MAYBE
Time: 0.217788
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()}
  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))
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    (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))
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    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(double(), app(s(), x)) -> app#(double(), x))
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    (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))
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    (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))))
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    (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))
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    (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))
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    (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))
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    (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))
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    (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))
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    (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)))
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    (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))
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    (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))
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    (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))
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    (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))
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    (app#(app(plus(), app(s(), x)), y) -> app#(plus(), app(app(minus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(double(), y))
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    (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)))
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    (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))
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    (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))
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    (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))
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    (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))
    (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#(filter(), f), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), app(app(minus(), x), y)), app(double(), y)))
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    (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))
   }
   EDG:
    {
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(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(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(double(), app(s(), x)) -> 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#(f, x), 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#(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#(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(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(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#(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#(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#(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#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (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#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), 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(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(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
     (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#(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#(f, x), 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(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#(minus(), x))
     (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(map(), 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#(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#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (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#(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#(f, 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(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(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(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(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(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(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(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#(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#(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#(filter(), f))
     (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#(f, x), 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(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#(minus(), x))
     (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#(f, x), 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), 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(), 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#(minus(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(s(), 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(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(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), 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#(plus(), x))
     (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#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> 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#(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(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#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> 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#(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(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#(filter2(), app(f, 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#(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#(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#(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#(double(), x))
     (app#(double(), app(s(), x)) -> app#(double(), x), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
     (app#(double(), app(s(), x)) -> app#(double(), x), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
     (app#(double(), app(s(), x)) -> app#(double(), x), app#(double(), app(s(), x)) -> app#(double(), x))
     (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))
    }
    EDG:
     {
      (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
      (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
      (app#(app(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(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(double(), app(s(), x)) -> 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#(f, x), 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#(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#(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(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(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#(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#(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#(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#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
      (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#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), 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(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(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
      (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#(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#(f, x), 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(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#(minus(), x))
      (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(map(), 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#(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#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
      (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#(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#(f, 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(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(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(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(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(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(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(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#(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#(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#(filter(), f))
      (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#(f, x), 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(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#(minus(), x))
      (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#(f, x), 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), 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(), 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#(minus(), x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(s(), 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(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(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), 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#(plus(), x))
      (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#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> 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#(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(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#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> 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#(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(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#(filter2(), app(f, 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#(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#(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#(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#(double(), x))
      (app#(double(), app(s(), x)) -> app#(double(), x), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
      (app#(double(), app(s(), x)) -> app#(double(), x), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
      (app#(double(), app(s(), x)) -> app#(double(), x), app#(double(), app(s(), x)) -> app#(double(), x))
      (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))
     }
     EDG:
      {
       (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
       (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
       (app#(app(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(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(double(), app(s(), x)) -> 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#(f, x), 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#(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#(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(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(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#(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#(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#(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#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
       (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#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), 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(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(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(s(), y))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(minus(), x))
       (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#(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#(f, x), 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(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#(minus(), x))
       (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(map(), 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#(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#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
       (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#(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#(f, 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(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(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(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(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(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(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(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#(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#(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#(filter(), f))
       (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#(f, x), 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(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#(minus(), x))
       (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#(f, x), 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), 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(), 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#(minus(), x))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(s(), 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(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(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), 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#(plus(), x))
       (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#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> 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#(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(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#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> 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#(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(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#(filter2(), app(f, 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#(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#(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#(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#(double(), x))
       (app#(double(), app(s(), x)) -> app#(double(), x), app#(double(), app(s(), x)) -> app#(s(), app(s(), app(double(), x))))
       (app#(double(), app(s(), x)) -> app#(double(), x), app#(double(), app(s(), x)) -> app#(s(), app(double(), x)))
       (app#(double(), app(s(), x)) -> app#(double(), x), app#(double(), app(s(), x)) -> app#(double(), x))
       (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))
      }
      STATUS:
       arrows: 0.869927
       SCCS (4):
        Scc:
         { 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(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(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)}
        Scc:
         {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))}
        Scc:
         {app#(double(), app(s(), x)) -> app#(double(), x)}
        Scc:
         {app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y)}
        
        SCC (6):
         Strict:
          { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), 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#(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#(f, x),
             app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)}
         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()}
         POLY:
          Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
          Interpretation:
           [app](x0, x1) = x0 + x1,
           
           [minus] = 1,
           
           [0] = 1,
           
           [s] = 1,
           
           [double] = 1,
           
           [plus] = 0,
           
           [nil] = 0,
           
           [map] = 0,
           
           [cons] = 1,
           
           [filter] = 0,
           
           [filter2] = 0,
           
           [true] = 0,
           
           [false] = 0,
           
           [app#](x0, x1) = x0
          Strict:
           app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)
           1 + 1x + 0f + 1xs >= 0 + 0x + 0f + 1xs
           app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)
           1 + 1x + 0f + 1xs >= 0 + 1x + 0f
           app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)
           1 + 1x + 0f + 1xs >= 0 + 0f + 1xs
           app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)
           1 + 1x + 0f + 1xs >= 0 + 1x + 0f
           app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs)
           0 + 0x + 0f + 1xs >= 0 + 0f + 1xs
           app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs)
           0 + 0x + 0f + 1xs >= 0 + 0f + 1xs
          Weak:
           app(double(), 0()) -> 0()
           2 >= 1
           app(double(), app(s(), x)) -> app(s(), app(s(), app(double(), x)))
           2 + 1x >= 3 + 1x
           app(app(filter(), f), nil()) -> nil()
           0 + 1f >= 0
           app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs)
           1 + 1x + 1f + 1xs >= 0 + 2x + 2f + 1xs
           app(app(map(), f), nil()) -> nil()
           0 + 1f >= 0
           app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs))
           1 + 1x + 1f + 1xs >= 1 + 1x + 2f + 1xs
           app(app(plus(), 0()), y) -> y
           1 + 1y >= 1y
           app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y)))
           1 + 1x + 1y >= 3 + 1x + 2y
           app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y))
           1 + 1x + 1y >= 1 + 1x + 1y
           app(app(plus(), app(s(), x)), y) -> app(app(plus(), x), app(s(), y))
           1 + 1x + 1y >= 1 + 1x + 1y
           app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y)
           3 + 1x + 1y >= 1 + 1x + 1y
           app(app(minus(), x), 0()) -> x
           2 + 1x >= 1x
           app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs)
           0 + 1x + 1f + 1xs >= 0 + 1f + 1xs
           app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs))
           0 + 1x + 1f + 1xs >= 1 + 1x + 1f + 1xs
         SCCS (0):
          
          
          
       
       
       
       
       
       
       
       
       SCC (3):
        Strict:
         {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))}
        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
       
       
       
       SCC (1):
        Strict:
         {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()}
        POLY:
         Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
         Interpretation:
          [app](x0, x1) = x0 + x1,
          
          [minus] = 1,
          
          [0] = 1,
          
          [s] = 1,
          
          [double] = 1,
          
          [plus] = 0,
          
          [nil] = 0,
          
          [map] = 0,
          
          [cons] = 0,
          
          [filter] = 0,
          
          [filter2] = 0,
          
          [true] = 0,
          
          [false] = 0,
          
          [app#](x0, x1) = x0 + x1
         Strict:
          app#(double(), app(s(), x)) -> app#(double(), x)
          2 + 1x >= 1 + 1x
         Weak:
          app(double(), 0()) -> 0()
          2 >= 1
          app(double(), app(s(), x)) -> app(s(), app(s(), app(double(), x)))
          2 + 1x >= 3 + 1x
          app(app(filter(), f), nil()) -> nil()
          0 + 1f >= 0
          app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs)
          0 + 1x + 1f + 1xs >= 0 + 2x + 2f + 1xs
          app(app(map(), f), nil()) -> nil()
          0 + 1f >= 0
          app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs))
          0 + 1x + 1f + 1xs >= 0 + 1x + 2f + 1xs
          app(app(plus(), 0()), y) -> y
          1 + 1y >= 1y
          app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y)))
          1 + 1x + 1y >= 3 + 1x + 2y
          app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y))
          1 + 1x + 1y >= 1 + 1x + 1y
          app(app(plus(), app(s(), x)), y) -> app(app(plus(), x), app(s(), y))
          1 + 1x + 1y >= 1 + 1x + 1y
          app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y)
          3 + 1x + 1y >= 1 + 1x + 1y
          app(app(minus(), x), 0()) -> x
          2 + 1x >= 1x
          app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs)
          0 + 1x + 1f + 1xs >= 0 + 1f + 1xs
          app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs))
          0 + 1x + 1f + 1xs >= 0 + 1x + 1f + 1xs
        Qed
       
       
       
       
       
       SCC (1):
        Strict:
         {app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y)}
        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()}
        POLY:
         Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
         Interpretation:
          [app](x0, x1) = x0 + x1,
          
          [minus] = 1,
          
          [0] = 1,
          
          [s] = 1,
          
          [double] = 1,
          
          [plus] = 0,
          
          [nil] = 0,
          
          [map] = 0,
          
          [cons] = 0,
          
          [filter] = 0,
          
          [filter2] = 0,
          
          [true] = 0,
          
          [false] = 0,
          
          [app#](x0, x1) = x0
         Strict:
          app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y)
          1 + 0x + 1y >= 0 + 0x + 1y
         Weak:
          app(double(), 0()) -> 0()
          2 >= 1
          app(double(), app(s(), x)) -> app(s(), app(s(), app(double(), x)))
          2 + 1x >= 3 + 1x
          app(app(filter(), f), nil()) -> nil()
          0 + 1f >= 0
          app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs)
          0 + 1x + 1f + 1xs >= 0 + 2x + 2f + 1xs
          app(app(map(), f), nil()) -> nil()
          0 + 1f >= 0
          app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs))
          0 + 1x + 1f + 1xs >= 0 + 1x + 2f + 1xs
          app(app(plus(), 0()), y) -> y
          1 + 1y >= 1y
          app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), app(app(minus(), x), y)), app(double(), y)))
          1 + 1x + 1y >= 3 + 1x + 2y
          app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y))
          1 + 1x + 1y >= 1 + 1x + 1y
          app(app(plus(), app(s(), x)), y) -> app(app(plus(), x), app(s(), y))
          1 + 1x + 1y >= 1 + 1x + 1y
          app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y)
          3 + 1x + 1y >= 1 + 1x + 1y
          app(app(minus(), x), 0()) -> x
          2 + 1x >= 1x
          app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs)
          0 + 1x + 1f + 1xs >= 0 + 1f + 1xs
          app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs))
          0 + 1x + 1f + 1xs >= 0 + 1x + 1f + 1xs
        Qed