YES
TRS:
 {                app(app(and(), true()), true()) -> true(),
                 app(app(and(), true()), false()) -> false(),
                 app(app(and(), false()), true()) -> false(),
                app(app(and(), false()), false()) -> false(),
                   app(app(or(), true()), true()) -> true(),
                  app(app(or(), true()), false()) -> true(),
                  app(app(or(), false()), true()) -> true(),
                 app(app(or(), false()), false()) -> false(),
   app(app(forall(), p), app(app(cons(), x), xs)) -> app(app(and(), app(p, x)), app(app(forall(), p), xs)),
                     app(app(forall(), p), nil()) -> true(),
  app(app(forsome(), p), app(app(cons(), x), xs)) -> app(app(or(), app(p, x)), app(app(forsome(), p), xs)),
                    app(app(forsome(), p), nil()) -> false()}
 DP:
  Strict:
   { app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x),
     app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(and(), app(p, x)), app(app(forall(), p), xs)),
     app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs),
     app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(and(), app(p, x)),
    app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x),
    app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(or(), app(p, x)), app(app(forsome(), p), xs)),
    app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs),
    app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(or(), app(p, x))}
  Weak:
  {                app(app(and(), true()), true()) -> true(),
                  app(app(and(), true()), false()) -> false(),
                  app(app(and(), false()), true()) -> false(),
                 app(app(and(), false()), false()) -> false(),
                    app(app(or(), true()), true()) -> true(),
                   app(app(or(), true()), false()) -> true(),
                   app(app(or(), false()), true()) -> true(),
                  app(app(or(), false()), false()) -> false(),
    app(app(forall(), p), app(app(cons(), x), xs)) -> app(app(and(), app(p, x)), app(app(forall(), p), xs)),
                      app(app(forall(), p), nil()) -> true(),
   app(app(forsome(), p), app(app(cons(), x), xs)) -> app(app(or(), app(p, x)), app(app(forsome(), p), xs)),
                     app(app(forsome(), p), nil()) -> false()}
  EDG:
   {(app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(or(), app(p, x)))
    (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs))
    (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(or(), app(p, x)), app(app(forsome(), p), xs)))
    (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x))
    (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(or(), app(p, x)))
    (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs))
    (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(or(), app(p, x)), app(app(forsome(), p), xs)))
    (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x))
    (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(and(), app(p, x)))
    (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs))
    (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(and(), app(p, x)), app(app(forall(), p), xs)))
    (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x))
    (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x))
    (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(and(), app(p, x)), app(app(forall(), p), xs)))
    (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs))
    (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(and(), app(p, x)))
    (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x))
    (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(or(), app(p, x)), app(app(forsome(), p), xs)))
    (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs))
    (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(or(), app(p, x)))
    (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x))
    (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(and(), app(p, x)), app(app(forall(), p), xs)))
    (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs))
    (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(and(), app(p, x)))}
   SCCS:
    Scc:
     { app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x),
       app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs),
      app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x),
      app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs)}
    SCC:
     Strict:
      { app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x),
        app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs),
       app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x),
       app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs)}
     Weak:
     {                app(app(and(), true()), true()) -> true(),
                     app(app(and(), true()), false()) -> false(),
                     app(app(and(), false()), true()) -> false(),
                    app(app(and(), false()), false()) -> false(),
                       app(app(or(), true()), true()) -> true(),
                      app(app(or(), true()), false()) -> true(),
                      app(app(or(), false()), true()) -> true(),
                     app(app(or(), false()), false()) -> false(),
       app(app(forall(), p), app(app(cons(), x), xs)) -> app(app(and(), app(p, x)), app(app(forall(), p), xs)),
                         app(app(forall(), p), nil()) -> true(),
      app(app(forsome(), p), app(app(cons(), x), xs)) -> app(app(or(), app(p, x)), app(app(forsome(), p), xs)),
                        app(app(forsome(), p), nil()) -> false()}
     SPSC:
      Simple Projection:
       pi(app#) = 0
      Strict:
       { app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x),
         app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs),
        app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs)}
      EDG:
       {(app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs))
        (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x))
        (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs))
        (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs))
        (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x))
        (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs))}
       SCCS:
        Scc:
         {app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs)}
        Scc:
         {app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x),
          app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs)}
        SCC:
         Strict:
          {app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs)}
         Weak:
         {                app(app(and(), true()), true()) -> true(),
                         app(app(and(), true()), false()) -> false(),
                         app(app(and(), false()), true()) -> false(),
                        app(app(and(), false()), false()) -> false(),
                           app(app(or(), true()), true()) -> true(),
                          app(app(or(), true()), false()) -> true(),
                          app(app(or(), false()), true()) -> true(),
                         app(app(or(), false()), false()) -> false(),
           app(app(forall(), p), app(app(cons(), x), xs)) -> app(app(and(), app(p, x)), app(app(forall(), p), xs)),
                             app(app(forall(), p), nil()) -> true(),
          app(app(forsome(), p), app(app(cons(), x), xs)) -> app(app(or(), app(p, x)), app(app(forsome(), p), xs)),
                            app(app(forsome(), p), nil()) -> false()}
         SPSC:
          Simple Projection:
           pi(app#) = 1
          Strict:
           {}
          Qed
        SCC:
         Strict:
          {app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x),
           app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs)}
         Weak:
         {                app(app(and(), true()), true()) -> true(),
                         app(app(and(), true()), false()) -> false(),
                         app(app(and(), false()), true()) -> false(),
                        app(app(and(), false()), false()) -> false(),
                           app(app(or(), true()), true()) -> true(),
                          app(app(or(), true()), false()) -> true(),
                          app(app(or(), false()), true()) -> true(),
                         app(app(or(), false()), false()) -> false(),
           app(app(forall(), p), app(app(cons(), x), xs)) -> app(app(and(), app(p, x)), app(app(forall(), p), xs)),
                             app(app(forall(), p), nil()) -> true(),
          app(app(forsome(), p), app(app(cons(), x), xs)) -> app(app(or(), app(p, x)), app(app(forsome(), p), xs)),
                            app(app(forsome(), p), nil()) -> false()}
         SPSC:
          Simple Projection:
           pi(app#) = 0
          Strict:
           {app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs)}
          EDG:
           {(app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs))}
           SCCS:
            Scc:
             {app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs)}
            SCC:
             Strict:
              {app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs)}
             Weak:
             {                app(app(and(), true()), true()) -> true(),
                             app(app(and(), true()), false()) -> false(),
                             app(app(and(), false()), true()) -> false(),
                            app(app(and(), false()), false()) -> false(),
                               app(app(or(), true()), true()) -> true(),
                              app(app(or(), true()), false()) -> true(),
                              app(app(or(), false()), true()) -> true(),
                             app(app(or(), false()), false()) -> false(),
               app(app(forall(), p), app(app(cons(), x), xs)) -> app(app(and(), app(p, x)), app(app(forall(), p), xs)),
                                 app(app(forall(), p), nil()) -> true(),
              app(app(forsome(), p), app(app(cons(), x), xs)) -> app(app(or(), app(p, x)), app(app(forsome(), p), xs)),
                                app(app(forsome(), p), nil()) -> false()}
             SPSC:
              Simple Projection:
               pi(app#) = 1
              Strict:
               {}
              Qed