diff --git a/logic.py b/logic.py
index 164e586e5b5af9f5b8581b9b77f52602147baf78..4fa1b8282429d4a5eb88f4589efd4ac2570ca4fc 100644
--- a/logic.py
+++ b/logic.py
@@ -480,7 +480,7 @@ def beta_reduction_choice_n(terme,n):
 def beta_reduction_interactive(terme, at):
     global counters
     if at != None:
-        # print(annotated_to_string(at))
+        print(annotated_to_string(at))
         choice = int(input("Choose a beta reduction: "))
         while choice <= 0 or choice > counters:
             print("Invalid choice")
@@ -503,7 +503,7 @@ def cleanReductions(l):
 
 def beta_reduction_interactive_totale(terme,path):
         if beta_reduction((terme)) != None:
-            # print(to_string(terme))
+            #print(to_string(terme))
             at = (annotate_beta_reduction((terme)))
             captureImage(at,path)
             choix=int(input("voulez-vous faire la reduction tapez sur 1 pour oui tapez sur 2 pour non "))
diff --git a/main.py b/main.py
index a717a7100b3042494ee136677db3d65ba18797cf..cff75061db93dcbc4b6447fcde9627cf9adf081b 100644
--- a/main.py
+++ b/main.py
@@ -92,15 +92,16 @@ def run_beta_reduction_totale(terme,path='beta_reduction_totale'):
     os.makedirs(path, exist_ok=True)# cree le rep si il existe pas, le vide si non
     if len(os.listdir(path)) > 0:
         logic.image_counter = 0
-    logic.beta_reduction_totale(terme,path)
-    save_image_choice = input('Do you want to save the images? (y/n): ')
-    while save_image_choice not in ['y','n']:
-            save_image_choice = input('Invalid choice. Do you want to save the images? (y/n): ')
-    if save_image_choice == 'y':
+    k=logic.beta_reduction_totale(terme,path)
+    print(" le terme obtenu est: "+logic.to_string(k))
+    save_image_choice = input('Do you want to save the images? (Y/n): ')
+    while save_image_choice not in ['y','n','']:
+            save_image_choice = input('Invalid choice. Do you want to save the images? (Y/n): ')
+    if save_image_choice == 'y' or save_image_choice=='':
         os.makedirs("./sauvegarde/"+path, exist_ok=True)
         moveImages(path,'./sauvegarde/'+path)
         os.rmdir(path)
-    elif save_image_choice == 'n':
+    elif save_image_choice=='n':
         delete_images(path)
         os.rmdir(path)
 
@@ -113,10 +114,10 @@ def run_beta_reduction_interactive_totale(terme,path='beta_reduction_interactive
     if len(os.listdir(path)) > 0:
         logic.image_counter = 0
     logic.beta_reduction_interactive_totale(terme,path)
-    save_image_choice = input('Do you want to save the images? (y/n): ')
-    while save_image_choice not in ['y','n']:
-            save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (y/n): ')
-    if save_image_choice == 'y':
+    save_image_choice = input('Do you want to save the images? (Y/n): ')
+    while save_image_choice not in ['y','n','']:
+            save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (Y/n): ')
+    if save_image_choice == 'y'or save_image_choice=='':
         os.makedirs("./sauvegarde/"+path, exist_ok=True)
         moveImages(path,'./sauvegarde/'+path)
         os.rmdir(path)
@@ -138,10 +139,10 @@ def run_show_numbers(path):
         t = app_functions.dec_to_church(terme)
         print('Voici le terme:',logic.to_string(t))
         logic.captureImage(t,path,'ENTIER'+str(terme),False)
-        save_image_choice = input('Do you want to save the images? (y/n): ')
-        while save_image_choice not in ['y','n']:
-                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (y/n): ')
-        if save_image_choice == 'y':
+        save_image_choice = input('Do you want to save the images? (Y/n): ')
+        while save_image_choice not in ['y','n','']:
+                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (Y/n): ')
+        if save_image_choice == 'y' or save_image_choice=='':
             os.makedirs("./sauvegarde/"+path, exist_ok=True)
             moveImages(path,'./sauvegarde/'+path)
             os.rmdir(path)
@@ -155,10 +156,10 @@ def run_show_numbers(path):
         t = app_functions.dec_to_lambda_relative_integers(terme)
         print('Voici le terme:',logic.to_string(t))
         logic.captureImage(t,path,'ENTIER-RELATIF-'+str(terme),False)
-        save_image_choice = input('Do you want to save the images? (y/n): ')
-        while save_image_choice not in ['y','n']:
-                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (y/n): ')
-        if save_image_choice == 'y':
+        save_image_choice = input('Do you want to save the images? (Y/n): ')
+        while save_image_choice not in ['y','n','']:
+                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (Y/n): ')
+        if save_image_choice == 'y' or save_image_choice=='':
             os.makedirs("./sauvegarde/"+path, exist_ok=True)
             moveImages(path,'./sauvegarde/'+path)
             os.rmdir(path)
@@ -181,10 +182,10 @@ def run_boolean_expression(path):
         t = app_functions.NOT
         print('Voici le terme:',logic.to_string(t))
         logic.captureImage(t,path,'NOT',False)
-        save_image_choice = input('Do you want to save the images? (y/n): ')
-        while save_image_choice not in ['y','n']:
-                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (y/n): ')
-        if save_image_choice == 'y':
+        save_image_choice = input('Do you want to save the images? (Y/n): ')
+        while save_image_choice not in ['y','n','']:
+                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (Y/n): ')
+        if save_image_choice == 'y' or save_image_choice=='':
             os.makedirs("./sauvegarde/"+path, exist_ok=True)
             moveImages(path,'./sauvegarde/'+path)
             os.rmdir(path)
@@ -196,10 +197,10 @@ def run_boolean_expression(path):
         t = app_functions.AND
         print('Voici le terme:',logic.to_string(t))
         logic.captureImage(t,path,'AND',False)
-        save_image_choice = input('Do you want to save the images? (y/n): ')
-        while save_image_choice not in ['y','n']:
-                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (y/n): ')
-        if save_image_choice == 'y':
+        save_image_choice = input('Do you want to save the images? (Y/n): ')
+        while save_image_choice not in ['y','n','']:
+                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (Y/n): ')
+        if save_image_choice == 'y' or save_image_choice=='':
             os.makedirs("./sauvegarde/"+path, exist_ok=True)
             moveImages(path,'./sauvegarde/'+path)
             os.rmdir(path)
@@ -211,10 +212,10 @@ def run_boolean_expression(path):
         t = app_functions.OR
         print('Voici le terme:',logic.to_string(t))
         logic.captureImage(t,path,'OR',False)
-        save_image_choice = input('Do you want to save the images? (y/n): ')
-        while save_image_choice not in ['y','n']:
-                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (y/n): ')
-        if save_image_choice == 'y':
+        save_image_choice = input('Do you want to save the images? (Y/n): ')
+        while save_image_choice not in ['y','n','']:
+                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (Y/n): ')
+        if save_image_choice == 'y' or save_image_choice=='':
             os.makedirs("./sauvegarde/"+path, exist_ok=True)
             moveImages(path,'./sauvegarde/'+path)
             os.rmdir(path)
@@ -226,10 +227,10 @@ def run_boolean_expression(path):
         t = app_functions.XOR
         print('Voici le terme:',logic.to_string(t))
         logic.captureImage(t,path,'XOR',False)
-        save_image_choice = input('Do you want to save the images? (y/n): ')
-        while save_image_choice not in ['y','n']:
-                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (y/n): ')
-        if save_image_choice == 'y':
+        save_image_choice = input('Do you want to save the images? (Y/n): ')
+        while save_image_choice not in ['y','n','']:
+                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (Y/n): ')
+        if save_image_choice == 'y' or save_image_choice=='':
             os.makedirs("./sauvegarde/"+path, exist_ok=True)
             moveImages(path,'./sauvegarde/'+path)
             os.rmdir(path)
@@ -242,10 +243,10 @@ def run_boolean_expression(path):
         t = app_functions.IS_ZERO
         print('Voici le terme:',logic.to_string(t))
         logic.captureImage(t,path,'IS_ZERO',False)
-        save_image_choice = input('Do you want to save the images? (y/n): ')
-        while save_image_choice not in ['y','n']:
-                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (y/n): ')
-        if save_image_choice == 'y':
+        save_image_choice = input('Do you want to save the images? (Y/n): ')
+        while save_image_choice not in ['y','n','']:
+                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (Y/n): ')
+        if save_image_choice == 'y' or save_image_choice=='':
             os.makedirs("./sauvegarde/"+path, exist_ok=True)
             moveImages(path,'./sauvegarde/'+path)
             os.rmdir(path)
@@ -322,19 +323,19 @@ def run_arithmetic_operations_menu(path='arithmetic expressions'):
         clear()
         print("Voici le terme: "+ logic.to_string(app_functions.ADD))
         logic.captureImage(app_functions.ADD,path,'ADD', False)
-        choix=(input("do you want to try an exemple? (y/n) : "))
-        while choix not in ['y','n']:
-            choix = input('Invalid choice. Do you want to try an exemple? (y/n): ')
-        if choix=='y':
+        choix=(input("do you want to try an exemple? (Y/n) : "))
+        while choix not in ['y','n','']:
+            choix = input('Invalid choice. Do you want to try an exemple? (Y/n): ')
+        if choix=='y' or choix=='':
             clear()
             print("you are going to try n+m")
             n=int(input("give n : "))
             m=int(input("give m : "))
             app_functions.add(app_functions.dec_to_church(n),app_functions.dec_to_church(m))
-        save_image_choice = input('Do you want to save the images? (y/n): ')
-        while save_image_choice not in ['y','n']:
-                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (y/n): ')
-        if save_image_choice == 'y':
+        save_image_choice = input('Do you want to save the images? (Y/n): ')
+        while save_image_choice not in ['y','n','']:
+                save_image_choice = input('Invalid choice. Do you want to save the images? (Y/n): ')
+        if save_image_choice == 'y' or save_image_choice=='':
             os.makedirs("./sauvegarde/"+path, exist_ok=True)
             moveImages(path,'./sauvegarde/'+path)
             os.rmdir(path)
@@ -346,19 +347,19 @@ def run_arithmetic_operations_menu(path='arithmetic expressions'):
         clear()
         print("Voici le terme: "+ logic.to_string(app_functions.SUB))
         logic.captureImage(app_functions.SUB,path,'SUB', False)
-        choix=(input("do you want to try an exemple? (y/n) : "))
-        while choix not in ['y','n']:
-            choix = input('Invalid choice. Do you want to try an exemple? (y/n): ')
-        if choix=='y':
+        choix=(input("do you want to try an exemple? (Y/n) : "))
+        while choix not in ['y','n','']:
+            choix = input('Invalid choice. Do you want to try an exemple? (Y/n): ')
+        if choix=='y' or choix=='':
             clear()
             print("you are going to try n-m")
             n=int(input("give n : "))
             m=int(input("give m : "))
             app_functions.sub(app_functions.dec_to_church(n),app_functions.dec_to_church(m))
-        save_image_choice = input('Do you want to save the images? (y/n): ')
-        while save_image_choice not in ['y','n']:
-                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (y/n): ')
-        if save_image_choice == 'y':
+        save_image_choice = input('Do you want to save the images? (Y/n): ')
+        while save_image_choice not in ['Y','n','']:
+                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (Y/n): ')
+        if save_image_choice == 'y' or save_image_choice=='':
             os.makedirs("./sauvegarde/"+path, exist_ok=True)
             moveImages(path,'./sauvegarde/'+path)
             os.rmdir(path)
@@ -370,19 +371,19 @@ def run_arithmetic_operations_menu(path='arithmetic expressions'):
         clear()
         print("Voici le terme: "+ logic.to_string(app_functions.MUL))
         logic.captureImage(app_functions.MUL,path,'MUL',False)
-        choix=(input("do you want to try an exemple? (y/n) : "))
-        while choix not in ['y','n']:
-            choix = input('Invalid choice. Do you want to try an exemple? (y/n): ')
-        if choix=='y':
+        choix=(input("do you want to try an exemple? (Y/n) : "))
+        while choix not in ['y','n','']:
+            choix = input('Invalid choice. Do you want to try an exemple? (Y/n): ')
+        if choix=='y' or choix=='':
             clear()
             print("you are going to try n*m")
             n=int(input("give n : "))
             m=int(input("give m : "))
             app_functions.mul(app_functions.dec_to_church(n),app_functions.dec_to_church(m))
-        save_image_choice = input('Do you want to save the images? (y/n): ')
-        while save_image_choice not in ['y','n']:
-                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (y/n): ')
-        if save_image_choice == 'y':
+        save_image_choice = input('Do you want to save the images? (Y/n): ')
+        while save_image_choice not in ['y','n','']:
+                save_image_choice = input('Invalid choice. Do you want to save the images? (Y/n): ')
+        if save_image_choice == 'y' or save_image_choice=='':
             os.makedirs("./sauvegarde/"+path, exist_ok=True)
             moveImages(path,'./sauvegarde/'+path)
             os.rmdir(path)
@@ -394,19 +395,19 @@ def run_arithmetic_operations_menu(path='arithmetic expressions'):
         clear()
         print("Voici le terme: "+ logic.to_string(app_functions.POW))
         logic.captureImage(app_functions.POW,path,'POWER',False)
-        choix=(input("do you want to try an exemple? (y/n) : "))
-        while choix not in ['y','n']:
-            choix = input('Invalid choice. Do you want to try an exemple? (y/n): ')
-        if choix=='y':
+        choix=(input("do you want to try an exemple? (Y/n) : "))
+        while choix not in ['y','n','']:
+            choix = input('Invalid choice. Do you want to try an exemple? (Y/n): ')
+        if choix=='y' or choix=='':
             clear()
             print("you are going to try n puiss m")
             n=int(input("give n : "))
             m=int(input("give m : "))
             app_functions.power(app_functions.dec_to_church(n),app_functions.dec_to_church(m))
-        save_image_choice = input('Do you want to save the images? (y/n): ')
-        while save_image_choice not in ['y','n']:
-                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (y/n): ')
-        if save_image_choice == 'y':
+        save_image_choice = input('Do you want to save the images? (Y/n): ')
+        while save_image_choice not in ['y','n','']:
+                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (Y/n): ')
+        if save_image_choice == 'y' or save_image_choice=='':
             os.makedirs("./sauvegarde/"+path, exist_ok=True)
             moveImages(path,'./sauvegarde/'+path)
             os.rmdir(path)
@@ -418,18 +419,18 @@ def run_arithmetic_operations_menu(path='arithmetic expressions'):
         clear()
         print("Voici le terme: "+ logic.to_string(app_functions.SUCCS))
         logic.captureImage(app_functions.SUCCS,path,'SUCCS',False)
-        choix=(input("do you want to try an exemple? (y/n) : "))
-        while choix not in ['y','n']:
-            choix = input('Invalid choice. Do you want to try an exemple? (y/n): ')
-        if choix=='y':
+        choix=(input("do you want to try an exemple? (Y/n) : "))
+        while choix not in ['y','n','']:
+            choix = input('Invalid choice. Do you want to try an exemple? (Y/n): ')
+        if choix=='y'or choix=='':
             clear()
             print("you are going to try n+1")
             n=int(input("give n : "))
             app_functions.succ(app_functions.dec_to_church(n))
-        save_image_choice = input('Do you want to save the images? (y/n): ')
-        while save_image_choice not in ['y','n']:
-                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (y/n): ')
-        if save_image_choice == 'y':
+        save_image_choice = input('Do you want to save the images? (Y/n): ')
+        while save_image_choice not in ['y','n','']:
+                save_image_choice = input('Invalid choice. Do you want to save the images ? (Y/n): ')
+        if save_image_choice == 'y' or save_image_choice=='':
             os.makedirs("./sauvegarde/"+path, exist_ok=True)
             moveImages(path,'./sauvegarde/'+path)
             os.rmdir(path)
@@ -441,18 +442,18 @@ def run_arithmetic_operations_menu(path='arithmetic expressions'):
         clear()
         print("Voici le terme: "+ logic.to_string(app_functions.PRED))
         logic.captureImage(app_functions.PRED,path,'PRED',False)
-        choix=(input("do you want to try an exemple? (y/n) : "))
-        while choix not in ['y','n']:
-            choix = input('Invalid choice. Do you want to try an exemple? (y/n): ')
-        if choix=='y':
+        choix=(input("do you want to try an exemple? (Y/n) : "))
+        while choix not in ['y','n','']:
+            choix = input('Invalid choice. Do you want to try an exemple? (Y/n): ')
+        if choix=='y' or choix=='':
             clear()
             print("you are going to try n-1")
             n=int(input("give n : "))
             app_functions.predec(app_functions.dec_to_church(n))
-        save_image_choice = input('Do you want to save the images? (y/n): ')
-        while save_image_choice not in ['y','n']:
-                save_image_choice = input('Invalid choice. Do you want to save the images of the reduction? (y/n): ')
-        if save_image_choice == 'y':
+        save_image_choice = input('Do you want to save the images? (Y/n): ')
+        while save_image_choice not in ['y','n','']:
+                save_image_choice = input('Invalid choice. Do you want to save the images? (Y/n): ')
+        if save_image_choice == 'y' or save_image_choice=='':
             os.makedirs("./sauvegarde/"+path, exist_ok=True)
             moveImages(path,'./sauvegarde/'+path)
             os.rmdir(path)