Mail/M'écrire


ANNEXE 2

(André Brouty)
Cet exposé est sous licence libre LLDD.

PETITE SESSION MONTRANT COMMENT FONCTIONNE CET ALGORITHME

Commençons par examiner les combinateurs de base.



? (ci (i)) <—– le combinateur I 
 (I)
 (0)
  JE MONTE ---->(0)
 COMBINATEUR INVERSIBLE
 VOICI L INVERSE:
 ----> (I)
 VOULEZ-VOUS VERIFIER?
? non
= OK
; time = 319 ms. ;
? (ci (c)) <—– le combinateur C 
 (C)
 (0 2 1)
  JE MONTE ---->(0 2 1)
 COMBINATEUR INVERSIBLE
 VOICI L INVERSE:
 ----> (C)
 VOULEZ-VOUS VERIFIER?
? non
= OK
; time = 410 ms. ;
? (ci (b)) <—– le combinateur B 
 (B)
 (0 (1 2))
 = (PAS DE COMBINATEUR EN DEBUT DE LISTE)
; time =  83 ms. ;
? (ci (w)) <—– le combinateur W 
 (W)
 (0 1 1)
  JE MONTE ---->(0 1 1)
= (IL Y A UNE SUITE DE VARIABLES QUI N 'EST PAS UNE PERMUTATION)
; time = 142 ms. ;
? (ci (k)) <—– le combinateur K 
 (K)
 (0)
  JE MONTE ---->(0)
= (IL Y A UNE SUITE DE VARIABLES QUI N 'EST PAS UNE PERMUTATION)
; time =  82 ms. ;
? (ci (s)) <—– le combinateur S 
 (S)
 (0 2 (1 2))
 = (PAS DE COMBINATEUR EN DEBUT DE LISTE)
; time =  78 ms. ;
les différents déguisements de C examinés précédemment.

? (ci (b(c(c(b(b(b(b c)b))c)c)k)b)) <—– C1 
 (B (C (C (B (B (B (B C) B)) C) C) K) B)
 (C (C (B (B (B (B C) B)) C) C) K (B 0))
 (C (B (B (B (B C) B)) C) C (B 0) K)
 (B (B (B (B C) B)) C (B 0) C K)
 (B (B (B C) B) (C (B 0)) C K)
 (B (B C) B (C (B 0) C) K)
 (B C (B (C (B 0) C)) K)
 (C (B (C (B 0) C) K))
 (B (C (B 0) C) K 2 1)
 (C (B 0) C (K 2) 1)
 (B 0 (K 2) C 1)
 (0 (K 2 C) 1)
  JE DESCENDS ----> (K 2 C)
 FAUT FAIRE UNE ABSTRACTION JE M EN OCCUPE
 VOILA ----> (C K C 2)
 JE DESCENDS ----> (C K C 2)
 (K 0 C)
 (0)
  JE MONTE ---->(0)
 1
 JE MONTE ---->(0 2 (0) 1)
 COMBINATEUR INVERSIBLE
 VOICI L INVERSE:
 ----> (C)
 VOULEZ-VOUS VERIFIER?
? non
= OK
; time =   2329 ms. ;
? (ci (b(c(b(b(c(b c)c)b))c)b)) <—–C2 
 (B (C (B (B (C (B C) C) B)) C) B)
 (C (B (B (C (B C) C) B)) C (B 0))
 (B (B (C (B C) C) B) (B 0) C)
 (B (C (B C) C) B (B 0 C))
 (C (B C) C (B (B 0 C)))
 (B C (B (B 0 C)) C)
 (C (B (B 0 C) C))
 (B (B 0 C) C 2 1)
 (B 0 C (C 2) 1)
 (0 (C (C 2)) 1)
  JE DESCENDS ----> (C (C 2))
 FAUT FAIRE UNE ABSTRACTION JE M EN OCCUPE
 VOILA ----> (B C C 2)
 JE DESCENDS ----> (B C C 2)
 (C (C 0))
 (C 0 2 1)
 (0 1 2)
  JE MONTE ---->(0 1 2)
 1
 JE MONTE ---->(0 2 (0 1 2) 1)
 COMBINATEUR INVERSIBLE
 VOICI L INVERSE:
 ----> (C)
 VOULEZ-VOUS VERIFIER?
? non
= OK
; time =   2179 ms. ;
? (ci (b(c(b c)(c b i))b)) <—– C3 
 (B (C (B C) (C B I)) B)
 (C (B C) (C B I) (B 0))
 (B C (B 0) (C B I))
 (C (B 0 (C B I)))
 (B 0 (C B I) 2 1)
 (0 (C B I 2) 1)
  JE DESCENDS ----> (C B I 2)
 (B 0 I)
 (0 (I 1))
  JE DESCENDS ----> (I 1)
 (0)
  JE MONTE ---->(0)
 NIL
 JE MONTE ---->(0 1 (0))
 1
 JE MONTE ---->(0 2 (0 1 (0)) 1)
 COMBINATEUR INVERSIBLE
 VOICI L INVERSE:
 ----> (C)
 VOULEZ-VOUS VERIFIER?
? non
= OK
; time =   1781 ms. ;
? (ci (b(b(b c(c b k))(b w))b)) <—– C4 
 (B (B (B C (C B K)) (B W)) B)
 (B (B C (C B K)) (B W) (B 0))
 (B C (C B K) (B W (B 0)))
 (C (C B K (B W (B 0))))
 (C B K (B W (B 0)) 2 1)
 (B (B W (B 0)) K 2 1)
 (B W (B 0) (K 2) 1)
 (W (B 0 (K 2)) 1)
 (B 0 (K 2) 1 1)
 (0 (K 2 1) 1)
  FAUT ESSAYER DE METTRE EN FORME NORMALE
  (2)
(2)
 JE MONTE ---->(0 2 1)
 COMBINATEUR INVERSIBLE
 VOICI L INVERSE:
 ----> (C)
 VOULEZ-VOUS VERIFIER?
? non
= OK
; time =   1497 ms. ;
? (ci (c(c(b(b(b(b(b(b w)b))b)(b c))b)(c b))(k i))) <—– C5 
 (C (C (B (B (B (B (B (B W) B)) B) (B C)) B) (C B)) (K I))
 (C (B (B (B (B (B (B W) B)) B) (B C)) B) (C B) 0 (K I))
 (B (B (B (B (B (B W) B)) B) (B C)) B 0 (C B) (K I))
 (B (B (B (B (B W) B)) B) (B C) (B 0) (C B) (K I))
 (B (B (B (B W) B)) B (B C (B 0)) (C B) (K I))
 (B (B (B W) B) (B (B C (B 0))) (C B) (K I))
 (B (B W) B (B (B C (B 0)) (C B)) (K I))
 (B W (B (B (B C (B 0)) (C B))) (K I))
 (W (B (B (B C (B 0)) (C B)) (K I)))
 (B (B (B C (B 0)) (C B)) (K I) 1 1)
 (B (B C (B 0)) (C B) (K I 1) 1)
 (B C (B 0) (C B (K I 1)) 1)
 (C (B 0 (C B (K I 1))) 1)
 (B 0 (C B (K I 1)) 2 1)
 (0 (C B (K I 1) 2) 1)
  FAUT ESSAYER DE METTRE EN FORME NORMALE
  (B 2 (K I 1))
 (I)
(B 2 (I))
 JE DESCENDS ----> (B 2 (I))
 FAUT FAIRE UNE ABSTRACTION JE M EN OCCUPE
 VOILA ----> (C B (I) 2)
 JE DESCENDS ----> (C B (I) 2)
 (B 0 I)
 (0 (I 1))
  JE DESCENDS ----> (I 1)
 (0)
  JE MONTE ---->(0)
 NIL
 JE MONTE ---->(0 1 (0))
 1
 JE MONTE ---->(0 2 (0 1 (0)) 1)
 COMBINATEUR INVERSIBLE
 VOICI L INVERSE:
 ----> (C)
 VOULEZ-VOUS VERIFIER?
? oui
 VOTRE COMBINATEUR ----> (C (C (B (B (B (B (B (B W) B)) B) (B C)) B) (
C B)) (K I))
 SON INVERSE ----> (C)
 (B (C (C (B (B (B (B (B (B W) B)) B) (B C)) B) (C B)) (K I)) C)
 (C (C (B (B (B (B (B (B W) B)) B) (B C)) B) (C B)) (K I) (C 0))
 (C (B (B (B (B (B (B W) B)) B) (B C)) B) (C B) (C 0) (K I))
 (B (B (B (B (B (B W) B)) B) (B C)) B (C 0) (C B) (K I))
 (B (B (B (B (B W) B)) B) (B C) (B (C 0)) (C B) (K I))
 (B (B (B (B W) B)) B (B C (B (C 0))) (C B) (K I))
 (B (B (B W) B) (B (B C (B (C 0)))) (C B) (K I))
 (B (B W) B (B (B C (B (C 0))) (C B)) (K I))
 (B W (B (B (B C (B (C 0))) (C B))) (K I))
 (W (B (B (B C (B (C 0))) (C B)) (K I)))
 (B (B (B C (B (C 0))) (C B)) (K I) 1 1)
 (B (B C (B (C 0))) (C B) (K I 1) 1)
 (B C (B (C 0)) (C B (K I 1)) 1)
 (C (B (C 0) (C B (K I 1))) 1)
 (B (C 0) (C B (K I 1)) 2 1)
 (C 0 (C B (K I 1) 2) 1)
 (0 1 (C B (K I 1) 2))
  FAUT ESSAYER DE METTRE EN FORME NORMALE
  (B 2 (K I 1))
 (I)
(B 2 (I))
 JE DESCENDS ----> (B 2 (I))
 FAUT FAIRE UNE ABSTRACTION JE M EN OCCUPE
 VOILA ----> (C B (I) 2)
 JE DESCENDS ----> (C B (I) 2)
 (B 0 I)
 (0 (I 1))
  JE DESCENDS ----> (I 1)
 (0)
  JE MONTE ---->(0)
 NIL
 JE MONTE ---->(0 1 (0))
 NIL
 JE MONTE ---->(0 1 2 (0 1 (0)))
= (VOILA VOUS RECONNAISSEZ L 'IDENTITE)
; time =   8573 ms. ;
voici un permutateur héréditairement fini, donc inversible,avec 9 niveaux d'imbrications de sous termes.
? super3
= (C B (C B (C B (C B (C B (C B (C B (C B (C B (B C (B C)))))))))))
; time =   0 ms. ;
? (ci super3) 
 (B 0 (C B (C B (C B (C B (C B (C B (C B (C B (B C (B C)))))))))))
 (0 (C B (C B (C B (C B (C B (C B (C B (C B (B C (B C))))))))) 1))
  JE DESCENDS ----> (C B (C B (C B (C B (C B (C B (C B (C B (B C (B C)
)))))))) 1)
 (B 0 (C B (C B (C B (C B (C B (C B (C B (B C (B C))))))))))
 (0 (C B (C B (C B (C B (C B (C B (C B (B C (B C)))))))) 1))
  JE DESCENDS ----> (C B (C B (C B (C B (C B (C B (C B (B C (B C))))))
)) 1)
 (B 0 (C B (C B (C B (C B (C B (C B (B C (B C)))))))))
 (0 (C B (C B (C B (C B (C B (C B (B C (B C))))))) 1))
  JE DESCENDS ----> (C B (C B (C B (C B (C B (C B (B C (B C))))))) 1)
 (B 0 (C B (C B (C B (C B (C B (B C (B C))))))))
 (0 (C B (C B (C B (C B (C B (B C (B C)))))) 1))
  JE DESCENDS ----> (C B (C B (C B (C B (C B (B C (B C)))))) 1)
 (B 0 (C B (C B (C B (C B (B C (B C)))))))
 (0 (C B (C B (C B (C B (B C (B C))))) 1))
  JE DESCENDS ----> (C B (C B (C B (C B (B C (B C))))) 1)
 (B 0 (C B (C B (C B (B C (B C))))))
 (0 (C B (C B (C B (B C (B C)))) 1))
  JE DESCENDS ----> (C B (C B (C B (B C (B C)))) 1)
 (B 0 (C B (C B (B C (B C)))))
 (0 (C B (C B (B C (B C))) 1))
  JE DESCENDS ----> (C B (C B (B C (B C))) 1)
 (B 0 (C B (B C (B C))))
 (0 (C B (B C (B C)) 1))
  JE DESCENDS ----> (C B (B C (B C)) 1)
 (B 0 (B C (B C)))
 (0 (B C (B C) 1))
  JE DESCENDS ----> (B C (B C) 1)
 (C (B C 0))
 (B C 0 2 1)
 (C (0 2) 1)
 (0 2 3 1)
  JE MONTE ---->(0 2 3 1)
 NIL
 JE MONTE ---->(0 1 (0 2 3 1))
 NIL
 JE MONTE ---->(0 1 (0 1 (0 2 3 1)))
 NIL
 JE MONTE ---->(0 1 (0 1 (0 1 (0 2 3 1))))
 NIL
 JE MONTE ---->(0 1 (0 1 (0 1 (0 1 (0 2 3 1)))))
 NIL
 JE MONTE ---->(0 1 (0 1 (0 1 (0 1 (0 1 (0 2 3 1))))))
 NIL
 JE MONTE ---->(0 1 (0 1 (0 1 (0 1 (0 1 (0 1 (0 2 3 1)))))))
 NIL
 JE MONTE ---->(0 1 (0 1 (0 1 (0 1 (0 1 (0 1 (0 1 (0 2 3 1))))))))
 NIL
 JE MONTE ---->(0 1 (0 1 (0 1 (0 1 (0 1 (0 1 (0 1 (0 1 (0 2 3 1)))))))
))
 NIL
 JE MONTE ---->(0 1 (0 1 (0 1 (0 1 (0 1 (0 1 (0 1 (0 1 (0 1 (0 2 3 1))
))))))))
 COMBINATEUR INVERSIBLE
 VOICI L INVERSE:
 ----> (C B (C B (C B (C B (C B (C B (C B (C B (C B (B (B C) C))))))))
))
 VOULEZ-VOUS VERIFIER?
? non
= OK
; time =  16457 ms. ;
un autre exemple intéressant 
? super4
= (C (B (B C) B) (C (C (B (B (B B C)) B) (C B (B C (B C)))) C))
; time =   0 ms. ;
? (ci super4) 
 (B (B C) B 0 (C (C (B (B (B B C)) B) (C B (B C (B C)))) C))
 (B C (B 0) (C (C (B (B (B B C)) B) (C B (B C (B C)))) C))
 (C (B 0 (C (C (B (B (B B C)) B) (C B (B C (B C)))) C)))
 (B 0 (C (C (B (B (B B C)) B) (C B (B C (B C)))) C) 2 1)
 (0 (C (C (B (B (B B C)) B) (C B (B C (B C)))) C 2) 1)
  JE DESCENDS ----> (C (C (B (B (B B C)) B) (C B (B C (B C)))) C 2)
 (C (B (B (B B C)) B) (C B (B C (B C))) 0 C)
 (B (B (B B C)) B 0 (C B (B C (B C))) C)
 (B (B B C) (B 0) (C B (B C (B C))) C)
 (B B C (B 0 (C B (B C (B C)))) C)
 (B (C (B 0 (C B (B C (B C))))) C)
 (C (B 0 (C B (B C (B C)))) (C 1))
 (B 0 (C B (B C (B C))) 2 (C 1))
 (0 (C B (B C (B C)) 2) (C 1))
  JE DESCENDS ----> (C B (B C (B C)) 2)
 (B 0 (B C (B C)))
 (0 (B C (B C) 1))
  JE DESCENDS ----> (B C (B C) 1)
 (C (B C 0))
 (B C 0 2 1)
 (C (0 2) 1)
 (0 2 3 1)
  JE MONTE ---->(0 2 3 1)
 NIL
 JE MONTE ---->(0 1 (0 2 3 1))
 (C 1)
 JE DESCENDS ----> (C 1)
 (0 2 1)
  JE MONTE ---->(0 2 1)
 NIL
 JE MONTE ---->(0 2 (0 1 (0 2 3 1)) 1 (0 2 1))
 1
 JE MONTE ---->(0 2 (0 2 (0 1 (0 2 3 1)) 1 (0 2 1)) 1)
 COMBINATEUR INVERSIBLE
 VOICI L INVERSE:
 ----> (C (B B C) (C (C (B (B (B B C)) B) C) (C B (B (B C) C))))
 VOULEZ-VOUS VERIFIER?
? oui
 VOTRE COMBINATEUR ----> (C (B (B C) B) (C (C (B (B (B B C)) B) (C B (
B C (B C)))) C))
 SON INVERSE ----> (C (B B C) (C (C (B (B (B B C)) B) C) (C B (B (B C)
C))))
 (B (C (B (B C) B) (C (C (B (B (B B C)) B) (C B (B C (B C)))) C)) (C (
B B C) (C (C (B (B (B B C)) B) C) (C B (B (B C) C)))))
 (C (B (B C) B) (C (C (B (B (B B C)) B) (C B (B C (B C)))) C) (C (B B
C) (C (C (B (B (B B C)) B) C) (C B (B (B C) C))) 0))
 (B (B C) B (C (B B C) (C (C (B (B (B B C)) B) C) (C B (B (B C) C))) 0
) (C (C (B (B (B B C)) B) (C B (B C (B C)))) C))
 (B C (B (C (B B C) (C (C (B (B (B B C)) B) C) (C B (B (B C) C))) 0))
(C (C (B (B (B B C)) B) (C B (B C (B C)))) C))
 (C (B (C (B B C) (C (C (B (B (B B C)) B) C) (C B (B (B C) C))) 0) (C
(C (B (B (B B C)) B) (C B (B C (B C)))) C)))
 (B (C (B B C) (C (C (B (B (B B C)) B) C) (C B (B (B C) C))) 0) (C (C
(B (B (B B C)) B) (C B (B C (B C)))) C) 2 1)
 (C (B B C) (C (C (B (B (B B C)) B) C) (C B (B (B C) C))) 0 (C (C (B (
B (B B C)) B) (C B (B C (B C)))) C 2) 1)
 (B B C 0 (C (C (B (B (B B C)) B) C) (C B (B (B C) C))) (C (C (B (B (B
B C)) B) (C B (B C (B C)))) C 2) 1)
 (B (C 0) (C (C (B (B (B B C)) B) C) (C B (B (B C) C))) (C (C (B (B (B
B C)) B) (C B (B C (B C)))) C 2) 1)
 (C 0 (C (C (B (B (B B C)) B) C) (C B (B (B C) C)) (C (C (B (B (B B C)
) B) (C B (B C (B C)))) C 2)) 1)
 (0 1 (C (C (B (B (B B C)) B) C) (C B (B (B C) C)) (C (C (B (B (B B C)
) B) (C B (B C (B C)))) C 2)))
  JE DESCENDS ----> (C (C (B (B (B B C)) B) C) (C B (B (B C) C)) (C (C
(B (B (B B C)) B) (C B (B C (B C)))) C 2))
 FAUT FAIRE UNE ABSTRACTION JE M EN OCCUPE
 VOILA ----> (B (C (C (B (B (B B C)) B) C) (C B (B (B C) C))) (C (C (B
(B (B B C)) B) (C B (B C (B C)))) C) 2)
 JE DESCENDS ----> (B (C (C (B (B (B B C)) B) C) (C B (B (B C) C))) (C
(C (B (B (B B C)) B) (C B (B C (B C)))) C) 2)
 (C (C (B (B (B B C)) B) C) (C B (B (B C) C)) (C (C (B (B (B B C)) B)
(C B (B C (B C)))) C 0))
 (C (B (B (B B C)) B) C (C (C (B (B (B B C)) B) (C B (B C (B C)))) C 0
) (C B (B (B C) C)))
 (B (B (B B C)) B (C (C (B (B (B B C)) B) (C B (B C (B C)))) C 0) C (C
B (B (B C) C)))
 (B (B B C) (B (C (C (B (B (B B C)) B) (C B (B C (B C)))) C 0)) C (C B
(B (B C) C)))
 (B B C (B (C (C (B (B (B B C)) B) (C B (B C (B C)))) C 0) C) (C B (B
(B C) C)))

 (B (C (B (C (C (B (B (B B C)) B) (C B (B C (B C)))) C 0) C)) (C B (B
(B C) C)))
 (C (B (C (C (B (B (B B C)) B) (C B (B C (B C)))) C 0) C) (C B (B (B C
) C) 1))
 (B (C (C (B (B (B B C)) B) (C B (B C (B C)))) C 0) C 2 (C B (B (B C)
C) 1))
 (C (C (B (B (B B C)) B) (C B (B C (B C)))) C 0 (C 2) (C B (B (B C) C)
1))
 (C (B (B (B B C)) B) (C B (B C (B C))) 0 C (C 2) (C B (B (B C) C) 1))
 (B (B (B B C)) B 0 (C B (B C (B C))) C (C 2) (C B (B (B C) C) 1))
 (B (B B C) (B 0) (C B (B C (B C))) C (C 2) (C B (B (B C) C) 1))
 (B B C (B 0 (C B (B C (B C)))) C (C 2) (C B (B (B C) C) 1))
 (B (C (B 0 (C B (B C (B C))))) C (C 2) (C B (B (B C) C) 1))
 (C (B 0 (C B (B C (B C)))) (C (C 2)) (C B (B (B C) C) 1))
 (B 0 (C B (B C (B C))) (C B (B (B C) C) 1) (C (C 2)))
 (0 (C B (B C (B C)) (C B (B (B C) C) 1)) (C (C 2)))
  JE DESCENDS ----> (C B (B C (B C)) (C B (B (B C) C) 1))
 FAUT FAIRE UNE ABSTRACTION JE M EN OCCUPE
 VOILA ----> (B (C B (B C (B C))) (C B (B (B C) C)) 1)
 JE DESCENDS ----> (B (C B (B C (B C))) (C B (B (B C) C)) 1)
 (C B (B C (B C)) (C B (B (B C) C) 0))
 (B (C B (B (B C) C) 0) (B C (B C)))
 (C B (B (B C) C) 0 (B C (B C) 1))
 (B 0 (B (B C) C) (B C (B C) 1))
 (0 (B (B C) C (B C (B C) 1)))
  JE DESCENDS ----> (B (B C) C (B C (B C) 1))
 FAUT FAIRE UNE ABSTRACTION JE M EN OCCUPE
 VOILA ----> (B (B (B C) C) (B C (B C)) 1)
 JE DESCENDS ----> (B (B (B C) C) (B C (B C)) 1)
 (B (B C) C (B C (B C) 0))
 (B C (C (B C (B C) 0)))
 (C (C (B C (B C) 0) 1))
 (C (B C (B C) 0) 1 3 2)
 (B C (B C) 0 3 1 2)
 (C (B C 0) 3 1 2)
 (B C 0 1 3 2)
 (C (0 1) 3 2)
 (0 1 2 3)
  JE MONTE ---->(0 1 2 3)
 NIL
 JE MONTE ---->(0 1 (0 1 2 3))
 (C (C 2))
 JE DESCENDS ----> (C (C 2))
 FAUT FAIRE UNE ABSTRACTION JE M EN OCCUPE
 VOILA ----> (B C C 2)
 JE DESCENDS ----> (B C C 2)
 (C (C 0))
 (C 0 2 1)
 (0 1 2)
  JE MONTE ---->(0 1 2)
 NIL
 JE MONTE ---->(0 1 (0 1 (0 1 2 3)) 2 (0 1 2))
 NIL
 JE MONTE ---->(0 1 2 (0 1 (0 1 (0 1 2 3)) 2 (0 1 2)))
= (VOILA VOUS RECONNAISSEZ L 'IDENTITE)
; time =  25286 ms. ;
voici deux combinateurs sans forme normale qui ne font pas boucler l'algorithme.

? (ci (c(b c(c i))(w w w))) 
 (C (B C (C I)) (W W W))
 (B C (C I) 0 (W W W))
 (C (C I 0) (W W W))
 (C I 0 1 (W W W))
 (I 1 0 (W W W))
 (1 0 (W W W))
= (PAS REGULIER)
; time = 459 ms. ;
? (ci (c c(w w w))) 
 (C C (W W W))
 (C 0 (W W W))
 (0 1 (W W W))
 = (PAS DE VARIABLE DANS UN SOUS TERME)
; time = 221 ms. ;
en voici un sans forme normale qui le fait boucler.

? (ci (c(b c(b b))(w w w))) 
 (C (B C (B B)) (W W W))
 (B C (B B) 0 (W W W))
 (C (B B 0) (W W W))
 (B B 0 1 (W W W))
 (B (0 1) (W W W))
 (0 1 (W W W 2))
  JE DESCENDS ----> (W W W 2)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
 (W W W)
voici pour terminer et arrêter le suspens introduit au début de ce chapitre le premier exemple présenté.

? (ci (b(b(c b c)(b(c(b(b(c(b b c)c))b)c)))c)) 
 (B (B (C B C) (B (C (B (B (C (B B C) C)) B) C))) C)
 (B (C B C) (B (C (B (B (C (B B C) C)) B) C)) (C 0))
 (C B C (B (C (B (B (C (B B C) C)) B) C) (C 0)))
 (B (B (C (B (B (C (B B C) C)) B) C) (C 0)) C)
 (B (C (B (B (C (B B C) C)) B) C) (C 0) (C 1))
 (C (B (B (C (B B C) C)) B) C (C 0 (C 1)))
 (B (B (C (B B C) C)) B (C 0 (C 1)) C)
 (B (C (B B C) C) (B (C 0 (C 1))) C)
 (C (B B C) C (B (C 0 (C 1)) C))
 (B B C (B (C 0 (C 1)) C) C)
 (B (C (B (C 0 (C 1)) C)) C)
 (C (B (C 0 (C 1)) C) (C 2))
 (B (C 0 (C 1)) C 3 (C 2))
 (C 0 (C 1) (C 3) (C 2))
 (0 (C 3) (C 1) (C 2))
  JE DESCENDS ----> (C 3)
 (0 2 1)
  JE MONTE ---->(0 2 1)
 (C 1)
 JE DESCENDS ----> (C 1)
 (0 2 1)
  JE MONTE ---->(0 2 1)
 (C 2)
 JE DESCENDS ----> (C 2)
 (0 2 1)
  JE MONTE ---->(0 2 1)
 NIL
 JE MONTE ---->(0 3 (0 2 1) 1 (0 2 1) 2 (0 2 1))
 COMBINATEUR INVERSIBLE
 VOICI L INVERSE:
 ----> (C (C (C (B (B (B (B (B (B B C)) C)) B) (B (B (B C) B))) C) C)
C)
 VOULEZ-VOUS VERIFIER?
? non
= OK

Annexe3: topoligie non séparée