MAYBE
Time: 0.219968
TRS:
 { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
  app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                         app(app(minus(), x), 0()) -> x,
       app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
                  app(app(plus(), app(s(), x)), y) -> app(app(plus(), x), app(s(), y)),
                  app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
                  app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))),
                          app(app(plus(), 0()), y) -> y,
       app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                         app(app(map(), f), nil()) -> nil(),
    app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                      app(app(filter(), f), nil()) -> nil(),
                        app(double(), app(s(), x)) -> app(s(), app(s(), app(double(), x))),
                                app(double(), 0()) -> 0()}
 DP:
  DP:
   { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f),
    app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
    app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f),
         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(plus(), app(s(), x)), y) -> app#(app(minus(), x), y),
                    app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y),
                    app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)),
                    app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)),
                    app#(app(plus(), app(s(), x)), y) -> app#(minus(), x),
                    app#(app(plus(), app(s(), x)), y) -> app#(s(), y),
                    app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)),
                    app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))),
                    app#(app(plus(), app(s(), x)), y) -> app#(double(), y),
                    app#(app(plus(), app(s(), x)), y) -> app#(plus(), x),
                    app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)),
                          app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))),
                          app#(double(), app(s(), x)) -> app#(s(), app(double(), x)),
                          app#(double(), app(s(), x)) -> app#(double(), x)}
  TRS:
  { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
   app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                          app(app(minus(), x), 0()) -> x,
        app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
                   app(app(plus(), app(s(), x)), y) -> app(app(plus(), x), app(s(), y)),
                   app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
                   app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))),
                           app(app(plus(), 0()), y) -> y,
        app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                          app(app(map(), f), nil()) -> nil(),
     app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                       app(app(filter(), f), nil()) -> nil(),
                         app(double(), app(s(), x)) -> app(s(), app(s(), app(double(), x))),
                                 app(double(), 0()) -> 0()}
  UR:
   { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
    app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                           app(app(minus(), x), 0()) -> x,
         app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
                    app(app(plus(), app(s(), x)), y) -> app(app(plus(), x), app(s(), y)),
                    app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
                    app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))),
                            app(app(plus(), 0()), y) -> y,
         app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                           app(app(map(), f), nil()) -> nil(),
      app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                        app(app(filter(), f), nil()) -> nil(),
                          app(double(), app(s(), x)) -> app(s(), app(s(), app(double(), x))),
                                  app(double(), 0()) -> 0(),
                                             a(z, w) -> z,
                                             a(z, w) -> w}
   EDG:
    {
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), 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#(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()), f), x), xs) -> app#(filter(), f))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(app(app(filter2(), true()), f), 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()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
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     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
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     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
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     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
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     (app#(app(plus(), app(s(), x)), y) -> app#(s(), y), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), y), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
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     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(double(), app(s(), x)) -> app#(s(), app(double(), x)), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
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     (app#(app(plus(), app(s(), x)), y) -> app#(minus(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(minus(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(plus(), app(s(), x)), y) -> app#(minus(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(minus(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(minus(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(minus(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(minus(), x), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(plus(), app(s(), x)), y) -> app#(minus(), x), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(minus(), x), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), 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()), f), x), xs) -> app#(cons(), x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))), app#(double(), app(s(), x)) -> app#(double(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(plus(), app(s(), x)), y) -> app#(app(minus(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(double(), app(s(), x)) -> app#(double(), x))
    }
    STATUS:
     arrows: 0.000000
     SCCS (1):
      Scc:
       { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)),
         app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
         app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x),
         app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f),
        app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
        app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f),
             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(plus(), app(s(), x)), y) -> app#(app(minus(), x), y),
                        app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y),
                        app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)),
                        app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)),
                        app#(app(plus(), app(s(), x)), y) -> app#(minus(), x),
                        app#(app(plus(), app(s(), x)), y) -> app#(s(), y),
                        app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)),
                        app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))),
                        app#(app(plus(), app(s(), x)), y) -> app#(double(), y),
                        app#(app(plus(), app(s(), x)), y) -> app#(plus(), x),
                        app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)),
             app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
             app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
             app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)),
             app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)),
          app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x),
          app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs),
          app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x),
          app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f),
          app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)),
                              app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))),
                              app#(double(), app(s(), x)) -> app#(s(), app(double(), x)),
                              app#(double(), app(s(), x)) -> app#(double(), x)}
      
      SCC (31):
       Strict:
        { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)),
          app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
          app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x),
          app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f),
         app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
         app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f),
              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(plus(), app(s(), x)), y) -> app#(app(minus(), x), y),
                         app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y),
                         app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), app(s(), y)),
                         app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)),
                         app#(app(plus(), app(s(), x)), y) -> app#(minus(), x),
                         app#(app(plus(), app(s(), x)), y) -> app#(s(), y),
                         app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)),
                         app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))),
                         app#(app(plus(), app(s(), x)), y) -> app#(double(), y),
                         app#(app(plus(), app(s(), x)), y) -> app#(plus(), x),
                         app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)),
              app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
              app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
              app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)),
              app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)),
           app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x),
           app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs),
           app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x),
           app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f),
           app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)),
                               app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))),
                               app#(double(), app(s(), x)) -> app#(s(), app(double(), x)),
                               app#(double(), app(s(), x)) -> app#(double(), x)}
       Weak:
       { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
        app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                               app(app(minus(), x), 0()) -> x,
             app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
                        app(app(plus(), app(s(), x)), y) -> app(app(plus(), x), app(s(), y)),
                        app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
                        app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y))),
                                app(app(plus(), 0()), y) -> y,
             app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                               app(app(map(), f), nil()) -> nil(),
          app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                            app(app(filter(), f), nil()) -> nil(),
                              app(double(), app(s(), x)) -> app(s(), app(s(), app(double(), x))),
                                      app(double(), 0()) -> 0()}
       Fail