✵ s s s ✵ r❡✇r✐t❡ r✉❧❡s ✿ ✵ ① ① s ① ② s ① ② r❡✇r✐t❡ st❡♣ s s ✵ s s s ✵ ♥♊r♠❛❧ ❢♊r♠ ❋❛❝t t❡r♠ r❡✇r✐t✐♥❣ ✐s ❚✉r✐♥❣ ❝♊♠♣❧❡t❡ ♠♊❞❡❧ ♊❢ ❝♊♠♣✉t❛t✐♊♥ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛ss✉♠❡ t❡r♠ str✉❝t✉r❡ ♊♥ ♊❜❥❡❝ts t♩ r❡✇r✐t❡ ◮ ❊①❛♠♣❧❡ ❢✉♥❝t✐♊♥ s②♠❜♊❧s ✵✱ s✱ + ✳ ✳ ✳ ❛♥❞ ✈❛r✐❛❜❧❡s✿ ① ✱ ② ✱ ③ ✱ ✳ ✳ ✳ ◮ ✶✵

  53. s s ✵ s s s ✵ s s ✵ s s s ✵ s s s s s ✵ r❡✇r✐t❡ r✉❧❡ ✐s ♣❛✐r ♊❢ t❡r♠s t❡r♠ r❡✇r✐t❡ s②st❡♠ ✭❚❘❙✮ ✐s s❡t ♊❢ r❡✇r✐t❡ r✉❧❡s r❡✇r✐t❡ st❡♣ ❛♣♣❧✐❡s r❡✇r✐t❡ r✉❧❡ ✉s✐♥❣ s✉❜st✐t✉t✐♊♥ ❛♥❞ ✐♥ ❝♊♥t❡①t ① s s ① ✵ ② r❡✇r✐t❡ r✉❧❡s ✿ ✵ ① ① s ① ② s ① ② r❡✇r✐t❡ st❡♣ s s ✵ s s s ✵ ♥♊r♠❛❧ ❢♊r♠ ❋❛❝t t❡r♠ r❡✇r✐t✐♥❣ ✐s ❚✉r✐♥❣ ❝♊♠♣❧❡t❡ ♠♊❞❡❧ ♊❢ ❝♊♠♣✉t❛t✐♊♥ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛ss✉♠❡ t❡r♠ str✉❝t✉r❡ ♊♥ ♊❜❥❡❝ts t♩ r❡✇r✐t❡ ◮ ❊①❛♠♣❧❡ ❢✉♥❝t✐♊♥ s②♠❜♊❧s ✵✱ s✱ + ✳ ✳ ✳ ❛♥❞ ✈❛r✐❛❜❧❡s✿ ① ✱ ② ✱ ③ ✱ ✳ ✳ ✳ ◮ t❡r♠s ✵ s ( ✵ ) s ( s ( ✵ )) s ( s ( s ( ✵ ))) ◮ ✶✵

  54. s s ✵ s s s ✵ s s ✵ s s s ✵ s s s s s ✵ r❡✇r✐t❡ r✉❧❡ ✐s ♣❛✐r ♊❢ t❡r♠s t❡r♠ r❡✇r✐t❡ s②st❡♠ ✭❚❘❙✮ ✐s s❡t ♊❢ r❡✇r✐t❡ r✉❧❡s r❡✇r✐t❡ st❡♣ ❛♣♣❧✐❡s r❡✇r✐t❡ r✉❧❡ ✉s✐♥❣ s✉❜st✐t✉t✐♊♥ ❛♥❞ ✐♥ ❝♊♥t❡①t r❡✇r✐t❡ r✉❧❡s ✿ ✵ ① ① s ① ② s ① ② r❡✇r✐t❡ st❡♣ s s ✵ s s s ✵ ♥♊r♠❛❧ ❢♊r♠ ❋❛❝t t❡r♠ r❡✇r✐t✐♥❣ ✐s ❚✉r✐♥❣ ❝♊♠♣❧❡t❡ ♠♊❞❡❧ ♊❢ ❝♊♠♣✉t❛t✐♊♥ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛ss✉♠❡ t❡r♠ str✉❝t✉r❡ ♊♥ ♊❜❥❡❝ts t♩ r❡✇r✐t❡ ◮ ❊①❛♠♣❧❡ ❢✉♥❝t✐♊♥ s②♠❜♊❧s ✵✱ s✱ + ✳ ✳ ✳ ❛♥❞ ✈❛r✐❛❜❧❡s✿ ① ✱ ② ✱ ③ ✱ ✳ ✳ ✳ ◮ t❡r♠s ✵ s ( ✵ ) s ( s ( ✵ )) s ( s ( s ( ✵ ))) ① s ( s ( ① )) ✵ + ② ◮ ✶✵

  55. s s ✵ s s s ✵ s s ✵ s s s ✵ s s s s s ✵ r❡✇r✐t❡ st❡♣ ❛♣♣❧✐❡s r❡✇r✐t❡ r✉❧❡ ✉s✐♥❣ s✉❜st✐t✉t✐♊♥ ❛♥❞ ✐♥ ❝♊♥t❡①t r❡✇r✐t❡ r✉❧❡s ✿ ✵ ① ① s ① ② s ① ② r❡✇r✐t❡ st❡♣ s s ✵ s s s ✵ ♥♊r♠❛❧ ❢♊r♠ ❋❛❝t t❡r♠ r❡✇r✐t✐♥❣ ✐s ❚✉r✐♥❣ ❝♊♠♣❧❡t❡ ♠♊❞❡❧ ♊❢ ❝♊♠♣✉t❛t✐♊♥ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛ss✉♠❡ t❡r♠ str✉❝t✉r❡ ♊♥ ♊❜❥❡❝ts t♩ r❡✇r✐t❡ ◮ r❡✇r✐t❡ r✉❧❡ ✐s ♣❛✐r ♊❢ t❡r♠s ℓ → r ◮ t❡r♠ r❡✇r✐t❡ s②st❡♠ ✭❚❘❙✮ ✐s s❡t ♊❢ r❡✇r✐t❡ r✉❧❡s ◮ ❊①❛♠♣❧❡ ❢✉♥❝t✐♊♥ s②♠❜♊❧s ✵✱ s✱ + ✳ ✳ ✳ ❛♥❞ ✈❛r✐❛❜❧❡s✿ ① ✱ ② ✱ ③ ✱ ✳ ✳ ✳ ◮ t❡r♠s ✵ s ( ✵ ) s ( s ( ✵ )) s ( s ( s ( ✵ ))) ① s ( s ( ① )) ✵ + ② ◮ ✶✵

  56. s s ✵ s s s ✵ s s ✵ s s s ✵ s s s s s ✵ r❡✇r✐t❡ st❡♣ ❛♣♣❧✐❡s r❡✇r✐t❡ r✉❧❡ ✉s✐♥❣ s✉❜st✐t✉t✐♊♥ ❛♥❞ ✐♥ ❝♊♥t❡①t r❡✇r✐t❡ st❡♣ s s ✵ s s s ✵ ♥♊r♠❛❧ ❢♊r♠ ❋❛❝t t❡r♠ r❡✇r✐t✐♥❣ ✐s ❚✉r✐♥❣ ❝♊♠♣❧❡t❡ ♠♊❞❡❧ ♊❢ ❝♊♠♣✉t❛t✐♊♥ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛ss✉♠❡ t❡r♠ str✉❝t✉r❡ ♊♥ ♊❜❥❡❝ts t♩ r❡✇r✐t❡ ◮ r❡✇r✐t❡ r✉❧❡ ✐s ♣❛✐r ♊❢ t❡r♠s ℓ → r ◮ t❡r♠ r❡✇r✐t❡ s②st❡♠ ✭❚❘❙✮ ✐s s❡t ♊❢ r❡✇r✐t❡ r✉❧❡s ◮ ❊①❛♠♣❧❡ ❢✉♥❝t✐♊♥ s②♠❜♊❧s ✵✱ s✱ + ✳ ✳ ✳ ❛♥❞ ✈❛r✐❛❜❧❡s✿ ① ✱ ② ✱ ③ ✱ ✳ ✳ ✳ ◮ t❡r♠s ✵ s ( ✵ ) s ( s ( ✵ )) s ( s ( s ( ✵ ))) ① s ( s ( ① )) ✵ + ② ◮ r❡✇r✐t❡ r✉❧❡s R ✿ ◮ ✵ + ① → ① s ( ① ) + ② → s ( ① + ② ) ✶✵

  57. s s ✵ s s s ✵ s s ✵ s s s ✵ s s s s s ✵ r❡✇r✐t❡ st❡♣ s s ✵ s s s ✵ ♥♊r♠❛❧ ❢♊r♠ ❋❛❝t t❡r♠ r❡✇r✐t✐♥❣ ✐s ❚✉r✐♥❣ ❝♊♠♣❧❡t❡ ♠♊❞❡❧ ♊❢ ❝♊♠♣✉t❛t✐♊♥ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛ss✉♠❡ t❡r♠ str✉❝t✉r❡ ♊♥ ♊❜❥❡❝ts t♩ r❡✇r✐t❡ ◮ r❡✇r✐t❡ r✉❧❡ ✐s ♣❛✐r ♊❢ t❡r♠s ℓ → r ◮ t❡r♠ r❡✇r✐t❡ s②st❡♠ ✭❚❘❙✮ ✐s s❡t ♊❢ r❡✇r✐t❡ r✉❧❡s ◮ r❡✇r✐t❡ st❡♣ ❛♣♣❧✐❡s r❡✇r✐t❡ r✉❧❡ ✉s✐♥❣ s✉❜st✐t✉t✐♊♥ ❛♥❞ ✐♥ ❝♊♥t❡①t ◮ ❊①❛♠♣❧❡ ❢✉♥❝t✐♊♥ s②♠❜♊❧s ✵✱ s✱ + ✳ ✳ ✳ ❛♥❞ ✈❛r✐❛❜❧❡s✿ ① ✱ ② ✱ ③ ✱ ✳ ✳ ✳ ◮ t❡r♠s ✵ s ( ✵ ) s ( s ( ✵ )) s ( s ( s ( ✵ ))) ① s ( s ( ① )) ✵ + ② ◮ r❡✇r✐t❡ r✉❧❡s R ✿ ◮ ✵ + ① → ① s ( ① ) + ② → s ( ① + ② ) ✶✵

  58. s s ✵ s s s ✵ s s ✵ s s s ✵ ♥♊r♠❛❧ ❢♊r♠ s s s s s ✵ ❋❛❝t t❡r♠ r❡✇r✐t✐♥❣ ✐s ❚✉r✐♥❣ ❝♊♠♣❧❡t❡ ♠♊❞❡❧ ♊❢ ❝♊♠♣✉t❛t✐♊♥ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛ss✉♠❡ t❡r♠ str✉❝t✉r❡ ♊♥ ♊❜❥❡❝ts t♩ r❡✇r✐t❡ ◮ r❡✇r✐t❡ r✉❧❡ ✐s ♣❛✐r ♊❢ t❡r♠s ℓ → r ◮ t❡r♠ r❡✇r✐t❡ s②st❡♠ ✭❚❘❙✮ ✐s s❡t ♊❢ r❡✇r✐t❡ r✉❧❡s ◮ r❡✇r✐t❡ st❡♣ ❛♣♣❧✐❡s r❡✇r✐t❡ r✉❧❡ ✉s✐♥❣ s✉❜st✐t✉t✐♊♥ ❛♥❞ ✐♥ ❝♊♥t❡①t ◮ ❊①❛♠♣❧❡ ❢✉♥❝t✐♊♥ s②♠❜♊❧s ✵✱ s✱ + ✳ ✳ ✳ ❛♥❞ ✈❛r✐❛❜❧❡s✿ ① ✱ ② ✱ ③ ✱ ✳ ✳ ✳ ◮ t❡r♠s ✵ s ( ✵ ) s ( s ( ✵ )) s ( s ( s ( ✵ ))) ① s ( s ( ① )) ✵ + ② ◮ r❡✇r✐t❡ r✉❧❡s R ✿ ◮ ✵ + ① → ① s ( ① ) + ② → s ( ① + ② ) r❡✇r✐t❡ st❡♣ ◮ s ( s ( ✵ )) + s ( s ( s ( ✵ ))) ✶✵

  59. s s ✵ s s s ✵ ♥♊r♠❛❧ ❢♊r♠ s s s s s ✵ ❋❛❝t t❡r♠ r❡✇r✐t✐♥❣ ✐s ❚✉r✐♥❣ ❝♊♠♣❧❡t❡ ♠♊❞❡❧ ♊❢ ❝♊♠♣✉t❛t✐♊♥ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛ss✉♠❡ t❡r♠ str✉❝t✉r❡ ♊♥ ♊❜❥❡❝ts t♩ r❡✇r✐t❡ ◮ r❡✇r✐t❡ r✉❧❡ ✐s ♣❛✐r ♊❢ t❡r♠s ℓ → r ◮ t❡r♠ r❡✇r✐t❡ s②st❡♠ ✭❚❘❙✮ ✐s s❡t ♊❢ r❡✇r✐t❡ r✉❧❡s ◮ r❡✇r✐t❡ st❡♣ ❛♣♣❧✐❡s r❡✇r✐t❡ r✉❧❡ ✉s✐♥❣ s✉❜st✐t✉t✐♊♥ ❛♥❞ ✐♥ ❝♊♥t❡①t ◮ ❊①❛♠♣❧❡ ❢✉♥❝t✐♊♥ s②♠❜♊❧s ✵✱ s✱ + ✳ ✳ ✳ ❛♥❞ ✈❛r✐❛❜❧❡s✿ ① ✱ ② ✱ ③ ✱ ✳ ✳ ✳ ◮ t❡r♠s ✵ s ( ✵ ) s ( s ( ✵ )) s ( s ( s ( ✵ ))) ① s ( s ( ① )) ✵ + ② ◮ r❡✇r✐t❡ r✉❧❡s R ✿ ◮ ✵ + ① → ① s ( ① ) + ② → s ( ① + ② ) r❡✇r✐t❡ st❡♣ ◮ s ( s ( ✵ )) + s ( s ( s ( ✵ ))) → R s ( s ( ✵ ) + s ( s ( s ( ✵ ))) ) ✶✵

  60. s s ✵ s s s ✵ ♥♊r♠❛❧ ❢♊r♠ s s s s s ✵ ❋❛❝t t❡r♠ r❡✇r✐t✐♥❣ ✐s ❚✉r✐♥❣ ❝♊♠♣❧❡t❡ ♠♊❞❡❧ ♊❢ ❝♊♠♣✉t❛t✐♊♥ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛ss✉♠❡ t❡r♠ str✉❝t✉r❡ ♊♥ ♊❜❥❡❝ts t♩ r❡✇r✐t❡ ◮ r❡✇r✐t❡ r✉❧❡ ✐s ♣❛✐r ♊❢ t❡r♠s ℓ → r ◮ t❡r♠ r❡✇r✐t❡ s②st❡♠ ✭❚❘❙✮ ✐s s❡t ♊❢ r❡✇r✐t❡ r✉❧❡s ◮ r❡✇r✐t❡ st❡♣ ❛♣♣❧✐❡s r❡✇r✐t❡ r✉❧❡ ✉s✐♥❣ s✉❜st✐t✉t✐♊♥ ❛♥❞ ✐♥ ❝♊♥t❡①t ◮ ❊①❛♠♣❧❡ ❢✉♥❝t✐♊♥ s②♠❜♊❧s ✵✱ s✱ + ✳ ✳ ✳ ❛♥❞ ✈❛r✐❛❜❧❡s✿ ① ✱ ② ✱ ③ ✱ ✳ ✳ ✳ ◮ t❡r♠s ✵ s ( ✵ ) s ( s ( ✵ )) s ( s ( s ( ✵ ))) ① s ( s ( ① )) ✵ + ② ◮ r❡✇r✐t❡ r✉❧❡s R ✿ ◮ ✵ + ① → ① s ( ① ) + ② → s ( ① + ② ) r❡✇r✐t❡ s❡q✉❡♥❝❡ ◮ s ( s ( ✵ )) + s ( s ( s ( ✵ ))) → R s ( s ( ✵ ) + s ( s ( s ( ✵ ))) ) ✶✵

  61. ♥♊r♠❛❧ ❢♊r♠ s s s s s ✵ ❋❛❝t t❡r♠ r❡✇r✐t✐♥❣ ✐s ❚✉r✐♥❣ ❝♊♠♣❧❡t❡ ♠♊❞❡❧ ♊❢ ❝♊♠♣✉t❛t✐♊♥ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛ss✉♠❡ t❡r♠ str✉❝t✉r❡ ♊♥ ♊❜❥❡❝ts t♩ r❡✇r✐t❡ ◮ r❡✇r✐t❡ r✉❧❡ ✐s ♣❛✐r ♊❢ t❡r♠s ℓ → r ◮ t❡r♠ r❡✇r✐t❡ s②st❡♠ ✭❚❘❙✮ ✐s s❡t ♊❢ r❡✇r✐t❡ r✉❧❡s ◮ r❡✇r✐t❡ st❡♣ ❛♣♣❧✐❡s r❡✇r✐t❡ r✉❧❡ ✉s✐♥❣ s✉❜st✐t✉t✐♊♥ ❛♥❞ ✐♥ ❝♊♥t❡①t ◮ ❊①❛♠♣❧❡ ❢✉♥❝t✐♊♥ s②♠❜♊❧s ✵✱ s✱ + ✳ ✳ ✳ ❛♥❞ ✈❛r✐❛❜❧❡s✿ ① ✱ ② ✱ ③ ✱ ✳ ✳ ✳ ◮ t❡r♠s ✵ s ( ✵ ) s ( s ( ✵ )) s ( s ( s ( ✵ ))) ① s ( s ( ① )) ✵ + ② ◮ r❡✇r✐t❡ r✉❧❡s R ✿ ◮ ✵ + ① → ① s ( ① ) + ② → s ( ① + ② ) r❡✇r✐t❡ s❡q✉❡♥❝❡ ◮ s ( s ( ✵ )) + s ( s ( s ( ✵ ))) → R s ( s ( ✵ ) + s ( s ( s ( ✵ ))) ) → R s ( s ( ✵ + s ( s ( s ( ✵ ))) ) ) ✶✵

  62. ♥♊r♠❛❧ ❢♊r♠ s s s s s ✵ ❋❛❝t t❡r♠ r❡✇r✐t✐♥❣ ✐s ❚✉r✐♥❣ ❝♊♠♣❧❡t❡ ♠♊❞❡❧ ♊❢ ❝♊♠♣✉t❛t✐♊♥ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛ss✉♠❡ t❡r♠ str✉❝t✉r❡ ♊♥ ♊❜❥❡❝ts t♩ r❡✇r✐t❡ ◮ r❡✇r✐t❡ r✉❧❡ ✐s ♣❛✐r ♊❢ t❡r♠s ℓ → r ◮ t❡r♠ r❡✇r✐t❡ s②st❡♠ ✭❚❘❙✮ ✐s s❡t ♊❢ r❡✇r✐t❡ r✉❧❡s ◮ r❡✇r✐t❡ st❡♣ ❛♣♣❧✐❡s r❡✇r✐t❡ r✉❧❡ ✉s✐♥❣ s✉❜st✐t✉t✐♊♥ ❛♥❞ ✐♥ ❝♊♥t❡①t ◮ ❊①❛♠♣❧❡ ❢✉♥❝t✐♊♥ s②♠❜♊❧s ✵✱ s✱ + ✳ ✳ ✳ ❛♥❞ ✈❛r✐❛❜❧❡s✿ ① ✱ ② ✱ ③ ✱ ✳ ✳ ✳ ◮ t❡r♠s ✵ s ( ✵ ) s ( s ( ✵ )) s ( s ( s ( ✵ ))) ① s ( s ( ① )) ✵ + ② ◮ r❡✇r✐t❡ r✉❧❡s R ✿ ◮ ✵ + ① → ① s ( ① ) + ② → s ( ① + ② ) r❡✇r✐t❡ s❡q✉❡♥❝❡ ◮ s ( s ( ✵ )) + s ( s ( s ( ✵ ))) → R s ( s ( ✵ ) + s ( s ( s ( ✵ ))) ) → R s ( s ( ✵ + s ( s ( s ( ✵ ))) ) ) ✶✵

  63. ♥♊r♠❛❧ ❢♊r♠ ❋❛❝t t❡r♠ r❡✇r✐t✐♥❣ ✐s ❚✉r✐♥❣ ❝♊♠♣❧❡t❡ ♠♊❞❡❧ ♊❢ ❝♊♠♣✉t❛t✐♊♥ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛ss✉♠❡ t❡r♠ str✉❝t✉r❡ ♊♥ ♊❜❥❡❝ts t♩ r❡✇r✐t❡ ◮ r❡✇r✐t❡ r✉❧❡ ✐s ♣❛✐r ♊❢ t❡r♠s ℓ → r ◮ t❡r♠ r❡✇r✐t❡ s②st❡♠ ✭❚❘❙✮ ✐s s❡t ♊❢ r❡✇r✐t❡ r✉❧❡s ◮ r❡✇r✐t❡ st❡♣ ❛♣♣❧✐❡s r❡✇r✐t❡ r✉❧❡ ✉s✐♥❣ s✉❜st✐t✉t✐♊♥ ❛♥❞ ✐♥ ❝♊♥t❡①t ◮ ❊①❛♠♣❧❡ ❢✉♥❝t✐♊♥ s②♠❜♊❧s ✵✱ s✱ + ✳ ✳ ✳ ❛♥❞ ✈❛r✐❛❜❧❡s✿ ① ✱ ② ✱ ③ ✱ ✳ ✳ ✳ ◮ t❡r♠s ✵ s ( ✵ ) s ( s ( ✵ )) s ( s ( s ( ✵ ))) ① s ( s ( ① )) ✵ + ② ◮ r❡✇r✐t❡ r✉❧❡s R ✿ ◮ ✵ + ① → ① s ( ① ) + ② → s ( ① + ② ) r❡✇r✐t❡ s❡q✉❡♥❝❡ ◮ s ( s ( ✵ )) + s ( s ( s ( ✵ ))) → R s ( s ( ✵ ) + s ( s ( s ( ✵ ))) ) → R s ( s ( ✵ + s ( s ( s ( ✵ ))) ) ) → R s ( s ( s ( s ( s ( ✵ ))) )) ✶✵

  64. ❋❛❝t t❡r♠ r❡✇r✐t✐♥❣ ✐s ❚✉r✐♥❣ ❝♊♠♣❧❡t❡ ♠♊❞❡❧ ♊❢ ❝♊♠♣✉t❛t✐♊♥ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛ss✉♠❡ t❡r♠ str✉❝t✉r❡ ♊♥ ♊❜❥❡❝ts t♩ r❡✇r✐t❡ ◮ r❡✇r✐t❡ r✉❧❡ ✐s ♣❛✐r ♊❢ t❡r♠s ℓ → r ◮ t❡r♠ r❡✇r✐t❡ s②st❡♠ ✭❚❘❙✮ ✐s s❡t ♊❢ r❡✇r✐t❡ r✉❧❡s ◮ r❡✇r✐t❡ st❡♣ ❛♣♣❧✐❡s r❡✇r✐t❡ r✉❧❡ ✉s✐♥❣ s✉❜st✐t✉t✐♊♥ ❛♥❞ ✐♥ ❝♊♥t❡①t ◮ ❊①❛♠♣❧❡ ❢✉♥❝t✐♊♥ s②♠❜♊❧s ✵✱ s✱ + ✳ ✳ ✳ ❛♥❞ ✈❛r✐❛❜❧❡s✿ ① ✱ ② ✱ ③ ✱ ✳ ✳ ✳ ◮ t❡r♠s ✵ s ( ✵ ) s ( s ( ✵ )) s ( s ( s ( ✵ ))) ① s ( s ( ① )) ✵ + ② ◮ r❡✇r✐t❡ r✉❧❡s R ✿ ◮ ✵ + ① → ① s ( ① ) + ② → s ( ① + ② ) r❡✇r✐t❡ s❡q✉❡♥❝❡ ◮ s ( s ( ✵ )) + s ( s ( s ( ✵ ))) → R s ( s ( ✵ ) + s ( s ( s ( ✵ ))) ) → R s ( s ( ✵ + s ( s ( s ( ✵ ))) ) ) ♥♊r♠❛❧ ❢♊r♠ → R s ( s ( s ( s ( s ( ✵ ))) )) ✶✵

  65. ♥♊r♠❛❧ ❢♊r♠ ❚❡r♠ ❘❡✇r✐t✐♥❣ ❛ss✉♠❡ t❡r♠ str✉❝t✉r❡ ♊♥ ♊❜❥❡❝ts t♩ r❡✇r✐t❡ ◮ r❡✇r✐t❡ r✉❧❡ ✐s ♣❛✐r ♊❢ t❡r♠s ℓ → r ◮ t❡r♠ r❡✇r✐t❡ s②st❡♠ ✭❚❘❙✮ ✐s s❡t ♊❢ r❡✇r✐t❡ r✉❧❡s ◮ r❡✇r✐t❡ st❡♣ ❛♣♣❧✐❡s r❡✇r✐t❡ r✉❧❡ ✉s✐♥❣ s✉❜st✐t✉t✐♊♥ ❛♥❞ ✐♥ ❝♊♥t❡①t ◮ ❊①❛♠♣❧❡ ❢✉♥❝t✐♊♥ s②♠❜♊❧s ✵✱ s✱ + ✳ ✳ ✳ ❛♥❞ ✈❛r✐❛❜❧❡s✿ ① ✱ ② ✱ ③ ✱ ✳ ✳ ✳ ◮ t❡r♠s ✵ s ( ✵ ) s ( s ( ✵ )) s ( s ( s ( ✵ ))) ① s ( s ( ① )) ✵ + ② ◮ r❡✇r✐t❡ r✉❧❡s R ✿ ◮ ✵ + ① → ① s ( ① ) + ② → s ( ① + ② ) r❡✇r✐t❡ s❡q✉❡♥❝❡ ◮ s ( s ( ✵ )) + s ( s ( s ( ✵ ))) → R s ( s ( ✵ ) + s ( s ( s ( ✵ ))) ) → R s ( s ( ✵ + s ( s ( s ( ✵ ))) ) ) → R s ( s ( s ( s ( s ( ✵ ))) )) ❋❛❝t t❡r♠ r❡✇r✐t✐♥❣ ✐s ❚✉r✐♥❣ ❝♊♠♣❧❡t❡ ♠♊❞❡❧ ♊❢ ❝♊♠♣✉t❛t✐♊♥ ✶✵

  66. ✐❢ ②❡s✱ ❀♊✇ ❧♊♥❣ ❞♩ s❡q✉❡♥❝❡s ❣❡t❄ ❝♊♠♣❧❡①✐t② ✐s r❡✇r✐t✐♥❣ ❞❡t❡r♠✐♥✐st✐❝❄ ❝♊♥✢✉❡♥❝❡ ❝❛♥ ✇❡ ❞❡❝✐❞❡ t❀❡ ❡q✉❛t✐♊♥❛❧ t❀❡♊r② ❄ ❝♊♠♣❧❡t✐♊♥ ✐s t❀❡ ✜rst✲♊r❞❡r t❀❡♊r② ♊❢ ❞❡❝✐❞❛❜❧❡❄ ❞❡❝✐❞❛❜✐❧✐t② ❛r❡ t✇♩ ❣✐✈❡♥ r❡✇r✐t❡ s❡q✉❡♥❝❡s ❡q✉✐✈❛❧❡♥t❄ ♣r♊♊❢ t❡r♠s Pr♊♣❡rt✐❡s ♊❢ ■♥t❡r❡st ❣✐✈❡♥ ❚❘❙ R ✱ ✐s ❡✈❡r② r❡✇r✐t❡ s❡q✉❡♥❝❡ t❡r♠✐♥❛t✐♥❣❄ t❡r♠✐♥❛t✐♊♥ ◮ ✶✶

  67. ✐s r❡✇r✐t✐♥❣ ❞❡t❡r♠✐♥✐st✐❝❄ ❝♊♥✢✉❡♥❝❡ ❝❛♥ ✇❡ ❞❡❝✐❞❡ t❀❡ ❡q✉❛t✐♊♥❛❧ t❀❡♊r② ❄ ❝♊♠♣❧❡t✐♊♥ ✐s t❀❡ ✜rst✲♊r❞❡r t❀❡♊r② ♊❢ ❞❡❝✐❞❛❜❧❡❄ ❞❡❝✐❞❛❜✐❧✐t② ❛r❡ t✇♩ ❣✐✈❡♥ r❡✇r✐t❡ s❡q✉❡♥❝❡s ❡q✉✐✈❛❧❡♥t❄ ♣r♊♊❢ t❡r♠s Pr♊♣❡rt✐❡s ♊❢ ■♥t❡r❡st ❣✐✈❡♥ ❚❘❙ R ✱ ✐s ❡✈❡r② r❡✇r✐t❡ s❡q✉❡♥❝❡ t❡r♠✐♥❛t✐♥❣❄ t❡r♠✐♥❛t✐♊♥ ◮ ✐❢ ②❡s✱ ❀♊✇ ❧♊♥❣ ❞♩ → R s❡q✉❡♥❝❡s ❣❡t❄ ❝♊♠♣❧❡①✐t② ◮ ✶✶

  68. ❝❛♥ ✇❡ ❞❡❝✐❞❡ t❀❡ ❡q✉❛t✐♊♥❛❧ t❀❡♊r② ❄ ❝♊♠♣❧❡t✐♊♥ ✐s t❀❡ ✜rst✲♊r❞❡r t❀❡♊r② ♊❢ ❞❡❝✐❞❛❜❧❡❄ ❞❡❝✐❞❛❜✐❧✐t② ❛r❡ t✇♩ ❣✐✈❡♥ r❡✇r✐t❡ s❡q✉❡♥❝❡s ❡q✉✐✈❛❧❡♥t❄ ♣r♊♊❢ t❡r♠s Pr♊♣❡rt✐❡s ♊❢ ■♥t❡r❡st ❣✐✈❡♥ ❚❘❙ R ✱ ✐s ❡✈❡r② r❡✇r✐t❡ s❡q✉❡♥❝❡ t❡r♠✐♥❛t✐♥❣❄ t❡r♠✐♥❛t✐♊♥ ◮ ✐❢ ②❡s✱ ❀♊✇ ❧♊♥❣ ❞♩ → R s❡q✉❡♥❝❡s ❣❡t❄ ❝♊♠♣❧❡①✐t② ◮ ✐s r❡✇r✐t✐♥❣ ❞❡t❡r♠✐♥✐st✐❝❄ ❝♊♥✢✉❡♥❝❡ ◮ ✶✶

  69. ✐s t❀❡ ✜rst✲♊r❞❡r t❀❡♊r② ♊❢ ❞❡❝✐❞❛❜❧❡❄ ❞❡❝✐❞❛❜✐❧✐t② ❛r❡ t✇♩ ❣✐✈❡♥ r❡✇r✐t❡ s❡q✉❡♥❝❡s ❡q✉✐✈❛❧❡♥t❄ ♣r♊♊❢ t❡r♠s Pr♊♣❡rt✐❡s ♊❢ ■♥t❡r❡st ❣✐✈❡♥ ❚❘❙ R ✱ ✐s ❡✈❡r② r❡✇r✐t❡ s❡q✉❡♥❝❡ t❡r♠✐♥❛t✐♥❣❄ t❡r♠✐♥❛t✐♊♥ ◮ ✐❢ ②❡s✱ ❀♊✇ ❧♊♥❣ ❞♩ → R s❡q✉❡♥❝❡s ❣❡t❄ ❝♊♠♣❧❡①✐t② ◮ ✐s r❡✇r✐t✐♥❣ ❞❡t❡r♠✐♥✐st✐❝❄ ❝♊♥✢✉❡♥❝❡ ◮ ❝❛♥ ✇❡ ❞❡❝✐❞❡ t❀❡ ❡q✉❛t✐♊♥❛❧ t❀❡♊r② ↔ ∗ R ❄ ❝♊♠♣❧❡t✐♊♥ ◮ ✶✶

  70. ❛r❡ t✇♩ ❣✐✈❡♥ r❡✇r✐t❡ s❡q✉❡♥❝❡s ❡q✉✐✈❛❧❡♥t❄ ♣r♊♊❢ t❡r♠s Pr♊♣❡rt✐❡s ♊❢ ■♥t❡r❡st ❣✐✈❡♥ ❚❘❙ R ✱ ✐s ❡✈❡r② r❡✇r✐t❡ s❡q✉❡♥❝❡ t❡r♠✐♥❛t✐♥❣❄ t❡r♠✐♥❛t✐♊♥ ◮ ✐❢ ②❡s✱ ❀♊✇ ❧♊♥❣ ❞♩ → R s❡q✉❡♥❝❡s ❣❡t❄ ❝♊♠♣❧❡①✐t② ◮ ✐s r❡✇r✐t✐♥❣ ❞❡t❡r♠✐♥✐st✐❝❄ ❝♊♥✢✉❡♥❝❡ ◮ ❝❛♥ ✇❡ ❞❡❝✐❞❡ t❀❡ ❡q✉❛t✐♊♥❛❧ t❀❡♊r② ↔ ∗ R ❄ ❝♊♠♣❧❡t✐♊♥ ◮ ✐s t❀❡ ✜rst✲♊r❞❡r t❀❡♊r② ♊❢ → R ❞❡❝✐❞❛❜❧❡❄ ❞❡❝✐❞❛❜✐❧✐t② ◮ ✶✶

  71. Pr♊♣❡rt✐❡s ♊❢ ■♥t❡r❡st ❣✐✈❡♥ ❚❘❙ R ✱ ✐s ❡✈❡r② r❡✇r✐t❡ s❡q✉❡♥❝❡ t❡r♠✐♥❛t✐♥❣❄ t❡r♠✐♥❛t✐♊♥ ◮ ✐❢ ②❡s✱ ❀♊✇ ❧♊♥❣ ❞♩ → R s❡q✉❡♥❝❡s ❣❡t❄ ❝♊♠♣❧❡①✐t② ◮ ✐s r❡✇r✐t✐♥❣ ❞❡t❡r♠✐♥✐st✐❝❄ ❝♊♥✢✉❡♥❝❡ ◮ ❝❛♥ ✇❡ ❞❡❝✐❞❡ t❀❡ ❡q✉❛t✐♊♥❛❧ t❀❡♊r② ↔ ∗ R ❄ ❝♊♠♣❧❡t✐♊♥ ◮ ✐s t❀❡ ✜rst✲♊r❞❡r t❀❡♊r② ♊❢ → R ❞❡❝✐❞❛❜❧❡❄ ❞❡❝✐❞❛❜✐❧✐t② ◮ ❛r❡ t✇♩ ❣✐✈❡♥ r❡✇r✐t❡ s❡q✉❡♥❝❡s ❡q✉✐✈❛❧❡♥t❄ ♣r♊♊❢ t❡r♠s ◮ ✶✶

  72. ❋♩r♠❛❧ ❆♥❛❧②s✐s ❚❡❝❀♥♊❧♊❣✐❡s ✶✷

  73. ❋♩r♠❛❧ ❆♥❛❧②s✐s ❚❡❝❀♥♊❧♊❣✐❡s ✶✷

  74. ❖✉t❧✐♥❡ ▌♊t✐✈❛t✐♥❣ ❊①❛♠♣❧❡s ❚❡r♠ ❘❡✇r✐t✐♥❣ ❚♩♩❧s ❋♩r♠❛❧✐③❛t✐♊♥ ❛♥❞ ❈❡rt✐✜❝❛t✐♊♥ ❈♊♥❝❧✉s✐♊♥ ✶✞

  75. ❚❡r♠✐♥❛t✐♊♥ ❚ ❚ ✷✿ ❚②r♊❧❡❛♥ ❚❡r♠✐♥❛t✐♊♥ ❚♩♩❧ ✷ ❚ ✐♥♣✉t✿ ❚❘❙ R ♩✉t♣✉t✿ ❹❊❙ ✰ t❡r♠✐♥❛t✐♊♥ ♣r♊♊❢✱ ♩r ◆❖ ✰ ❝♊✉♥t❡r❡①❛♠♣❧❡ ❹❊❙ R ❄ ◆❖ ✶✹ ❑♩r♣ ❡t ❛❧✳✱ ❚②r♊❧❡❛♥ ❚❡r♠✐♥❛t✐♊♥ ❚♩♩❧ ✷ ✱ ✷✵✵✟✳

  76. ❚❡r♠✐♥❛t✐♊♥ ❚ ❚ ✷✿ ❚②r♊❧❡❛♥ ❚❡r♠✐♥❛t✐♊♥ ❚♩♩❧ ✷ ❚ ✐♥♣✉t✿ ❚❘❙ R ♩✉t♣✉t✿ ❹❊❙ ✰ t❡r♠✐♥❛t✐♊♥ ♣r♊♊❢✱ ♩r ◆❖ ✰ ❝♊✉♥t❡r❡①❛♠♣❧❡ ❹❊❙ R ❄ ◆❖ ❉❡✜♥✐t✐♊♥ ❚❘❙ R ✐s t❡r♠✐♥❛t✐♥❣ ✐❢ ∄ t ✶ → t ✷ → t ✾ → . . . ✶✹

  77. ❚❡r♠✐♥❛t✐♊♥ ❚ ❚ ✷✿ ❚②r♊❧❡❛♥ ❚❡r♠✐♥❛t✐♊♥ ❚♩♩❧ ✷ ❚ ✐♥♣✉t✿ ❚❘❙ R ♩✉t♣✉t✿ ❹❊❙ ✰ t❡r♠✐♥❛t✐♊♥ ♣r♊♊❢✱ ♩r ◆❖ ✰ ❝♊✉♥t❡r❡①❛♠♣❧❡ ❹❊❙ R ❄ ◆❖ ❊①❛♠♣❧❡ ✭❆❞❞✐t✐♊♥✮ ✵ + x → x s ( x ) + ② → s ( ① + ② ) ✶✹

  78. ❚❡r♠✐♥❛t✐♊♥ ❚ ❚ ✷✿ ❚②r♊❧❡❛♥ ❚❡r♠✐♥❛t✐♊♥ ❚♩♩❧ ✷ ❚ ✐♥♣✉t✿ ❚❘❙ R ♩✉t♣✉t✿ ❹❊❙ ✰ t❡r♠✐♥❛t✐♊♥ ♣r♊♊❢✱ ♩r ◆❖ ✰ ❝♊✉♥t❡r❡①❛♠♣❧❡ ❹❊❙ R ❄ ◆❖ ❊①❛♠♣❧❡ ✭❆❞❞✐t✐♊♥✮ ✵ + x → x s ( x ) + ② → s ( ① + ② ) ✶✹

  79. ❚❡r♠✐♥❛t✐♊♥ ❚ ❚ ✷✿ ❚②r♊❧❡❛♥ ❚❡r♠✐♥❛t✐♊♥ ❚♩♩❧ ✷ ❚ ✐♥♣✉t✿ ❚❘❙ R ♩✉t♣✉t✿ ❹❊❙ ✰ t❡r♠✐♥❛t✐♊♥ ♣r♊♊❢✱ ♩r ◆❖ ✰ ❝♊✉♥t❡r❡①❛♠♣❧❡ ❹❊❙ R ❄ ◆❖ ❊①❛♠♣❧❡ ✭❙✐♠♣❧❡ ●❛♠❡✮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ✶✹

  80. ❚❡r♠✐♥❛t✐♊♥ ❚ ❚ ✷✿ ❚②r♊❧❡❛♥ ❚❡r♠✐♥❛t✐♊♥ ❚♩♩❧ ✷ ❚ ✐♥♣✉t✿ ❚❘❙ R ♩✉t♣✉t✿ ❹❊❙ ✰ t❡r♠✐♥❛t✐♊♥ ♣r♊♊❢✱ ♩r ◆❖ ✰ ❝♊✉♥t❡r❡①❛♠♣❧❡ ❹❊❙ R ❄ ◆❖ ❊①❛♠♣❧❡ ✭❙✐♠♣❧❡ ●❛♠❡✮ • • → ◩ ◩ ◩ → ◩ • ◩ → • ◩ • → • ✶✹

  81. ❚❡r♠✐♥❛t✐♊♥ ❚ ❚ ✷✿ ❚②r♊❧❡❛♥ ❚❡r♠✐♥❛t✐♊♥ ❚♩♩❧ ✷ ❚ ✐♥♣✉t✿ ❚❘❙ R ♩✉t♣✉t✿ ❹❊❙ ✰ t❡r♠✐♥❛t✐♊♥ ♣r♊♊❢✱ ♩r ◆❖ ✰ ❝♊✉♥t❡r❡①❛♠♣❧❡ ❹❊❙ R ❄ ◆❖ ❊①❛♠♣❧❡ ✭❙✐❡✈❡ ♊❢ ❊r❛t♩st❀❡♥❡s✮ ♣r✐♠❡s → s✐❡✈❡ ( ❢r♩♠ ( s ( s ( ✵ )))) s✐❡✈❡ ( ✵ : y ) → s✐❡✈❡ ( y ) ❢r♩♠ ( x ) → x : ❢r♩♠ ( s ( x )) s✐❡✈❡ ( s ( x ): y ) → s ( x ): s✐❡✈❡ ( ✜❧t❡r ( x , y , x )) ❀❞ ( x : y ) → x ✜❧t❡r ( ✵ , y : z , w ) → ✵ : ✜❧t❡r ( w , z , w ) t❧ ( x : y ) → y ✜❧t❡r ( s ( x ) , y : z , w ) → y : ✜❧t❡r ( x , z , w ) ✶✹

  82. ❚❡r♠✐♥❛t✐♊♥ ❚ ❚ ✷✿ ❚②r♊❧❡❛♥ ❚❡r♠✐♥❛t✐♊♥ ❚♩♩❧ ✷ ❚ ✐♥♣✉t✿ ❚❘❙ R ♩✉t♣✉t✿ ❹❊❙ ✰ t❡r♠✐♥❛t✐♊♥ ♣r♊♊❢✱ ♩r ◆❖ ✰ ❝♊✉♥t❡r❡①❛♠♣❧❡ ❹❊❙ R ❄ ◆❖ ❊①❛♠♣❧❡ ✭❙✐❡✈❡ ♊❢ ❊r❛t♩st❀❡♥❡s✮ ♣r✐♠❡s → s✐❡✈❡ ( ❢r♩♠ ( s ( s ( ✵ )))) s✐❡✈❡ ( ✵ : y ) → s✐❡✈❡ ( y ) ❢r♩♠ ( x ) → x : ❢r♩♠ ( s ( x )) s✐❡✈❡ ( s ( x ): y ) → s ( x ): s✐❡✈❡ ( ✜❧t❡r ( x , y , x )) ❀❞ ( x : y ) → x ✜❧t❡r ( ✵ , y : z , w ) → ✵ : ✜❧t❡r ( w , z , w ) t❧ ( x : y ) → y ✜❧t❡r ( s ( x ) , y : z , w ) → y : ✜❧t❡r ( x , z , w ) ✶✹

  83. ❚❡r♠✐♥❛t✐♊♥ ❈♊♠♣❡t✐t✐♊♥ ❛♥♥✉❛❧ ❝♊♠♣❡t✐t✐♊♥ t❡r♠ r❡✇r✐t✐♥❣✿ st❛♥❞❛r❞ ❚❘❙✱ str✐♥❣ r❡✇r✐t✐♥❣✱ r❡❧❛t✐✈❡ t❡r♠✐♥❛t✐♊♥✱ t❡r♠✐♥❛t✐♊♥ ♠♊❞✉❧♊✱ ❝♊♥❞✐t✐♊♥❛❧✱ ✐♥♥❡r♠♩st ♣r♊❣r❛♠s✿ ❈✱ ❧♊❣✐❝ ♣r♊❣r❛♠♠✐♥❣✱ ✐♥t❡❣❡r tr❛♥s✐t✐♊♥ s②st❡♠s ❀tt♣✿✎✎t❡r♠✐♥❛t✐♊♥✲♣♊rt❛❧✳♊r❣ ❚ ❚ ✷✿ ❚❡❝❀♥✐q✉❡s ❚ ❞❡♣❡♥❞❡♥❝② ♣❛✐r ✭❉P✮ ❢r❛♠❡✇♊r❊ ◮ ❞❡♣❡♥❞❡♥❝② ❣r❛♣❀ ❛♣♣r♩①✐♠❛t✐♊♥s ◮ ✐♥t❡r♣r❡t❛t✐♊♥ ♠❡t❀♊❞s✿ ♣♊❧②♥♊♠✐❛❧s✱ ♠❛tr✐❝❡s✱ ❛r❝t✐❝✱ ♩r❞✐♥❛❧s ◮ r❡❞✉❝t✐♊♥ ♩r❞❡rs✿ ❧❡①✐❝♊❣r❛♣❀✐❝ ♣❛t❀ ♩r❞❡r✱ ❑♥✉t❀✲❇❡♥❞✐① ♩r❞❡r✱ ◮ ✇❡✐❣❀t❡❞ ♣❛t❀ ♩r❞❡r ❧❛❜❡❧✐♥❣ t❡❝❀♥✐q✉❡s✿ s❡♠❛♥t✐❝ ❧❛❜❡❧❧✐♥❣✱ ♠❛t❝❀❜♊✉♥❞s ◮ ♥♊♥✲t❡r♠✐♥❛t✐♊♥✿ ❧♊♊♣s ❛♥❞ ✉♥❢♊❧❞✐♥❣s ◮ ✳ ✳ ✳ ◮ ✶✺

  84. ❚ ❚ ✷✿ ❚❡❝❀♥✐q✉❡s ❚ ❞❡♣❡♥❞❡♥❝② ♣❛✐r ✭❉P✮ ❢r❛♠❡✇♊r❊ ◮ ❞❡♣❡♥❞❡♥❝② ❣r❛♣❀ ❛♣♣r♩①✐♠❛t✐♊♥s ◮ ✐♥t❡r♣r❡t❛t✐♊♥ ♠❡t❀♊❞s✿ ♣♊❧②♥♊♠✐❛❧s✱ ♠❛tr✐❝❡s✱ ❛r❝t✐❝✱ ♩r❞✐♥❛❧s ◮ r❡❞✉❝t✐♊♥ ♩r❞❡rs✿ ❧❡①✐❝♊❣r❛♣❀✐❝ ♣❛t❀ ♩r❞❡r✱ ❑♥✉t❀✲❇❡♥❞✐① ♩r❞❡r✱ ◮ ✇❡✐❣❀t❡❞ ♣❛t❀ ♩r❞❡r ❧❛❜❡❧✐♥❣ t❡❝❀♥✐q✉❡s✿ s❡♠❛♥t✐❝ ❧❛❜❡❧❧✐♥❣✱ ♠❛t❝❀❜♊✉♥❞s ◮ ♥♊♥✲t❡r♠✐♥❛t✐♊♥✿ ❧♊♊♣s ❛♥❞ ✉♥❢♊❧❞✐♥❣s ◮ ✳ ✳ ✳ ◮ ❚❡r♠✐♥❛t✐♊♥ ❈♊♠♣❡t✐t✐♊♥ ❛♥♥✉❛❧ ❝♊♠♣❡t✐t✐♊♥ ◮ t❡r♠ r❡✇r✐t✐♥❣✿ st❛♥❞❛r❞ ❚❘❙✱ str✐♥❣ r❡✇r✐t✐♥❣✱ r❡❧❛t✐✈❡ t❡r♠✐♥❛t✐♊♥✱ ◮ t❡r♠✐♥❛t✐♊♥ ♠♊❞✉❧♊✱ ❝♊♥❞✐t✐♊♥❛❧✱ ✐♥♥❡r♠♩st ♣r♊❣r❛♠s✿ ❈✱ ❧♊❣✐❝ ♣r♊❣r❛♠♠✐♥❣✱ ✐♥t❡❣❡r tr❛♥s✐t✐♊♥ s②st❡♠s ◮ ❀tt♣✿✎✎t❡r♠✐♥❛t✐♊♥✲♣♊rt❛❧✳♊r❣ ◮ ✶✺

  85. ❘❡s❡❛r❝❀ ❊①❛♠♣❧❡✿ ❇❛tt❧❡ ♊❢ ❍❡r❝✉❧❡s ❛♥❞ ❍②❞r❛ ✭✶✮ ❍②❞r❛ ✐s ❛ tr❡❡✲s❀❛♣❡❞ ♠♊♥st❡r ✇❀✐❝❀ ❣r♩✇s ✇❀❡♥❡✈❡r ❍❡r❝✉❧❡s ❝❀♊♣s ♩✛ ❛ ❀❡❛❞✿ ■❢ t❀❡ ❝✉t✲♊✛ ❀❡❛❞ ❀❛s ❛ ❣r❛♥❞♣❛r❡♥t ✐♥ t❀❡ tr❡❡ t❀❡♥ t❀❡ ❜r❛♥❝❀ ❢r♩♠ t❀✐s ❣r❛♥❞♣❛r❡♥t ♠✉❧t✐♣❧✐❡s✳ ❍②❞r❛ ❣❡ts ♠♩r❡ ❛♥❞ ♠♩r❡ ❛♥❣r②✿ t❀❡ ♥✉♠❜❡r ♊❢ ❝♊♣✐❡s ❝♩rr❡s♣♊♥❞s t♩ t❀❡ ♥✉♠❜❡r ♊❢ ❀❡❛❞s ❛❧r❡❛❞② ❝✉t ♊✛✳ ❲✐❧❧ ❍②❞r❛ ❡✈❡r ❞✐❡✱ s✉❝❀ t❀❛t ❍❡r❝✉❧❡s ✇✐♥s❄ ✶✻

  86. ❚ ❚ ❚ ✷ ▲♊♥❣✲❙t❛♥❞✐♥❣ ❖♣❡♥ Pr♊❜❧❡♠ s❀♊✇ t❡r♠✐♥❛t✐♊♥ ♊❢ ❛✉t♩♠❛t✐❝❛❧❧② ❘❡s❡❛r❝❀ ❊①❛♠♣❧❡✿ ❇❛tt❧❡ ♊❢ ❍❡r❝✉❧❡s ❛♥❞ ❍②❞r❛ ✭✷✮ ♣r♊❝❡ss ✐s ♠♊❞❡❧❧❡❞ ❜② ❚❘❙ R ✿ ◩ ( x ) → • ( ï¿œ ( x )) • ( ï¿œ ( x )) → ï¿œ ( • ( • ( x ))) • ( x ) → x ï¿œ ( ◩ ( x )) → ◩ ( ï¿œ ( x )) • ( ❝ ✶ ( x , y )) → ❝ ✶ ( x , ❍ ( x , y )) ❍ ( ✵ , x ) → ◩ ( x ) • ( ❍ ( ❍ ( ✵ , y ) , z )) → ❝ ✶ ( y , z ) ❝ ✷ ( x , y , z ) → ◩ ( ❍ ( y , z )) • ( ❍ ( ❍ ( ❍ ( ✵ , x ) , y ) , z )) → ❝ ✷ ( x , y , z ) ❝ ✶ ( y , z ) → ◩ ( z ) • ( ❝ ✷ ( x , y , z )) → ❝ ✷ ( x , ❍ ( x , y ) , z ) ❚♊✉③❡t✱ ❊♥❝♊❞✐♥❣ t❀❡ ❍②❞r❛ ❇❛tt❧❡ ❛s ❛ ❘❡✇r✐t❡ ❙②st❡♠ ✱ ✶✟✟✜✳ ✶✌

  87. ❚ ❚ ❚ ✷ ❘❡s❡❛r❝❀ ❊①❛♠♣❧❡✿ ❇❛tt❧❡ ♊❢ ❍❡r❝✉❧❡s ❛♥❞ ❍②❞r❛ ✭✷✮ ♣r♊❝❡ss ✐s ♠♊❞❡❧❧❡❞ ❜② ❚❘❙ R ✿ ◩ ( x ) → • ( ï¿œ ( x )) • ( ï¿œ ( x )) → ï¿œ ( • ( • ( x ))) • ( x ) → x ï¿œ ( ◩ ( x )) → ◩ ( ï¿œ ( x )) • ( ❝ ✶ ( x , y )) → ❝ ✶ ( x , ❍ ( x , y )) ❍ ( ✵ , x ) → ◩ ( x ) • ( ❍ ( ❍ ( ✵ , y ) , z )) → ❝ ✶ ( y , z ) ❝ ✷ ( x , y , z ) → ◩ ( ❍ ( y , z )) • ( ❍ ( ❍ ( ❍ ( ✵ , x ) , y ) , z )) → ❝ ✷ ( x , y , z ) ❝ ✶ ( y , z ) → ◩ ( z ) • ( ❝ ✷ ( x , y , z )) → ❝ ✷ ( x , ❍ ( x , y ) , z ) ▲♊♥❣✲❙t❛♥❞✐♥❣ ❖♣❡♥ Pr♊❜❧❡♠ s❀♊✇ t❡r♠✐♥❛t✐♊♥ ♊❢ R ❛✉t♩♠❛t✐❝❛❧❧② ✶✌

  88. ❚ ❚ ❚ ✷ ❘❡s❡❛r❝❀ ❊①❛♠♣❧❡✿ ❇❛tt❧❡ ♊❢ ❍❡r❝✉❧❡s ❛♥❞ ❍②❞r❛ ✭✷✮ ♣r♊❝❡ss ✐s ♠♊❞❡❧❧❡❞ ❜② ❚❘❙ R ✿ ◩ ( x ) → • ( ï¿œ ( x )) • ( ï¿œ ( x )) → ï¿œ ( • ( • ( x ))) • ( x ) → x ï¿œ ( ◩ ( x )) → ◩ ( ï¿œ ( x )) • ( ❝ ✶ ( x , y )) → ❝ ✶ ( x , ❍ ( x , y )) ❍ ( ✵ , x ) → ◩ ( x ) • ( ❍ ( ❍ ( ✵ , y ) , z )) → ❝ ✶ ( y , z ) ❝ ✷ ( x , y , z ) → ◩ ( ❍ ( y , z )) • ( ❍ ( ❍ ( ❍ ( ✵ , x ) , y ) , z )) → ❝ ✷ ( x , y , z ) ❝ ✶ ( y , z ) → ◩ ( z ) • ( ❝ ✷ ( x , y , z )) → ❝ ✷ ( x , ❍ ( x , y ) , z ) ▲♊♥❣✲❙t❛♥❞✐♥❣ ❖♣❡♥ Pr♊❜❧❡♠ s❀♊✇ t❡r♠✐♥❛t✐♊♥ ♊❢ R ❛✉t♩♠❛t✐❝❛❧❧② ❩❛♥❊❧✱ ❲✐♥❊❧❡r✱ ❛♥❞ ▌✐❞❞❡❧❞♊r♣✱ ❇❡②♊♥❞ P♊❧②♥♊♠✐❛❧s ❛♥❞ P❡❛♥♊ ❆r✐t❀♠❡t✐❝ ✕ ❆✉t♩♠❛t✐♊♥ ♊❢ ✶✌ ❊❧❡♠❡♥t❛r② ❛♥❞ ❖r❞✐♥❛❧ ■♥t❡r♣r❡t❛t✐♊♥s ✱ ✷✵✶✺✳

  89. ❘❡s❡❛r❝❀ ❊①❛♠♣❧❡✿ ❇❛tt❧❡ ♊❢ ❍❡r❝✉❧❡s ❛♥❞ ❍②❞r❛ ✭✷✮ ♣r♊❝❡ss ✐s ♠♊❞❡❧❧❡❞ ❜② ❚❘❙ R ✿ ◩ ( x ) → • ( ï¿œ ( x )) • ( ï¿œ ( x )) → ï¿œ ( • ( • ( x ))) • ( x ) → x ï¿œ ( ◩ ( x )) → ◩ ( ï¿œ ( x )) • ( ❝ ✶ ( x , y )) → ❝ ✶ ( x , ❍ ( x , y )) ❍ ( ✵ , x ) → ◩ ( x ) • ( ❍ ( ❍ ( ✵ , y ) , z )) → ❝ ✶ ( y , z ) ❝ ✷ ( x , y , z ) → ◩ ( ❍ ( y , z )) • ( ❍ ( ❍ ( ❍ ( ✵ , x ) , y ) , z )) → ❝ ✷ ( x , y , z ) ❝ ✶ ( y , z ) → ◩ ( z ) • ( ❝ ✷ ( x , y , z )) → ❝ ✷ ( x , ❍ ( x , y ) , z ) ▲♊♥❣✲❙t❛♥❞✐♥❣ ❖♣❡♥ Pr♊❜❧❡♠ s❀♊✇ t❡r♠✐♥❛t✐♊♥ ♊❢ R ❛✉t♩♠❛t✐❝❛❧❧② ❚ ❚ ❚ ✷ ❩❛♥❊❧✱ ❲✐♥❊❧❡r✱ ❛♥❞ ▌✐❞❞❡❧❞♊r♣✱ ❇❡②♊♥❞ P♊❧②♥♊♠✐❛❧s ❛♥❞ P❡❛♥♊ ❆r✐t❀♠❡t✐❝ ✕ ❆✉t♩♠❛t✐♊♥ ♊❢ ✶✌ ❊❧❡♠❡♥t❛r② ❛♥❞ ❖r❞✐♥❛❧ ■♥t❡r♣r❡t❛t✐♊♥s ✱ ✷✵✶✺✳

  90. ❝❛❧❝ ♠✉❧ s✉❜ ✶ ✜ ✶ ✜ ✶✷✜ ✜ ✶✵✵✵ ❛❧❣❡❜r❛✐❝ s✐♠♣❧✐✜❝❛t✐♊♥s ♊❢ ❡①♣r❡ss✐♊♥s✿ ♠✉❧t✐♣❧✐❝❛t✐♊♥s t♩ s❀✐❢ts✱ r❡♊r❞❡r✐♥❣ ❜✐t✇✐s❡ ♊♣❡r❛t✐♊♥s✱ ✳ ✳ ✳ ♊♣t✐♠✐③❛t✐♊♥ s❡t ✐s ❝♊♠♠✉♥✐t② ♠❛✐♥t❛✐♥❡❞✱ t❡r♠✐♥❛t✐♊♥ ✐s ❝r✉❝✐❛❧ ❈tr❧ ❝❛♥ ❞❡t❡❝t ❧♊♊♣✿ ♠✉❧ s✉❜ ✶ ✜ ✶ ✜ ♠✉❧ s✉❜ ✶ ✜ ✶ ✜ ❛❜s ✶✷✜ ✜ ✶✷✜ ✜ ■♥st❝♊♠❜✐♥❡ P❛ss ✐♥ ▲▲❱▌ ▌✐❞❞❧❡ ❊♥❞ ▲▲❱▌ ♣r♊✈✐❞❡s ✇✐❞❡❧② ✉s❡❞ ❝♊♠♣✐❧❛t✐♊♥ t♊♊❧❝❀❛✐♥ ❘❡s❡❛r❝❀ ❊①❛♠♣❧❡✿ ▲▲❱▌ ❊①♣r❡ss✐♊♥ ❙✐♠♣❧✐✜❝❛t✐♊♥ s✐♠♣❧✐✜❝❛t✐♊♥ s❡❡❊✐♥❣ ♊♣♣♊rt✉♥✐t② t♩ r❡♣❧❛❝❡ ♠✉❧ ❜② s❀✐❢t✿ ♠✉❧ s✉❜ ♠✉❧ s✉❜ ❛❜s ✐sP♊✇❡r❖❢✷ ❛❜s ✵ ✜ ❈tr❧ t♩♩❧ t♩ ❛♥❛❧②③❡ ♣r♊♣❡rt✐❡s ♊❢ ❧♊❣✐❝❛❧❧② ❝♊♥str❛✐♥❡❞ r❡✇r✐t❡ s②st❡♠s✿ ❛❧❧♩✇ r❡✇r✐t❡ r✉❧❡s ✇✐t❀ s✐❞❡ ❝♊♥❞✐t✐♊♥s ♊✈❡r ❞❡❝✐❞❛❜❧❡ ❧♊❣✐❝ ✶✜ ❑♊♣ ❛♥❞ ◆✐s❀✐❞❛✱ ❈♊♥str❛✐♥❡❞ ❚❡r♠ ❘❡✇r✐t✐♥❣ t♊♊▲ ✱ ✷✵✶✺✳

  91. ❝❛❧❝ ♠✉❧ s✉❜ ✶ ✜ ✶ ✜ ✶✷✜ ✜ ❈tr❧ ❝❛♥ ❞❡t❡❝t ❧♊♊♣✿ ♠✉❧ s✉❜ ✶ ✜ ✶ ✜ ♠✉❧ s✉❜ ✶ ✜ ✶ ✜ ❛❜s ✶✷✜ ✜ ✶✷✜ ✜ ✶✵✵✵ ❛❧❣❡❜r❛✐❝ s✐♠♣❧✐✜❝❛t✐♊♥s ♊❢ ❡①♣r❡ss✐♊♥s✿ ♠✉❧t✐♣❧✐❝❛t✐♊♥s t♩ s❀✐❢ts✱ r❡♊r❞❡r✐♥❣ ❜✐t✇✐s❡ ♊♣❡r❛t✐♊♥s✱ ✳ ✳ ✳ ♊♣t✐♠✐③❛t✐♊♥ s❡t ✐s ❝♊♠♠✉♥✐t② ♠❛✐♥t❛✐♥❡❞✱ t❡r♠✐♥❛t✐♊♥ ✐s ❝r✉❝✐❛❧ ❘❡s❡❛r❝❀ ❊①❛♠♣❧❡✿ ▲▲❱▌ ❊①♣r❡ss✐♊♥ ❙✐♠♣❧✐✜❝❛t✐♊♥ s✐♠♣❧✐✜❝❛t✐♊♥ s❡❡❊✐♥❣ ♊♣♣♊rt✉♥✐t② t♩ r❡♣❧❛❝❡ ♠✉❧ ❜② s❀✐❢t✿ ♠✉❧ s✉❜ ♠✉❧ s✉❜ ❛❜s ✐sP♊✇❡r❖❢✷ ❛❜s ✵ ✜ ❈tr❧ t♩♩❧ t♩ ❛♥❛❧②③❡ ♣r♊♣❡rt✐❡s ♊❢ ❧♊❣✐❝❛❧❧② ❝♊♥str❛✐♥❡❞ r❡✇r✐t❡ s②st❡♠s✿ ❛❧❧♩✇ r❡✇r✐t❡ r✉❧❡s ✇✐t❀ s✐❞❡ ❝♊♥❞✐t✐♊♥s ♊✈❡r ❞❡❝✐❞❛❜❧❡ ❧♊❣✐❝ ■♥st❝♊♠❜✐♥❡ P❛ss ✐♥ ▲▲❱▌ ▌✐❞❞❧❡ ❊♥❞ ▲▲❱▌ ♣r♊✈✐❞❡s ✇✐❞❡❧② ✉s❡❞ ❝♊♠♣✐❧❛t✐♊♥ t♊♊❧❝❀❛✐♥ ◮ ✶✜

  92. ❝❛❧❝ ♠✉❧ s✉❜ ✶ ✜ ✶ ✜ ✶✷✜ ✜ ❈tr❧ ❝❛♥ ❞❡t❡❝t ❧♊♊♣✿ ♠✉❧ s✉❜ ✶ ✜ ✶ ✜ ♠✉❧ s✉❜ ✶ ✜ ✶ ✜ ❛❜s ✶✷✜ ✜ ✶✷✜ ✜ ♊♣t✐♠✐③❛t✐♊♥ s❡t ✐s ❝♊♠♠✉♥✐t② ♠❛✐♥t❛✐♥❡❞✱ t❡r♠✐♥❛t✐♊♥ ✐s ❝r✉❝✐❛❧ ❘❡s❡❛r❝❀ ❊①❛♠♣❧❡✿ ▲▲❱▌ ❊①♣r❡ss✐♊♥ ❙✐♠♣❧✐✜❝❛t✐♊♥ s✐♠♣❧✐✜❝❛t✐♊♥ s❡❡❊✐♥❣ ♊♣♣♊rt✉♥✐t② t♩ r❡♣❧❛❝❡ ♠✉❧ ❜② s❀✐❢t✿ ♠✉❧ s✉❜ ♠✉❧ s✉❜ ❛❜s ✐sP♊✇❡r❖❢✷ ❛❜s ✵ ✜ ❈tr❧ t♩♩❧ t♩ ❛♥❛❧②③❡ ♣r♊♣❡rt✐❡s ♊❢ ❧♊❣✐❝❛❧❧② ❝♊♥str❛✐♥❡❞ r❡✇r✐t❡ s②st❡♠s✿ ❛❧❧♩✇ r❡✇r✐t❡ r✉❧❡s ✇✐t❀ s✐❞❡ ❝♊♥❞✐t✐♊♥s ♊✈❡r ❞❡❝✐❞❛❜❧❡ ❧♊❣✐❝ ■♥st❝♊♠❜✐♥❡ P❛ss ✐♥ ▲▲❱▌ ▌✐❞❞❧❡ ❊♥❞ ▲▲❱▌ ♣r♊✈✐❞❡s ✇✐❞❡❧② ✉s❡❞ ❝♊♠♣✐❧❛t✐♊♥ t♊♊❧❝❀❛✐♥ ◮ > ✶✵✵✵ ❛❧❣❡❜r❛✐❝ s✐♠♣❧✐✜❝❛t✐♊♥s ♊❢ ❡①♣r❡ss✐♊♥s✿ ◮ ♠✉❧t✐♣❧✐❝❛t✐♊♥s t♩ s❀✐❢ts✱ r❡♊r❞❡r✐♥❣ ❜✐t✇✐s❡ ♊♣❡r❛t✐♊♥s✱ ✳ ✳ ✳ ✶✜

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