MAYBE
Time: 1.181837
TRS:
 {app(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)),
          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(g(), 0()), 1()) -> 0(),
                                    app(app(g(), 0()), 1()) -> 1(),
              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(h(), app(app(g(), x), y)) -> app(h(), x)}
 DP:
  DP:
   {app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)),
    app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)),
    app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)),
    app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)),
    app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(h(), 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(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(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)),
                                app#(h(), app(app(g(), x), y)) -> app#(h(), x)}
  TRS:
  {app(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)),
           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(g(), 0()), 1()) -> 0(),
                                     app(app(g(), 0()), 1()) -> 1(),
               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(h(), app(app(g(), x), y)) -> app(h(), x)}
  EDG:
   {
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(h(), app(app(g(), x), y)) -> app#(h(), x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), 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(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(h(), x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(h(), app(app(g(), x), y)) -> app#(h(), x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), 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(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(h(), x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(h(), app(app(g(), x), y)) -> app#(h(), 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(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(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(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(h(), 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(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), 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(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), 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(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), 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(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(h(), app(app(g(), x), y)) -> app#(h(), 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#(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(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
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    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(h(), app(app(g(), x), y)) -> app#(h(), x))
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    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(h(), x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), 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(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app#(h(), app(app(g(), x), y)) -> app#(h(), x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(h(), x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), 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(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), 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(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(h(), app(app(g(), x), y)) -> app#(h(), x))
   }
   EDG:
    {
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(h(), app(app(g(), x), y)) -> app#(h(), 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(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(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(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(h(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), 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(), 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#(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(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#(fun, x))
     (app#(h(), app(app(g(), x), y)) -> app#(h(), x), app#(h(), app(app(g(), x), y)) -> app#(h(), x))
     (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(h(), x), app#(h(), app(app(g(), x), y)) -> app#(h(), 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(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(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(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(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(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(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#(filter2(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(h(), 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(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(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(h(), app(app(g(), x), y)) -> app#(h(), x))
     (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)))
     (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)))
     (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(f(), app(app(g(), x), y)), app(app(g(), x), y)))
     (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(f(), app(app(g(), x), y)))
     (app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)), app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(h(), x))
    }
    STATUS:
     arrows: 0.857143
     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)}
      Scc:
       {app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x))}
      Scc:
       {app#(h(), app(app(g(), x), y)) -> app#(h(), 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(f(), 0()), 1()), app(app(g(), x), y)), z) -> app(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)),
                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(g(), 0()), 1()) -> 0(),
                                          app(app(g(), 0()), 1()) -> 1(),
                    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(h(), app(app(g(), x), y)) -> app(h(), x)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [app](x0, x1) = x0 + x1,
         
         [f] = 1,
         
         [g] = 1,
         
         [h] = 0,
         
         [0] = 1,
         
         [1] = 1,
         
         [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#(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(h(), app(app(g(), x), y)) -> app(h(), x)
         1 + 1x + 1y >= 0 + 1x
         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(), 0()), 1()) -> 1()
         3 >= 1
         app(app(g(), 0()), 1()) -> 0()
         3 >= 1
         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
         app(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x))
         4 + 1x + 1y + 1z >= 4 + 4x + 3y
       SCCS (0):
        
        
        
     
     
     
     
     
     
     
     
     
     
     SCC (1):
      Strict:
       {app#(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app#(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x))}
      Weak:
      {app(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)),
               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(g(), 0()), 1()) -> 0(),
                                         app(app(g(), 0()), 1()) -> 1(),
                   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(h(), app(app(g(), x), y)) -> app(h(), x)}
      Fail
     
     SCC (1):
      Strict:
       {app#(h(), app(app(g(), x), y)) -> app#(h(), x)}
      Weak:
      {app(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x)),
               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(g(), 0()), 1()) -> 0(),
                                         app(app(g(), 0()), 1()) -> 1(),
                   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(h(), app(app(g(), x), y)) -> app(h(), x)}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [app](x0, x1) = x0 + x1,
        
        [f] = 0,
        
        [g] = 1,
        
        [h] = 0,
        
        [0] = 1,
        
        [1] = 0,
        
        [nil] = 0,
        
        [map] = 0,
        
        [cons] = 0,
        
        [filter] = 0,
        
        [filter2] = 0,
        
        [true] = 0,
        
        [false] = 0,
        
        [app#](x0, x1) = x0 + 1
       Strict:
        app#(h(), app(app(g(), x), y)) -> app#(h(), x)
        2 + 1x + 1y >= 1 + 1x
       Weak:
        app(h(), app(app(g(), x), y)) -> app(h(), x)
        1 + 1x + 1y >= 0 + 1x
        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(), 0()), 1()) -> 1()
        2 >= 0
        app(app(g(), 0()), 1()) -> 0()
        2 >= 1
        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
        app(app(app(app(f(), 0()), 1()), app(app(g(), x), y)), z) -> app(app(app(app(f(), app(app(g(), x), y)), app(app(g(), x), y)), app(app(g(), x), y)), app(h(), x))
        2 + 1x + 1y + 1z >= 3 + 4x + 3y
      Qed