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