MAYBE
Time: 0.028415
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(app(f(), x), y), app(s(), z)) -> app(s(), app(app(app(f(), 0()), 1()), z)),
                     app(app(app(f(), 0()), 1()), x) -> app(app(app(f(), app(s(), x)), x), 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), 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()}
 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(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z),
                 app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()),
                 app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()),
                 app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)),
                       app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x),
                       app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x),
                       app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)),
                       app#(app(app(f(), 0()), 1()), x) -> app#(s(), 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#(app(cons(), app(fun, x)), 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))}
  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(app(f(), x), y), app(s(), z)) -> app(s(), app(app(app(f(), 0()), 1()), z)),
                      app(app(app(f(), 0()), 1()), x) -> app(app(app(f(), app(s(), x)), x), 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), 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()}
  EDG:
   {
    (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(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#(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(f(), 0()), 1()), x) -> app#(s(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
    (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#(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#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), 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#(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#(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(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#(cons(), x))
    (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(), 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(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(s(), 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(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#(cons(), 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(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#(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(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#(filter2(), app(fun, x)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
   }
   STATUS:
    arrows: 0.863894
    SCCS (2):
     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#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z),
             app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), 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(app(f(), x), y), app(s(), z)) -> app(s(), app(app(app(f(), 0()), 1()), z)),
                          app(app(app(f(), 0()), 1()), x) -> app(app(app(f(), app(s(), x)), x), 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), 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()}
      Open
     
     
     
     
     
     
     
     
     SCC (2):
      Strict:
       {app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z),
              app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), 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(app(f(), x), y), app(s(), z)) -> app(s(), app(app(app(f(), 0()), 1()), z)),
                          app(app(app(f(), 0()), 1()), x) -> app(app(app(f(), app(s(), x)), x), 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), 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()}
      Open