Table of Contents

1  Texte d'oral de modélisation - Agrégation Option Informatique

1.1  Préparation à l'agrégation - ENS de Rennes, 2016-17

1.2  À propos de ce document

1.3  Question de programmation

1.4  Réponse à l'exercice requis

1.4.1  Structures de données

1.4.2  Arithmétiques sur nos entiers étendus

1.4.2.1  Max/min

1.4.2.2  Somme/produit

1.4.3  Opérations de base, $\oplus$ et $\otimes$

1.4.3.1  Intersection

1.4.3.2  Composition

1.4.3.3  Union

1.4.3.4  Exemples

1.4.3.5  Une étape de plus : ne pas inclure des intervalles inclus dans ceux déjà présents

1.4.4  L'algorithme PC

1.4.4.1  Structure de données pour les réseaux STP

1.4.4.2  L'algorithme PC

1.4.5  Exemple de réseau non distributif

1.4.6  D'autres exemples

1.5  Conclusion

Texte d'oral de modélisation - Agrégation Option Informatique

Préparation à l'agrégation - ENS de Rennes, 2016-17

• Date : 7 avril 2017
• Auteur : Lilian Besson
• Texte: Annale 2009, "Contraintes temporelles"

À propos de ce document

• Ceci est une proposition de correction, partielle et probablement non-optimale, pour la partie implémentation d'un texte d'annale de l'agrégation de mathématiques, option informatique.
• Ce document est un notebook Jupyter, et est open-source sous Licence MIT sur GitHub, comme les autres solutions de textes de modélisation que j'ai écrite cette année.
• L'implémentation sera faite en OCaml, version 4+ :

Sys.command "ocaml -version";;

The OCaml toplevel, version 4.04.2

- : int = 0

Notez que certaines fonctions des modules usuels List et Array ne sont pas disponibles en OCaml 3.12. J'essaie autant que possible de ne pas les utiliser, ou alors de les redéfinir si je m'en sers.

---

Question de programmation

La question de programmation pour ce texte était donnée en question 1 en page 9 :

"Programmer l'algorithme PC. Faites le tourner sur l'exemple de réseau non distributif."

La consigne était très courte, mais avec aucune indication. Notez qu'il est rare que le texte exige un exemple particulier.

---

Réponse à l'exercice requis

Ça va être assez long, en fait...

1. D'abord, il faut définir les types de données avec lesquels on va travailler,
2. Ensuite, implémenter les deux opérations $\oplus$ et $\otimes$ sur les ensembles d'intervalles,
3. Puis implémenter l'algorithme PC (similaire à Floyd-Warshall),
4. Et enfin, l'exécuter sur l'exemple de réseau non distributif donné en page 8.

Si possible, on va essayer de faire des tests pour chaque fonction intermédiaire, et un exemple de plus à la fin.

Un des problèmes que l'on va rencontrer est le fait que l'on doit manipuler $-\infty$ et $+\infty$, pour pouvoir gérer une contrainte qui n'est pas une contrainte, à savoir l'interavalle $(-\infty, +\infty)$.

---

Structures de données

On va travailler avec des valeurs entières ou $\pm\infty$. En écrivant nous même les opérations arithmétiques ($+,max$) sur les entiers "étendus" on obtiendra ce qu'on veut.

type entier_etendu = MInf | PInf | E of int;;

type entier_etendu = MInf | PInf | E of int

On se restreint aux intervalles à coordonnées entières, et on considère des listes d'intervalles. Tous les intervalles sont fermés à gauche et à droite.

type intervalle = (entier_etendu * entier_etendu);;  (* (a, b) représente l'intervalle [a, b] *)

type intervalle = entier_etendu * entier_etendu

type intervalles = intervalle list;;

type intervalles = intervalle list

On définit tout de suite deux exemples, $T_a$ et $S_a$ tirés de la Figure 2.a) et $T_b,S_b$ de la Figure 2.b). Cela permettra de vérifier les opérations $\oplus$ et $\otimes$.

• $T_a = \{ [1, 4], [6, 8] \}$ et $S_a = \{ [0, 1], [3, 5], [6, 7] \}$.

let t_a : intervalles = [
    (E(1), E(4));
    (E(6), E(8))
];;

let s_a : intervalles = [
    (E(0), E(1));
    (E(3), E(5));
    (E(6), E(7))
];;

val t_a : intervalles = [(E 1, E 4); (E 6, E 8)]

val s_a : intervalles = [(E 0, E 1); (E 3, E 5); (E 6, E 7)]

• $T_b = \{ [-1, 0], [2, 4] \}$ et $S_b = \{ [0, 1], [4, 4] \}$.

let t_b : intervalles = [
    (E(-1), E(0));
    (E(2), E(4))
];;

let s_b : intervalles = [
    (E(0), E(1));
    (E(4), E(4))  (* Intervalle de longueur nulle *)
];;

val t_b : intervalles = [(E (-1), E 0); (E 2, E 4)]

val s_b : intervalles = [(E 0, E 1); (E 4, E 4)]

• Et la contrainte vide, $T = \{[-\infty, +\infty\}$ :

let t_vide : intervalles = [
    (MInf, PInf)
];;

val t_vide : intervalles = [(MInf, PInf)]

---

Arithmétiques sur nos entiers étendus

Max/min

let max_ee x y =
    match x, y with
    | MInf, _ -> y
    | PInf, _ -> PInf
    | _, MInf -> x
    | _, PInf -> PInf
    | E(vx), E(vy) -> E(max vx vy)
;;

val max_ee : entier_etendu -> entier_etendu -> entier_etendu = <fun>

max_ee MInf (E(10));;
max_ee PInf (E(10));;
max_ee (E(10)) MInf;;
max_ee (E(10)) PInf;;
max_ee (E(-10)) (E(10));;
max_ee (E(10)) (E(-10));;

- : entier_etendu = E 10

- : entier_etendu = PInf

- : entier_etendu = E 10

- : entier_etendu = PInf

- : entier_etendu = E 10

- : entier_etendu = E 10

let min_ee x y =
    match x, y with
    | PInf, _ -> y
    | MInf, _ -> MInf
    | _, PInf -> x
    | _, MInf -> MInf
    | E(vx), E(vy) -> E(min vx vy)
;;

val min_ee : entier_etendu -> entier_etendu -> entier_etendu = <fun>

min_ee MInf (E(10));;
min_ee PInf (E(10));;
min_ee (E(10)) MInf;;
min_ee (E(10)) PInf;;
min_ee (E(-10)) (E(10));;
min_ee (E(10)) (E(-10));;

- : entier_etendu = MInf

- : entier_etendu = E 10

- : entier_etendu = MInf

- : entier_etendu = E 10

- : entier_etendu = E (-10)

- : entier_etendu = E (-10)

On peut utiliser la fonction minimum pour trier deux entiers étendus :

let pluspetiteq_ee x y =
    let m = min_ee x y in
    m = x || x = y
;;

val pluspetiteq_ee : entier_etendu -> entier_etendu -> bool = <fun>

let pluspetit_ee x y =
    let m = min_ee x y in
    m = x && x != y
;;

val pluspetit_ee : entier_etendu -> entier_etendu -> bool = <fun>

Somme/produit

let plus_ee x y =
    match x, y with
    | MInf, PInf -> failwith "-inf + +inf = ?"
    | PInf, MInf -> failwith "-inf + +inf = ?"
    | PInf, _ -> PInf
    | MInf, _ -> MInf
    | _, MInf -> MInf
    | _, PInf -> PInf
    | E(vx), E(vy) -> E(vx + vy)
;;

val plus_ee : entier_etendu -> entier_etendu -> entier_etendu = <fun>

plus_ee MInf (E(10));;
plus_ee PInf (E(10));;
plus_ee (E(10)) MInf;;
plus_ee (E(10)) PInf;;
plus_ee (E(-10)) (E(10));;
plus_ee (E(10)) (E(-10));;
plus_ee (E(10)) (E(10));;
plus_ee (E(-10)) (E(-10));;

- : entier_etendu = MInf

- : entier_etendu = PInf

- : entier_etendu = MInf

- : entier_etendu = PInf

- : entier_etendu = E 0

- : entier_etendu = E 0

- : entier_etendu = E 20

- : entier_etendu = E (-20)

let produit_ee x y =
    match x, y with
    | MInf, PInf -> MInf
    | PInf, MInf -> PInf
    | PInf, E(vy) when vy < 0 -> MInf
    | PInf, _ -> PInf
    | MInf, E(vy) when vy < 0 -> PInf
    | MInf, _ -> MInf
    | E(vx), PInf when vx < 0 -> MInf
    | _, PInf -> PInf
    | E(vx), MInf when vx < 0 -> PInf
    | _, MInf -> MInf
    | E(vx), E(vy) -> E(vx * vy)
;;

val produit_ee : entier_etendu -> entier_etendu -> entier_etendu = <fun>

produit_ee MInf (E(10));;
produit_ee PInf (E(10));;
produit_ee (E(10)) MInf;;
produit_ee (E(10)) PInf;;
produit_ee (E(-10)) (E(10));;
produit_ee (E(10)) (E(-10));;
produit_ee (E(10)) (E(10));;
produit_ee (E(-10)) (E(-10));;

- : entier_etendu = MInf

- : entier_etendu = PInf

- : entier_etendu = MInf

- : entier_etendu = PInf

- : entier_etendu = E (-100)

- : entier_etendu = E (-100)

- : entier_etendu = E 100

- : entier_etendu = E 100

---

Opérations de base, $\oplus$ et $\otimes$

On peut écrire des opérations d'intersection et de composition sur deux intervalles, ensuite il suffira de les généraliser à un ensemble d'intervalle.

On suit les définitions de l'énoncé.

Intersection

$$ \forall T = (I_1,\dots,I_l), \forall S = (J_1,\dots,J_m),\\ T \oplus S := \{ K_1, \dots, K_n\} \;\;\text{Où}\;\; K_k = I_i \cap J_j. $$

Notez que $n \leq l + m$ ici.

Pour l'intersection de deux intervalles, l'intervalle vide $\emptyset$ peut être obtenu, donc la fonction suivante renvoie un type intervalle option : soit None si $I \cap J = \emptyset$, soit Some (x, y) si $I \cap J = [x, y]$.

let intersection (i : intervalle) (j : intervalle) : intervalle option =
    let a = fst i and b = snd i in
    let c = fst j and d = snd j in
    if pluspetit_ee b c || pluspetit_ee d a then
        None
    else
        Some (max_ee a c, min_ee b d)
;;

val intersection : intervalle -> intervalle -> intervalle option = <fun>

Ensuite, il suffit d'explorer tous les couples $(I, J)$ possible, et de ne garder que ceux qui donnent un intervalle. On supprimera les doublons en vérifiant au fur et à mesure (ça a la même complexité que si on le fait à la fin).

En manipulant une liste d'intervalle option, on doit ruser un peu pour n'ajouter que ceux qui ne sont pas dans acc et qui sont des vrais intervalles.

let ajoute_nouveaux_option (acc : intervalles) (liste_option : intervalle option list) =
    List.map
    (fun i -> match i with Some i2 -> i2 | None -> (MInf, PInf))
    (List.filter (fun i ->
        match i with
        | None -> false
        | Some i2 -> not (List.mem i2 acc)
    ) liste_option)
;;

val ajoute_nouveaux_option :
  intervalles -> intervalle option list -> intervalle list = <fun>

Avec tout ça, on a une belle fonction récursive, avec un accumulateur acc qui contient la liste des intervalles dans $T \oplus S$, construite en considérant les intervalles de $S$ les un après les autres.

On s'assure de n'avoir ni intervalles vide, ni doublon, grâce à ajoute_nouveaux_option.

let intersections (t : intervalles) (s : intervalles) : intervalles =
    let rec inter_aux acc tx sx =
        match sx with
        | [] -> acc    (* Plus rien à ajouter *)
        | j :: s2 ->   (* On traite j, puis récursivement la suite de s *)
            let t_inter_j = List.map (intersection j) tx in
            inter_aux ((ajoute_nouveaux_option acc t_inter_j) @ acc) tx s2
    in
    List.sort compare (inter_aux [] t s)
    (* On trie pour les avoir en ordre croissant, c'est tout *)
;;

val intersections : intervalles -> intervalles -> intervalles = <fun>

Pour frimer un peu et simplifier l'écriture de l'algorithme PC, on peut définir une opération infixe en raccourci : $$ T \oplus S = \texttt{t ++ s}.$$

let ( ++ ) = intersections;;

val ( ++ ) : intervalles -> intervalles -> intervalles = <fun>

Composition

Ce sera plus facile. $$ \forall T = (I_1,\dots,I_l), \forall S = (J_1,\dots,J_m),\\ T \otimes S := \{ K_1, \dots, K_n\} \;\;\text{Où}\;\; K_k = [a + c, b + d], \;\text{si}\; I_i = [a, b], J_j = [c, d]. $$ Notez que $n \leq l \times m$ ici.

Pour la composition de deux intervalles, il n'y pas de difficulté particulière :

let composition (i : intervalle) (j : intervalle) : intervalle =
    let a = fst i and b = snd i in
    let c = fst j and d = snd j in
    (* (a + c, b + d) *)
    ((plus_ee a c), (plus_ee d b))
;;

val composition : intervalle -> intervalle -> intervalle = <fun>

Et on les combine facilement, en gardant la même architecture que pour intersections.

let ajoute_nouveaux (acc : intervalles) (liste : intervalles) : intervalles =
    List.filter (fun i -> not (List.mem i acc)) liste
;;

val ajoute_nouveaux : intervalles -> intervalles -> intervalles = <fun>

let compositions (t : intervalles) (s : intervalles) : intervalles =
    let rec compo_aux acc tx sx =
        match sx with
        | [] -> acc    (* Plus rien à ajouter *)
        | j :: s2 ->   (* On traite j, puis récursivement la suite de s *)
            let t_compo_j = List.map (composition j) tx in
            compo_aux ((ajoute_nouveaux acc t_compo_j) @ acc) tx s2
    in
    List.sort compare (compo_aux [] t s)
    (* On trie pour les avoir en ordre croissant, c'est tout *)
;;

val compositions : intervalles -> intervalles -> intervalles = <fun>

Pour frimer un peu et simplifier l'écriture de l'algorithme PC, on peut définir une opération infixe en raccourci : $$ T \otimes S = \texttt{t ** s}.$$

let ( ** ) = compositions;;

val ( ** ) : intervalles -> intervalles -> intervalles = <fun>

Union

On peut aussi rapidement définier $T \cup S$, pour l'union. C'est très facile.

let union (t : intervalles) (s : intervalles) : intervalles =
    List.append t s
;;

val union : intervalles -> intervalles -> intervalles = <fun>

Exemples

On aimerait reproduire les exemples de la Figure 2 du texte.

• Pour les deux intervalles de la Figure 2.a) : $T_a = \{ [1, 4], [6, 8] \}$ et $S_a = \{ [0, 1], [3, 5], [6, 7] \}$.

t_a ++ s_a;;

- : intervalles = [(E 3, E 4); (E 6, E 7)]

On retrouve bien le résultat de la Figure 2.a).

t_a ** s_a;;
union t_a s_a;;

- : intervalles =
[(E 1, E 5); (E 4, E 9); (E 6, E 9); (E 7, E 11); (E 9, E 13); (E 12, E 15)]

- : intervalles =
[(E 1, E 4); (E 6, E 8); (E 0, E 1); (E 3, E 5); (E 6, E 7)]

• Pour les deux intervalles de la Figure 2.b) : $T_b = \{ [-1, 0], [2, 4] \}$ et $S_b = \{ [0, 1], [4, 4] \}$.

t_b ** s_b;;

- : intervalles = [(E (-1), E 1); (E 2, E 5); (E 3, E 4); (E 6, E 8)]

On retrouve bien le résultat de la Figure 2.b).

L'intervalle $[3, 4]$ est inclus dans $[2, 5]$, donc on devrait ajouter une étape de nettoyage pour donner une forme canonique aux intervalles produit par composition. On le fait plus bas.

t_b;;
s_b;;

- : intervalles = [(E (-1), E 0); (E 2, E 4)]

- : intervalles = [(E 0, E 1); (E 4, E 4)]

t_b ++ s_b;;
union t_b s_b;;

- : intervalles = []

- : intervalles = [(E (-1), E 0); (E 2, E 4); (E 0, E 1); (E 4, E 4)]

On remarque que les intervalles sont bien donnés dans l'ordre croissant, puisqu'on a pensé à trier la sortie des deux fonctions, mais ça ne change rien.

Une étape de plus : ne pas inclure des intervalles inclus dans ceux déjà présents

On va raffiner les fonctions définis ci-dessus en ajoutant un test, sur leur résultat final.

• est_inclus i j teste si $I \subseteq J$.

let est_inclus (i : intervalle) (j : intervalle) : bool =
    let a = fst i and b = snd i in
    let c = fst j and d = snd j in
    (* on peut aussi écrire directement
    let a, b = i and c, d = j in
    pour extraire les valeurs d'un coupe i=(a,b) et j=(c,d)
    *)
    (* c <= a && b <= d *)
    (pluspetiteq_ee c a) && (pluspetiteq_ee b d)
;;

val est_inclus : intervalle -> intervalle -> bool = <fun>

est_inclus (E(3), E(4)) (E(2), E(5));; (* true *)
est_inclus (E(2), E(5)) (E(3), E(4));; (* false *)
est_inclus (E(1), E(1)) (E(1), E(1));; (* true *)

- : bool = true

- : bool = false

- : bool = true

• est_inclus_dans_un i acc teste si $I \subseteq J$ pour un $J \neq I \in \mathrm{Acc}$.

let est_inclus_dans_un (i : intervalle) (acc : intervalles) : bool =
    List.exists (fun j -> (i != j) && (est_inclus i j)) acc
;;

val est_inclus_dans_un : intervalle -> intervalles -> bool = <fun>

• On peut écrire une fonction filtre qui retire les intervalles inclus dans d'autres, puis retire les doublons.

let retire_les_inclus (liste : intervalles) : intervalles =
    List.filter (fun i -> not (est_inclus_dans_un i liste)) liste
;;

let retire_les_doublons (liste : intervalles) : intervalles =
    let reponse = ref [] in
    List.iter (fun i ->
        if not (List.mem i !reponse) then
        reponse := i :: !reponse
    ) liste;
    !reponse
;;

let filtre liste =
    retire_les_doublons (retire_les_inclus liste)
;;

val retire_les_inclus : intervalles -> intervalles = <fun>

val retire_les_doublons : intervalles -> intervalles = <fun>

val filtre : intervalles -> intervalles = <fun>

• L'intersection ne devrait pas être impactée.

let intersections2 (t : intervalles) (s : intervalles) : intervalles =
    List.sort compare (filtre (intersections t s))
    (* On trie pour les avoir en ordre croissant, c'est tout *)
;;

val intersections2 : intervalles -> intervalles -> intervalles = <fun>

let ( ++ ) = intersections2;;

t_a ++ s_a;;

val ( ++ ) : intervalles -> intervalles -> intervalles = <fun>

- : intervalles = [(E 3, E 4); (E 6, E 7)]

• Mais la composition va donner la bonne réponse désormais pour l'exemple de la figure 2.b).

let compositions2 (t : intervalles) (s : intervalles) : intervalles =
    List.sort compare (filtre (compositions t s))
    (* On trie pour les avoir en ordre croissant, c'est tout *)
;;

val compositions2 : intervalles -> intervalles -> intervalles = <fun>

let ( ** ) = compositions2;;

t_b ** s_b;;

val ( ** ) : intervalles -> intervalles -> intervalles = <fun>

- : intervalles = [(E (-1), E 1); (E 2, E 5); (E 6, E 8)]

C'était un peu long, mais c'est propre au moins.

Notez que pour obtenir une vraie forme canonique, il faudrait aussi rassembler les intervalles consécutifs ($\{ [0, 1], [1, 2] \} \rightarrow \{ [0, 1] \}$) et se recoupant ($\{ [0, 3], [2, 4] \} \rightarrow \{ [0, 4] \}$).

Ça prendrait trop de temps. Et ce n'était pas exigé.

---

L'algorithme PC

Structure de données pour les réseaux STP

On a besoin désormais de considérer des réseaux STP, qui sont des graphes dont les sommets sont des entiers, et dont les arêtes sont étiquetées par des listes (non vides) d'intervalles.

L'algorithme PC demande de pouvoir accéder rapidement et facilement à l'arête entre deux sommets $x,y$, $T_{x,y}$. Ainsi, la structure de matrice d'adjacence semble appropriée. Les arêtes inexistantes dans le réseau auront simplement $T_{x,y} = \emptyset$, c'est-à-dire [] (liste vide).

On supposera que toutes les matrices données aux différentes fonctions définies plus bas sont carrées, on ne le vérifie pas (mais ce serait facile).

type sommet = int;;
type arete = intervalles;; (* c'est l'idée *)

type reseauSTP = intervalles array array;;

type sommet = int

type arete = intervalles

type reseauSTP = intervalles array array

On essaie tout de suite notre structure de données avec l'exemple du réseau STP de la figure 4 :

let t_01 : intervalles = [(E(0), E(1)); (E(10), E(20))];;
let t_12 : intervalles = [(E(0), E(10))];;
let t_13 : intervalles = [(E(25), E(50))];;
let t_23 : intervalles = [(E(0), E(20)); (E(40), E(40))];;

let t_vide = [(MInf, PInf)];;

let stp_4 : reseauSTP = [|
    [| t_vide; t_01;   t_vide; t_vide |];
    [| t_vide; t_vide; t_12;   t_13 |];
    [| t_vide; t_vide; t_vide; t_23 |];
    [| t_vide; t_vide; t_vide; t_vide |];
|];;

val t_01 : intervalles = [(E 0, E 1); (E 10, E 20)]

val t_12 : intervalles = [(E 0, E 10)]

val t_13 : intervalles = [(E 25, E 50)]

val t_23 : intervalles = [(E 0, E 20); (E 40, E 40)]

val t_vide : (entier_etendu * entier_etendu) list = [(MInf, PInf)]

val stp_4 : reseauSTP =
  [|[|[(MInf, PInf)]; [(E 0, E 1); (E 10, E 20)]; [(MInf, PInf)];
      [(MInf, PInf)]|];
    [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 10)]; [(E 25, E 50)]|];
    [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
      [(E 0, E 20); (E 40, E 40)]|];
    [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]|]|]

On peut vérifier qu'il n'est pas distributif, en prenant l'exemple du texte (fin page 8) :

let s_13 = t_12 ** t_23;;

t_13 ++ s_13;;
t_01 ** (t_13 ++ s_13);;  (* 1er cas *)

t_01 ** t_13;;
t_01 ** s_13;;
(t_01 ** t_13) ++ (t_01 ** s_13);; (* 2nd cas *)

val s_13 : intervalles = [(E 0, E 30); (E 40, E 50)]

- : intervalles = [(E 25, E 30); (E 40, E 50)]

- : intervalles = [(E 25, E 31); (E 35, E 50); (E 40, E 51); (E 50, E 70)]

- : intervalles = [(E 25, E 51); (E 35, E 70)]

- : intervalles = [(E 0, E 31); (E 10, E 50); (E 40, E 51); (E 50, E 70)]

- : intervalles = [(E 25, E 50); (E 50, E 70)]

En simplifiant, on obtient :

• $T_{01} \otimes (T_{13} \oplus S_{13} = \{ [25, 31], [35, 70] \}$,
• $(T_{01} \otimes T_{13}) \oplus (T_{01} \otimes S_{13}) = \{ [25, 70] \}$,

qui sont bien différents.

Enfin, on peut rapidement vérifier si la matrice d'un graphe est bien carrée :

let est_carree matrice =
    let n = Array.length matrice in
    Array.fold_left (fun b x -> b && (n = (Array.length x))) true matrice
;;

val est_carree : 'a array array -> bool = <fun>

est_carree stp_4;;

- : bool = true

L'algorithme PC

Ça semble être un bon choix. Maintenant, passons à l'algorithme PC.

.

Il n'y a pas de boucle until en Caml, mais avec une boucle while on arrivera presque à la même chose.

exception Fini;; (* Pour faire le [exit]. *)

exception Fini

On peut l'écrire avant pour la rendre plus claire, mais l'étape clé de l'algorithme PC (et Floyd-Warshall) est une opération dite de relaxation : $$ T_{i,j} \oplus (T_{i,k} \otimes T_{k,j}).$$

let relaxe (reseau : reseauSTP) i j k =
    let t_ij = reseau.(i).(j)
    and t_ik = reseau.(i).(k)
    and t_kj = reseau.(k).(j)
    in t_ij ++ (t_ik ** t_kj)
;;

val relaxe : reseauSTP -> int -> int -> int -> intervalles = <fun>

On a tout ce qu'il faut pour écrire l'algorithme. Mais comme il ne marche pas encore, on va le débogguer.

let string_of_entieretendu = function
    | MInf -> "-oo"
    | PInf -> "+oo"
    | E(x) -> string_of_int x
;;

val string_of_entieretendu : entier_etendu -> string = <fun>

let print_intervalle (une_contrainte : intervalle) =
    let a, b = une_contrainte in
    Printf.printf "(%s, %s) " (string_of_entieretendu a) (string_of_entieretendu b)
;;

val print_intervalle : intervalle -> unit = <fun>

let print_intervalles (contraintes : intervalles) =
    List.iter print_intervalle contraintes
;;

val print_intervalles : intervalles -> unit = <fun>

let flush_force () =
    Printf.printf "\n";
    flush_all();
    Printf.printf "\n";
    flush_all();
    Printf.printf "\n";
    flush_all();
;;

val flush_force : unit -> unit = <fun>

let print_reseau (reseau : reseauSTP) : unit =
    flush_force ();
    Printf.printf "\nReseau =\n";
    Array.iteri (fun i ligne ->
        Array.iteri (fun j case ->
            if case != [(MInf, PInf)] then begin
            Printf.printf "\n    T[i=%i, j=%i] = [" i j;
            print_intervalles case;
            Printf.printf "]";
        end) ligne
    ) reseau;
    flush_all ();
;;

val print_reseau : reseauSTP -> unit = <fun>

stp_4;;

- : reseauSTP =
[|[|[(MInf, PInf)]; [(E 0, E 1); (E 10, E 20)]; [(MInf, PInf)];
    [(MInf, PInf)]|];
  [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 10)]; [(E 25, E 50)]|];
  [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
    [(E 0, E 20); (E 40, E 40)]|];
  [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]|]|]

flush_force();;

    T[i=3, j=3] = [(-oo, +oo) ]

- : unit = ()

print_reseau stp_4;;

Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]

- : unit = ()

On est prêt à écrire l'algorithme :

let algorithmePC ?(max_etape=10) (reseau : reseauSTP) : (reseauSTP * intervalles list) =
    let resT = Array.map Array.copy reseau in (* on ne modifie pas l'entrée *)
    let resS = ref [||] in
    let n = Array.length resT in
    let allseen = ref [] in (* Pour débogguer, je veux la liste des Tij vus *)
    let etape = ref 0 in
    begin
        try begin
        while !etape < max_etape && !resS != resT do
            incr etape;
            resS := Array.map Array.copy resT; (* S := T *)
            for k = 0 to n - 1 do
                for i = 0 to n - 1 do
                    for j = 0 to n - 1 do
                        Printf.printf "\n\nEtape %i, k = %i, i = %i, j = %i.\n" !etape k i j;
                        print_string "Contraintes :";
                        print_reseau resT;
                        resT.(i).(j) <- relaxe resT i j k;
                        allseen := (resT.(i).(j)) :: !allseen; (* on l'ajoute *)
                        if resT.(i).(j) = [] then
                            raise Fini
                    done
                done
            done
        done;
        end
        with Fini -> () (* On ignore l'exception, on a juste terminé. *)
    end;
    resT, !allseen
;;

val algorithmePC :
  ?max_etape:int -> reseauSTP -> reseauSTP * intervalles list = <fun>

---

Exemple de réseau non distributif

On va traiter l'exemple de la Figure 4 du texte, comme défini plus haut :

stp_4;;

- : reseauSTP =
[|[|[(MInf, PInf)]; [(E 0, E 1); (E 10, E 20)]; [(MInf, PInf)];
    [(MInf, PInf)]|];
  [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 10)]; [(E 25, E 50)]|];
  [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
    [(E 0, E 20); (E 40, E 40)]|];
  [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]|]|]

relaxe stp_4 1 2 3;;

- : intervalles = [(E 0, E 10)]

stp_4.(1).(3)

- : intervalles = [(E 25, E 50)]

algorithmePC stp_4;;

    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]
    T[i=3, j=3] = [(-oo, +oo) ]

Etape 1, k = 1, i = 0, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(0, 1) (10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(0, 10) ]
    T[i=1, j=3] = [(25, 50) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(0, 20) (40, 40) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(-oo, +oo) ]

- : reseauSTP * intervalles list =
([|[|[]; [(E 0, E 1); (E 10, E 20)]; [(MInf, PInf)]; [(MInf, PInf)]|];
   [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 10)]; [(E 25, E 50)]|];
   [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
     [(E 0, E 20); (E 40, E 40)]|];
   [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]|]|],
 [[]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
  [(E 0, E 20); (E 40, E 40)]; [(MInf, PInf)]; [(MInf, PInf)];
  [(MInf, PInf)]; [(E 25, E 50)]; [(E 0, E 10)]; [(MInf, PInf)];
  [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 1); (E 10, E 20)];
  [(MInf, PInf)]])

Je ne suis pas sûr de comment interprêter ce résultat...

• soit j'ai fait une erreur dans l'implémentation,
• soit l'algorithme PC devait ne rien modifier à $T$ sur cet exemple...

---

D'autres exemples

On peut étudier le STP de la Figure 1., en enlevant la contrainte $[60, \infty)$, qui ne rentre pas dans notre implémentation.

.

let t_01 : intervalles = [(E(10), E(20))];;
let t_12 : intervalles = [(E(30), E(40))];;
let t_32 : intervalles = [(E(10), E(20))];;
let t_34 : intervalles = [(E(20), E(30)); (E(40), E(50))];;
let t_40 : intervalles = [(E(60), E(70))];;

let stp_1 : reseauSTP = [|
    [| t_vide; t_01; t_vide; t_vide; t_vide |];
    [| t_vide; t_vide; t_12; t_vide; t_vide |];
    [| t_vide; t_vide; t_vide; t_vide; t_vide   |];
    [| t_vide; t_vide; t_32; t_vide; t_34 |];
    [| t_40; t_vide; t_vide; t_vide; t_vide |];
|];;

val t_01 : intervalles = [(E 10, E 20)]

val t_12 : intervalles = [(E 30, E 40)]

val t_32 : intervalles = [(E 10, E 20)]

val t_34 : intervalles = [(E 20, E 30); (E 40, E 50)]

val t_40 : intervalles = [(E 60, E 70)]

val stp_1 : reseauSTP =
  [|[|[(MInf, PInf)]; [(E 10, E 20)]; [(MInf, PInf)]; [(MInf, PInf)];
      [(MInf, PInf)]|];
    [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 30, E 40)]; [(MInf, PInf)];
      [(MInf, PInf)]|];
    [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
      [(MInf, PInf)]|];
    [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 10, E 20)]; [(MInf, PInf)];
      [(E 20, E 30); (E 40, E 50)]|];
    [|[(E 60, E 70)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
      [(MInf, PInf)]|]|]

print_reseau stp_1;;

- : unit = ()

    T[i=3, j=3] = [(-oo, +oo) ]



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]

algorithmePC stp_1;;

    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 0, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 1, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 2, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 3, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 4, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 4, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(-oo, +oo) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 4, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 4, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 0, i = 4, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 0, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 0, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 0, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(-oo, +oo) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 0, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 0, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 1, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 1, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 1, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 1, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 1, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 2, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 2, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 2, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 2, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 2, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 3, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 3, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 3, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 3, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 3, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 4, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 4, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 4, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(-oo, +oo) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 4, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 1, i = 4, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 0, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 0, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 0, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 0, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 0, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 1, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 1, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 1, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 1, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 1, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 2, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 2, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 2, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 2, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 2, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 3, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 3, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 3, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 3, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 3, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 4, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 4, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 4, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 4, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 2, i = 4, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 0, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 0, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 0, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 0, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 0, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 1, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 1, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 1, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 1, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 1, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 2, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 2, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 2, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 2, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 2, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 3, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 3, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 3, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 3, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 3, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 4, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 4, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 4, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 4, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 3, i = 4, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 0, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 0, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 0, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 0, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 0, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 1, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 1, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 1, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 1, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 1, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 2, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 2, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 2, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 2, j = 3.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 2, j = 4.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 3, j = 0.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(-oo, +oo) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 3, j = 1.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(80, 100) (100, 120) ]
    T[i=3, j=1] = [(-oo, +oo) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]
    T[i=4, j=4] = [(-oo, +oo) ]

Etape 1, k = 4, i = 3, j = 2.
Contraintes :



Reseau =

    T[i=0, j=0] = [(-oo, +oo) ]
    T[i=0, j=1] = [(10, 20) ]
    T[i=0, j=2] = [(40, 60) ]
    T[i=0, j=3] = [(-oo, +oo) ]
    T[i=0, j=4] = [(-oo, +oo) ]
    T[i=1, j=0] = [(-oo, +oo) ]
    T[i=1, j=1] = [(-oo, +oo) ]
    T[i=1, j=2] = [(30, 40) ]
    T[i=1, j=3] = [(-oo, +oo) ]
    T[i=1, j=4] = [(-oo, +oo) ]
    T[i=2, j=0] = [(-oo, +oo) ]
    T[i=2, j=1] = [(-oo, +oo) ]
    T[i=2, j=2] = [(-oo, +oo) ]
    T[i=2, j=3] = [(-oo, +oo) ]
    T[i=2, j=4] = [(-oo, +oo) ]
    T[i=3, j=0] = [(80, 100) (100, 120) ]
    T[i=3, j=1] = [(90, 120) (110, 140) ]
    T[i=3, j=2] = [(10, 20) ]
    T[i=3, j=3] = [(-oo, +oo) ]
    T[i=3, j=4] = [(20, 30) (40, 50) ]
    T[i=4, j=0] = [(60, 70) ]
    T[i=4, j=1] = [(70, 90) ]
    T[i=4, j=2] = [(100, 130) ]
    T[i=4, j=3] = [(-oo, +oo) ]

- : reseauSTP * intervalles list =
([|[|[(MInf, PInf)]; [(E 10, E 20)]; [(E 40, E 60)]; [(MInf, PInf)];
     [(MInf, PInf)]|];
   [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 30, E 40)]; [(MInf, PInf)];
     [(MInf, PInf)]|];
   [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
     [(MInf, PInf)]|];
   [|[(E 80, E 100); (E 100, E 120)]; [(E 90, E 120); (E 110, E 140)]; 
     []; [(MInf, PInf)]; [(E 20, E 30); (E 40, E 50)]|];
   [|[(E 60, E 70)]; [(E 70, E 90)]; [(E 100, E 130)]; [(MInf, PInf)];
     [(MInf, PInf)]|]|],
 [[]; [(E 90, E 120); (E 110, E 140)]; [(E 80, E 100); (E 100, E 120)];
  [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
  [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(E 30, E 40)];
  [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
  [(E ...); ...]; ...])

Je ne suis pas sûr de comment interprêter ce résultat...

• soit j'ai fait une erreur dans l'implémentation,
• soit l'algorithme PC devait ne rien modifier à $T$ sur cet exemple...

---

Conclusion

Voilà pour la question obligatoire de programmation :

• on a décomposé le problème en sous-fonctions,
• on a essayé d'être fainéant, en réutilisant les sous-fonctions,
• on a fait des exemples et on les garde dans ce qu'on présente au jury,
• on a testé la fonction exigée sur de petits exemples et sur un exemple de taille réelle (venant du texte)

Et on a essayé de faire un peu plus, en implémentant la vérification d'une contrainte de plus.

Bien-sûr, ce petit notebook ne se prétend pas être une solution optimale, ni exhaustive.