MAYBE
Time: 0.055214
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(minus(), x), 0()) -> x,
         app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), 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(),
                               app(f(), app(s(), x)) -> app(app(minus(), app(s(), x)), app(g(), app(f(), x))),
                                       app(f(), 0()) -> app(s(), 0()),
                               app(g(), app(s(), x)) -> app(app(minus(), app(s(), x)), app(f(), app(g(), x))),
                                       app(g(), 0()) -> 0()}
 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(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y),
           app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)),
                                 app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))),
                                 app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)),
                                 app#(f(), app(s(), x)) -> app#(f(), x),
                                 app#(f(), app(s(), x)) -> app#(g(), app(f(), x)),
                                         app#(f(), 0()) -> app#(s(), 0()),
                                 app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))),
                                 app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)),
                                 app#(g(), app(s(), x)) -> app#(f(), app(g(), x)),
                                 app#(g(), app(s(), x)) -> app#(g(), 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(minus(), x), 0()) -> x,
          app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), 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(),
                                app(f(), app(s(), x)) -> app(app(minus(), app(s(), x)), app(g(), app(f(), x))),
                                        app(f(), 0()) -> app(s(), 0()),
                                app(g(), app(s(), x)) -> app(app(minus(), app(s(), x)), app(f(), app(g(), x))),
                                        app(g(), 0()) -> 0()}
  UR:
   { 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(minus(), x), 0()) -> x,
           app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), 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(),
                                 app(f(), app(s(), x)) -> app(app(minus(), app(s(), x)), app(g(), app(f(), x))),
                                         app(f(), 0()) -> app(s(), 0()),
                                 app(g(), app(s(), x)) -> app(app(minus(), app(s(), x)), app(f(), app(g(), x))),
                                         app(g(), 0()) -> 0(),
                                               a(z, w) -> z,
                                               a(z, w) -> w}
   EDG:
    {
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(f(), 0()) -> app#(s(), 0()))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(f(), 0()) -> app#(s(), 0()), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(f(), 0()) -> app#(s(), 0()), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
     (app#(f(), 0()) -> app#(s(), 0()), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(f(), 0()) -> app#(s(), 0()), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
     (app#(f(), 0()) -> app#(s(), 0()), app#(f(), 0()) -> app#(s(), 0()))
     (app#(f(), 0()) -> app#(s(), 0()), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
     (app#(f(), 0()) -> app#(s(), 0()), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(f(), 0()) -> app#(s(), 0()), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(f(), 0()) -> app#(s(), 0()), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
     (app#(f(), 0()) -> app#(s(), 0()), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(f(), 0()) -> app#(s(), 0()), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(f(), 0()) -> app#(s(), 0()), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(f(), 0()) -> app#(s(), 0()), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(f(), 0()) -> app#(s(), 0()), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(f(), 0()) -> app#(s(), 0()), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(f(), 0()) -> app#(s(), 0()), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(f(), 0()) -> app#(s(), 0()), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(f(), 0()) -> app#(s(), 0()), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(f(), 0()) -> app#(s(), 0()), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(f(), 0()) -> app#(s(), 0()), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(f(), 0()) -> app#(s(), 0()), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(f(), 0()) -> app#(s(), 0()), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(f(), 0()) -> app#(s(), 0()), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(f(), 0()) -> app#(s(), 0()), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(f(), 0()) -> app#(s(), 0()), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(f(), 0()) -> app#(s(), 0()), 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#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), 0()) -> app#(s(), 0()))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), 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#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(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(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#(fun, x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (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(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> 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#(filter(), fun))
     (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(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), 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(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#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(f(), 0()) -> app#(s(), 0()))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), 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#(app(app(app(filter2(), app(fun, x)), fun), x), xs), 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#(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(app(app(filter2(), app(fun, x)), fun), x), xs), 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(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(app(filter2(), app(fun, x)), fun), x), 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#(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#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> 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#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
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     (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(), 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(), 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#(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)))
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     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
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     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
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     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
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     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
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     (app#(g(), app(s(), x)) -> app#(g(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
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     (app#(g(), app(s(), x)) -> app#(g(), 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#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
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     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
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     (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
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     (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
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     (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
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     (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), 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#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(f(), 0()) -> app#(s(), 0()))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(f(), app(s(), 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#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), 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(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(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), 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(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#(g(), app(s(), x)) -> app#(g(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(f(), 0()) -> app#(s(), 0()))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), 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(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (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#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(f(), 0()) -> app#(s(), 0()))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), 0()) -> app#(s(), 0()))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(f(), 0()) -> app#(s(), 0()))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
     (app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
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     (app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)), app#(g(), app(s(), x)) -> app#(minus(), app(s(), 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(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(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
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     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(g(), app(s(), x)) -> app#(g(), 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(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), 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(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)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(f(), 0()) -> app#(s(), 0()))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(g(), app(s(), x)) -> app#(g(), x))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(f(), 0()) -> app#(s(), 0()))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
     (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(g(), app(s(), x)) -> app#(g(), x))
     (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(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> 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#(cons(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (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(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
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     (app#(app(app(app(filter2(), true()), fun), x), xs) -> 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(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(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), 0()) -> app#(s(), 0()))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(g(), app(s(), x)) -> app#(g(), 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#(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(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#(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#(filter(), fun))
     (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(filter2(), app(fun, x)), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), 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(filter2(), app(fun, x)), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> 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(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#(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(filter2(), app(fun, x)), fun), 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(filter2(), app(fun, x)), fun), 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#(app(filter2(), app(fun, x)), fun))
     (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(filter2(), app(fun, x)), fun), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(f(), 0()) -> app#(s(), 0()))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(g(), app(s(), x)) -> app#(g(), 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#(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(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#(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#(filter(), fun))
     (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(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), 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(filter2(), app(fun, x)), 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#(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(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(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(filter2(), app(fun, x)), 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(app(filter2(), app(fun, x)), 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#(app(filter2(), app(fun, x)), fun))
     (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(filter2(), app(fun, x)), fun), x), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(f(), app(s(), x)) -> app#(f(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(f(), 0()) -> app#(s(), 0()))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(g(), app(s(), x)) -> app#(g(), x))
    }
    EDG:
     {
      (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
      (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
      (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#(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(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(), 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(), 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#(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#(g(), app(s(), x)) -> app#(g(), x), app#(g(), app(s(), x)) -> app#(g(), x))
      (app#(g(), app(s(), x)) -> app#(g(), x), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
      (app#(g(), app(s(), x)) -> app#(g(), x), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
      (app#(g(), app(s(), x)) -> app#(g(), x), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(g(), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), 0()) -> app#(s(), 0()))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(f(), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(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(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
      (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
      (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
      (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(g(), app(s(), x)) -> app#(g(), x))
      (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
      (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
      (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
      (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), 0()) -> app#(s(), 0()))
      (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
      (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), app(s(), x)) -> app#(f(), x))
      (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
      (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
      (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
      (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), 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(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(f(), x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), 0()) -> app#(s(), 0()))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(g(), x))
      (app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
      (app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
      (app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(f(), x))
      (app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
      (app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), 0()) -> app#(s(), 0()))
      (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)))
     }
     EDG:
      {
       (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
       (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
       (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#(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(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(), 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(), 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#(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#(g(), app(s(), x)) -> app#(g(), x), app#(g(), app(s(), x)) -> app#(g(), x))
       (app#(g(), app(s(), x)) -> app#(g(), x), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
       (app#(g(), app(s(), x)) -> app#(g(), x), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
       (app#(g(), app(s(), x)) -> app#(g(), x), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(g(), x))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), 0()) -> app#(s(), 0()))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(f(), x))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(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(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
       (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
       (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
       (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(g(), app(s(), x)) -> app#(g(), x))
       (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
       (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
       (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
       (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), 0()) -> app#(s(), 0()))
       (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
       (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), app(s(), x)) -> app#(f(), x))
       (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
       (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
       (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
       (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), 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(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(f(), x))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), 0()) -> app#(s(), 0()))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(g(), x))
       (app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
       (app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
       (app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(f(), x))
       (app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
       (app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), 0()) -> app#(s(), 0()))
       (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)))
      }
      EDG:
       {
        (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
        (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
        (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#(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(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(), 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(), 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#(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#(g(), app(s(), x)) -> app#(g(), x), app#(g(), app(s(), x)) -> app#(g(), x))
        (app#(g(), app(s(), x)) -> app#(g(), x), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
        (app#(g(), app(s(), x)) -> app#(g(), x), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
        (app#(g(), app(s(), x)) -> app#(g(), x), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(g(), x))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), 0()) -> app#(s(), 0()))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(f(), x))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(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(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
        (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
        (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
        (app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
        (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(g(), app(s(), x)) -> app#(g(), x))
        (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
        (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
        (app#(f(), app(s(), x)) -> app#(g(), app(f(), x)), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
        (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), 0()) -> app#(s(), 0()))
        (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
        (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), app(s(), x)) -> app#(f(), x))
        (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
        (app#(g(), app(s(), x)) -> app#(f(), app(g(), x)), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
        (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
        (app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), 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(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(f(), x))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), 0()) -> app#(s(), 0()))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(f(), app(g(), x))))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(minus(), app(s(), x)))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(f(), app(g(), x)))
        (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(s(), x)) -> app#(g(), x))
        (app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(app(minus(), app(s(), x)), app(g(), app(f(), x))))
        (app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(minus(), app(s(), x)))
        (app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(f(), x))
        (app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(g(), app(f(), x)))
        (app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), 0()) -> app#(s(), 0()))
        (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)))
       }
       STATUS:
        arrows: 0.857988
        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#(f(), app(s(), x)) -> app#(f(), x),
           app#(f(), app(s(), x)) -> app#(g(), app(f(), x)),
           app#(g(), app(s(), x)) -> app#(f(), app(g(), x)),
           app#(g(), app(s(), x)) -> app#(g(), x)}
         Scc:
          {app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), 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(minus(), x), 0()) -> x,
                  app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), 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(),
                                        app(f(), app(s(), x)) -> app(app(minus(), app(s(), x)), app(g(), app(f(), x))),
                                                app(f(), 0()) -> app(s(), 0()),
                                        app(g(), app(s(), x)) -> app(app(minus(), app(s(), x)), app(f(), app(g(), x))),
                                                app(g(), 0()) -> 0()}
          Open
         SCC (4):
          Strict:
           {app#(f(), app(s(), x)) -> app#(f(), x),
            app#(f(), app(s(), x)) -> app#(g(), app(f(), x)),
            app#(g(), app(s(), x)) -> app#(f(), app(g(), x)),
            app#(g(), app(s(), x)) -> app#(g(), 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(minus(), x), 0()) -> x,
                  app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), 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(),
                                        app(f(), app(s(), x)) -> app(app(minus(), app(s(), x)), app(g(), app(f(), x))),
                                                app(f(), 0()) -> app(s(), 0()),
                                        app(g(), app(s(), x)) -> app(app(minus(), app(s(), x)), app(f(), app(g(), x))),
                                                app(g(), 0()) -> 0()}
          Open
         
         
         
         
         
         
         
         
         
         
         
         
         
         SCC (1):
          Strict:
           {app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), 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(minus(), x), 0()) -> x,
                  app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), 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(),
                                        app(f(), app(s(), x)) -> app(app(minus(), app(s(), x)), app(g(), app(f(), x))),
                                                app(f(), 0()) -> app(s(), 0()),
                                        app(g(), app(s(), x)) -> app(app(minus(), app(s(), x)), app(f(), app(g(), x))),
                                                app(g(), 0()) -> 0()}
          Open