MAYBE
Time: 1.140692
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(), 0()), app(s(), 0())), x) -> app(app(app(f(), x), app(app(plus(), x), x)), x),
                    app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                            app(app(plus(), x), 0()) -> x,
                                 app(app(g(), x), y) -> x,
                                 app(app(g(), x), y) -> y,
       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(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x),
             app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x),
             app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)),
             app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x),
             app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x),
                      app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y),
                      app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)),
         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(), 0()), app(s(), 0())), x) -> app(app(app(f(), x), app(app(plus(), x), x)), x),
                     app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                             app(app(plus(), x), 0()) -> x,
                                  app(app(g(), x), y) -> x,
                                  app(app(g(), x), y) -> y,
        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(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), 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#(app(cons(), app(fun, x)), app(app(map(), 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#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), 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#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), 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#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), 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#(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(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(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(cons(), app(fun, x)), 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(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#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), 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(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), 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(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), true()), 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(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#(filter2(), 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#(filter2(), 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#(filter2(), 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#(filter2(), 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#(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#(filter2(), 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#(filter2(), 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#(filter2(), 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#(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#(filter2(), app(fun, x)), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), 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#(filter2(), 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#(filter2(), 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#(filter2(), 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#(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#(filter2(), 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#(cons(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), 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#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), 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#(cons(), x), 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#(cons(), x), 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(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), 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#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (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#(cons(), x), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), false()), 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(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), 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#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
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    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), 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#(cons(), 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#(cons(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), 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(cons(), x), app(app(filter(), fun), xs)), 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(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#(app(cons(), x), 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#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (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(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#(filter(), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
    (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(cons(), x), app(app(filter(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (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#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (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#(cons(), 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#(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#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (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#(app(app(filter2(), app(fun, x)), 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#(app(filter2(), app(fun, x)), fun))
    (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#(filter2(), app(fun, x)))
   }
   EDG:
    {
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (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(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(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#(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(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), 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#(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#(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#(cons(), x))
     (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(), 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#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (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(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#(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#(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#(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(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#(filter2(), 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(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#(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#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (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#(filter(), fun))
     (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(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), 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#(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(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
    }
    STATUS:
     arrows: 0.849174
     SCCS (3):
      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),
          app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)}
      Scc:
       {app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x)}
      Scc:
       {app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y)}
      
      SCC (6):
       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),
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)}
       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(), 0()), app(s(), 0())), x) -> app(app(app(f(), x), app(app(plus(), x), x)), x),
                          app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                                  app(app(plus(), x), 0()) -> x,
                                       app(app(g(), x), y) -> x,
                                       app(app(g(), x), y) -> y,
             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()}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [app](x0, x1) = x0 + x1,
         
         [plus] = 1,
         
         [0] = 1,
         
         [s] = 1,
         
         [f] = 1,
         
         [g] = 0,
         
         [nil] = 0,
         
         [map] = 0,
         
         [cons] = 1,
         
         [filter] = 0,
         
         [filter2] = 0,
         
         [true] = 0,
         
         [false] = 0,
         
         [app#](x0, x1) = x0
        Strict:
         app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)
         1 + 1x + 0fun + 1xs >= 0 + 0x + 0fun + 1xs
         app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)
         1 + 1x + 0fun + 1xs >= 0 + 1x + 0fun
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs)
         1 + 1x + 0fun + 1xs >= 0 + 0fun + 1xs
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x)
         1 + 1x + 0fun + 1xs >= 0 + 1x + 0fun
         app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs)
         0 + 0x + 0fun + 1xs >= 0 + 0fun + 1xs
         app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs)
         0 + 0x + 0fun + 1xs >= 0 + 0fun + 1xs
        Weak:
         app(app(filter(), fun), nil()) -> nil()
         0 + 1fun >= 0
         app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs)
         1 + 1x + 1fun + 1xs >= 0 + 2x + 2fun + 1xs
         app(app(map(), fun), nil()) -> nil()
         0 + 1fun >= 0
         app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs))
         1 + 1x + 1fun + 1xs >= 1 + 1x + 2fun + 1xs
         app(app(g(), x), y) -> y
         0 + 1x + 1y >= 1y
         app(app(g(), x), y) -> x
         0 + 1x + 1y >= 1x
         app(app(plus(), x), 0()) -> x
         2 + 1x >= 1x
         app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y))
         2 + 1x + 1y >= 2 + 1x + 1y
         app(app(app(f(), 0()), app(s(), 0())), x) -> app(app(app(f(), x), app(app(plus(), x), x)), x)
         4 + 1x >= 2 + 4x
         app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs)
         0 + 1x + 1fun + 1xs >= 0 + 1fun + 1xs
         app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs))
         0 + 1x + 1fun + 1xs >= 1 + 1x + 1fun + 1xs
       SCCS (0):
        
        
        
     
     
     
     
     SCC (1):
      Strict:
       {app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), 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(), 0()), app(s(), 0())), x) -> app(app(app(f(), x), app(app(plus(), x), x)), x),
                         app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                                 app(app(plus(), x), 0()) -> x,
                                      app(app(g(), x), y) -> x,
                                      app(app(g(), x), y) -> y,
            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()}
      Fail
     
     
     
     
     SCC (1):
      Strict:
       {app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), 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(app(f(), 0()), app(s(), 0())), x) -> app(app(app(f(), x), app(app(plus(), x), x)), x),
                         app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                                 app(app(plus(), x), 0()) -> x,
                                      app(app(g(), x), y) -> x,
                                      app(app(g(), x), y) -> y,
            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()}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [app](x0, x1) = x0 + x1,
        
        [plus] = 0,
        
        [0] = 0,
        
        [s] = 1,
        
        [f] = 1,
        
        [g] = 0,
        
        [nil] = 0,
        
        [map] = 0,
        
        [cons] = 0,
        
        [filter] = 0,
        
        [filter2] = 0,
        
        [true] = 0,
        
        [false] = 0,
        
        [app#](x0, x1) = x0 + 1
       Strict:
        app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y)
        2 + 0x + 1y >= 1 + 0x + 1y
       Weak:
        app(app(filter(), fun), nil()) -> nil()
        0 + 1fun >= 0
        app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs)
        0 + 1x + 1fun + 1xs >= 0 + 2x + 2fun + 1xs
        app(app(map(), fun), nil()) -> nil()
        0 + 1fun >= 0
        app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs))
        0 + 1x + 1fun + 1xs >= 0 + 1x + 2fun + 1xs
        app(app(g(), x), y) -> y
        0 + 1x + 1y >= 1y
        app(app(g(), x), y) -> x
        0 + 1x + 1y >= 1x
        app(app(plus(), x), 0()) -> x
        0 + 1x >= 1x
        app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y))
        1 + 1x + 1y >= 1 + 1x + 1y
        app(app(app(f(), 0()), app(s(), 0())), x) -> app(app(app(f(), x), app(app(plus(), x), x)), x)
        2 + 1x >= 1 + 4x
        app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs)
        0 + 1x + 1fun + 1xs >= 0 + 1fun + 1xs
        app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs))
        0 + 1x + 1fun + 1xs >= 0 + 1x + 1fun + 1xs
      Qed