MAYBE
Time: 0.022963
TRS:
 { app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
  app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
       app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                         app(app(map(), fun), nil()) -> nil(),
    app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                      app(app(filter(), fun), nil()) -> nil(),
                               app(f(), app(s(), x)) -> app(f(), x),
          app(g(), app(app(cons(), app(s(), x)), y)) -> app(s(), x),
                  app(g(), app(app(cons(), 0()), y)) -> app(g(), y),
                    app(h(), app(app(cons(), x), y)) -> app(h(), app(g(), app(app(cons(), x), y)))}
 DP:
  DP:
   { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)),
     app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs),
     app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x),
     app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun),
    app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
    app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)),
                                 app#(f(), app(s(), x)) -> app#(f(), x),
                    app#(g(), app(app(cons(), 0()), y)) -> app#(g(), y),
                      app#(h(), app(app(cons(), x), y)) -> app#(g(), app(app(cons(), x), y)),
                      app#(h(), app(app(cons(), x), y)) -> app#(h(), app(g(), app(app(cons(), x), y)))}
  TRS:
  { app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
   app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
        app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                          app(app(map(), fun), nil()) -> nil(),
     app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                       app(app(filter(), fun), nil()) -> nil(),
                                app(f(), app(s(), x)) -> app(f(), x),
           app(g(), app(app(cons(), app(s(), x)), y)) -> app(s(), x),
                   app(g(), app(app(cons(), 0()), y)) -> app(g(), y),
                     app(h(), app(app(cons(), x), y)) -> app(h(), app(g(), app(app(cons(), x), y)))}
  EDG:
   {(app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(f(), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(h(), app(app(cons(), x), y)) -> app#(h(), app(g(), app(app(cons(), x), y))))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(h(), app(app(cons(), x), y)) -> app#(g(), app(app(cons(), x), y)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(app(cons(), 0()), y)) -> app#(g(), y))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(f(), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(h(), app(app(cons(), x), y)) -> app#(h(), app(g(), app(app(cons(), x), y))))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(h(), app(app(cons(), x), y)) -> app#(g(), app(app(cons(), x), y)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(app(cons(), 0()), y)) -> app#(g(), y))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(f(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(g(), app(app(cons(), 0()), y)) -> app#(g(), y), app#(g(), app(app(cons(), 0()), y)) -> app#(g(), y))
    (app#(h(), app(app(cons(), x), y)) -> app#(g(), app(app(cons(), x), y)), app#(g(), app(app(cons(), 0()), y)) -> app#(g(), y))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(h(), app(app(cons(), x), y)) -> app#(h(), app(g(), app(app(cons(), x), y))), app#(h(), app(app(cons(), x), y)) -> app#(g(), app(app(cons(), x), y)))
    (app#(h(), app(app(cons(), x), y)) -> app#(h(), app(g(), app(app(cons(), x), y))), app#(h(), app(app(cons(), x), y)) -> app#(h(), app(g(), app(app(cons(), x), y))))}
   STATUS:
    arrows: 0.842105
    SCCS (4):
     Scc:
      { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs),
       app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
            app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
            app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
         app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)}
     Scc:
      {app#(h(), app(app(cons(), x), y)) -> app#(h(), app(g(), app(app(cons(), x), y)))}
     Scc:
      {app#(g(), app(app(cons(), 0()), y)) -> app#(g(), y)}
     Scc:
      {app#(f(), app(s(), x)) -> app#(f(), x)}
     
     SCC (5):
      Strict:
       { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs),
        app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
             app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
             app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
          app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)}
      Weak:
      { app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
       app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
            app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                              app(app(map(), fun), nil()) -> nil(),
         app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                           app(app(filter(), fun), nil()) -> nil(),
                                    app(f(), app(s(), x)) -> app(f(), x),
               app(g(), app(app(cons(), app(s(), x)), y)) -> app(s(), x),
                       app(g(), app(app(cons(), 0()), y)) -> app(g(), y),
                         app(h(), app(app(cons(), x), y)) -> app(h(), app(g(), app(app(cons(), x), y)))}
      Open
     
     
     
     
     
     
     
     SCC (1):
      Strict:
       {app#(h(), app(app(cons(), x), y)) -> app#(h(), app(g(), app(app(cons(), x), y)))}
      Weak:
      { app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
       app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
            app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                              app(app(map(), fun), nil()) -> nil(),
         app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                           app(app(filter(), fun), nil()) -> nil(),
                                    app(f(), app(s(), x)) -> app(f(), x),
               app(g(), app(app(cons(), app(s(), x)), y)) -> app(s(), x),
                       app(g(), app(app(cons(), 0()), y)) -> app(g(), y),
                         app(h(), app(app(cons(), x), y)) -> app(h(), app(g(), app(app(cons(), x), y)))}
      Open
     
     SCC (1):
      Strict:
       {app#(g(), app(app(cons(), 0()), y)) -> app#(g(), y)}
      Weak:
      { app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
       app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
            app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                              app(app(map(), fun), nil()) -> nil(),
         app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                           app(app(filter(), fun), nil()) -> nil(),
                                    app(f(), app(s(), x)) -> app(f(), x),
               app(g(), app(app(cons(), app(s(), x)), y)) -> app(s(), x),
                       app(g(), app(app(cons(), 0()), y)) -> app(g(), y),
                         app(h(), app(app(cons(), x), y)) -> app(h(), app(g(), app(app(cons(), x), y)))}
      Open
     SCC (1):
      Strict:
       {app#(f(), app(s(), x)) -> app#(f(), x)}
      Weak:
      { app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
       app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
            app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                              app(app(map(), fun), nil()) -> nil(),
         app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                           app(app(filter(), fun), nil()) -> nil(),
                                    app(f(), app(s(), x)) -> app(f(), x),
               app(g(), app(app(cons(), app(s(), x)), y)) -> app(s(), x),
                       app(g(), app(app(cons(), 0()), y)) -> app(g(), y),
                         app(h(), app(app(cons(), x), y)) -> app(h(), app(g(), app(app(cons(), x), y)))}
      Open