YES
TRS:
 {             app(app(app(comp(), f), g), x) -> app(f, app(g, x)),
                    app(app(map(), f), nil()) -> nil(),
  app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                              app(twice(), f) -> app(app(comp(), f), f)}
 DP:
  Strict:
   {             app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)),
                 app#(app(app(comp(), f), g), x) -> app#(g, x),
    app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
    app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
    app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)),
    app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)),
                                app#(twice(), f) -> app#(app(comp(), f), f),
                                app#(twice(), f) -> app#(comp(), f)}
  Weak:
  {             app(app(app(comp(), f), g), x) -> app(f, app(g, x)),
                     app(app(map(), f), nil()) -> nil(),
   app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                               app(twice(), f) -> app(app(comp(), f), f)}
  EDG:
   {(app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(twice(), f) -> app#(comp(), f))
    (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(twice(), f) -> app#(app(comp(), f), f))
    (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
    (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
    (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
    (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(app(comp(), f), g), x) -> app#(g, x))
    (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(twice(), f) -> app#(comp(), f))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(twice(), f) -> app#(app(comp(), f), f))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(comp(), f), g), x) -> app#(g, x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)))
    (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)))
    (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(app(comp(), f), g), x) -> app#(g, x))
    (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
    (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
    (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
    (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(twice(), f) -> app#(app(comp(), f), f))
    (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(twice(), f) -> app#(comp(), f))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))}
   SCCS:
    Scc:
     {             app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)),
                   app#(app(app(comp(), f), g), x) -> app#(g, x),
      app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
      app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)}
    SCC:
     Strict:
      {             app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)),
                    app#(app(app(comp(), f), g), x) -> app#(g, x),
       app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
       app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)}
     Weak:
     {             app(app(app(comp(), f), g), x) -> app(f, app(g, x)),
                        app(app(map(), f), nil()) -> nil(),
      app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                                  app(twice(), f) -> app(app(comp(), f), f)}
     SPSC:
      Simple Projection:
       pi(app#) = 0
      Strict:
       {             app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)),
                     app#(app(app(comp(), f), g), x) -> app#(g, x),
        app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)}
      EDG:
       {(app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
        (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)))
        (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(app(comp(), f), g), x) -> app#(g, x))
        (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
        (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)))
        (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(app(comp(), f), g), x) -> app#(g, x))
        (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))}
       SCCS:
        Scc:
         {app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)}
        Scc:
         {app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)),
          app#(app(app(comp(), f), g), x) -> app#(g, x)}
        SCC:
         Strict:
          {app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)}
         Weak:
         {             app(app(app(comp(), f), g), x) -> app(f, app(g, x)),
                            app(app(map(), f), nil()) -> nil(),
          app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                                      app(twice(), f) -> app(app(comp(), f), f)}
         SPSC:
          Simple Projection:
           pi(app#) = 1
          Strict:
           {}
          Qed
        SCC:
         Strict:
          {app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)),
           app#(app(app(comp(), f), g), x) -> app#(g, x)}
         Weak:
         {             app(app(app(comp(), f), g), x) -> app(f, app(g, x)),
                            app(app(map(), f), nil()) -> nil(),
          app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                                      app(twice(), f) -> app(app(comp(), f), f)}
         SPSC:
          Simple Projection:
           pi(app#) = 0
          Strict:
           {app#(app(app(comp(), f), g), x) -> app#(g, x)}
          EDG:
           {(app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(app(comp(), f), g), x) -> app#(g, x))}
           SCCS:
            Scc:
             {app#(app(app(comp(), f), g), x) -> app#(g, x)}
            SCC:
             Strict:
              {app#(app(app(comp(), f), g), x) -> app#(g, x)}
             Weak:
             {             app(app(app(comp(), f), g), x) -> app(f, app(g, x)),
                                app(app(map(), f), nil()) -> nil(),
              app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                                          app(twice(), f) -> app(app(comp(), f), f)}
             SPSC:
              Simple Projection:
               pi(app#) = 0
              Strict:
               {}
              Qed