YES
Time: 0.098305
TRS:
 { app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
  app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
               app(app(app(f(), x), y), app(s(), z)) -> app(s(), app(app(app(f(), 0()), 1()), z)),
                     app(app(app(f(), 0()), 1()), x) -> app(app(app(f(), app(s(), x)), x), x),
       app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                         app(app(map(), fun), nil()) -> nil(),
    app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                      app(app(filter(), fun), nil()) -> nil()}
 DP:
  DP:
   { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)),
     app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs),
     app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x),
     app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun),
    app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
    app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun),
                 app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z),
                 app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()),
                 app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()),
                 app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)),
                       app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x),
                       app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x),
                       app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)),
                       app#(app(app(f(), 0()), 1()), x) -> app#(s(), x),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x))}
  TRS:
  { app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
   app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
                app(app(app(f(), x), y), app(s(), z)) -> app(s(), app(app(app(f(), 0()), 1()), z)),
                      app(app(app(f(), 0()), 1()), x) -> app(app(app(f(), app(s(), x)), x), x),
        app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                          app(app(map(), fun), nil()) -> nil(),
     app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                       app(app(filter(), fun), nil()) -> nil()}
  EDG:
   {
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
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    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
   }
   EDG:
    {
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
     (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
     (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
     (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
     (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
     (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
     (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
     (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
     (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
     (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
     (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
     (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
    }
    EDG:
     {
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
      (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
      (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
      (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
      (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
      (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
      (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
      (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
      (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
      (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
      (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
      (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
      (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
      (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
      (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
      (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
      (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
      (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
      (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
      (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
      (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
     }
     EDG:
      {
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
       (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
       (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
       (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
       (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
       (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
       (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
       (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
       (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
       (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
       (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
       (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
       (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
       (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
       (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
       (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
       (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
       (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x))
       (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), 0()), 1()), x) -> app#(app(f(), app(s(), x)), x))
       (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), 0()), 1()), x) -> app#(f(), app(s(), x)))
       (app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z), app#(app(app(f(), 0()), 1()), x) -> app#(s(), x))
       (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z))
       (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(app(f(), 0()), 1()))
       (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(f(), 0()))
       (app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x), app#(app(app(f(), x), y), app(s(), z)) -> app#(s(), app(app(app(f(), 0()), 1()), z)))
      }
      STATUS:
       arrows: 0.863894
       SCCS (2):
        Scc:
         { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs),
          app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
               app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
               app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
            app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)}
        Scc:
         {app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z),
                app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x)}
        
        SCC (5):
         Strict:
          { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs),
           app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
                app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
                app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
             app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)}
         Weak:
         { app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
          app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
                       app(app(app(f(), x), y), app(s(), z)) -> app(s(), app(app(app(f(), 0()), 1()), z)),
                             app(app(app(f(), 0()), 1()), x) -> app(app(app(f(), app(s(), x)), x), x),
               app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                                 app(app(map(), fun), nil()) -> nil(),
            app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                              app(app(filter(), fun), nil()) -> nil()}
         POLY:
          Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
          Interpretation:
           [app](x0, x1) = x0 + x1 + 1,
           
           [f] = 1,
           
           [s] = 0,
           
           [0] = 1,
           
           [1] = 1,
           
           [nil] = 1,
           
           [map] = 1,
           
           [cons] = 0,
           
           [filter] = 1,
           
           [filter2] = 0,
           
           [true] = 0,
           
           [false] = 0,
           
           [app#](x0, x1) = x0
          Strict:
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x)
           2 + 1x + 0fun + 1xs >= 0 + 1x + 0fun
           app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs)
           2 + 1x + 0fun + 1xs >= 0 + 0fun + 1xs
           app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x)
           2 + 1x + 0fun + 1xs >= 0 + 1x + 0fun
           app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs)
           0 + 0x + 0fun + 1xs >= 0 + 0fun + 1xs
           app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs)
           0 + 0x + 0fun + 1xs >= 0 + 0fun + 1xs
          Weak:
           app(app(filter(), fun), nil()) -> nil()
           4 + 1fun >= 1
           app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs)
           5 + 1x + 1fun + 1xs >= 5 + 2x + 2fun + 1xs
           app(app(map(), fun), nil()) -> nil()
           4 + 1fun >= 1
           app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs))
           5 + 1x + 1fun + 1xs >= 6 + 1x + 2fun + 1xs
           app(app(app(f(), 0()), 1()), x) -> app(app(app(f(), app(s(), x)), x), x)
           6 + 1x >= 5 + 3x
           app(app(app(f(), x), y), app(s(), z)) -> app(s(), app(app(app(f(), 0()), 1()), z))
           5 + 1x + 1z + 1y >= 7 + 1z
           app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs)
           4 + 1x + 1fun + 1xs >= 3 + 1fun + 1xs
           app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs))
           4 + 1x + 1fun + 1xs >= 5 + 1x + 1fun + 1xs
         SCCS (0):
          
          
          
       
       
       
       
       
       
       
       
       SCC (2):
        Strict:
         {app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z),
                app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x)}
        Weak:
        { app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
         app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
                      app(app(app(f(), x), y), app(s(), z)) -> app(s(), app(app(app(f(), 0()), 1()), z)),
                            app(app(app(f(), 0()), 1()), x) -> app(app(app(f(), app(s(), x)), x), x),
              app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                                app(app(map(), fun), nil()) -> nil(),
           app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                             app(app(filter(), fun), nil()) -> nil()}
        POLY:
         Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
         Interpretation:
          [app](x0, x1) = x0 + x1,
          
          [f] = 0,
          
          [s] = 1,
          
          [0] = 0,
          
          [1] = 0,
          
          [nil] = 0,
          
          [map] = 0,
          
          [cons] = 0,
          
          [filter] = 0,
          
          [filter2] = 0,
          
          [true] = 0,
          
          [false] = 0,
          
          [app#](x0, x1) = x0
         Strict:
          app#(app(app(f(), 0()), 1()), x) -> app#(app(app(f(), app(s(), x)), x), x)
          0 + 1x >= 0 + 1x
          app#(app(app(f(), x), y), app(s(), z)) -> app#(app(app(f(), 0()), 1()), z)
          1 + 0x + 1z + 0y >= 0 + 1z
         Weak:
          app(app(filter(), fun), nil()) -> nil()
          0 + 1fun >= 0
          app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs)
          0 + 1x + 1fun + 1xs >= 0 + 2x + 2fun + 1xs
          app(app(map(), fun), nil()) -> nil()
          0 + 1fun >= 0
          app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs))
          0 + 1x + 1fun + 1xs >= 0 + 1x + 2fun + 1xs
          app(app(app(f(), 0()), 1()), x) -> app(app(app(f(), app(s(), x)), x), x)
          0 + 1x >= 1 + 3x
          app(app(app(f(), x), y), app(s(), z)) -> app(s(), app(app(app(f(), 0()), 1()), z))
          1 + 1x + 1z + 1y >= 1 + 1z
          app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs)
          0 + 1x + 1fun + 1xs >= 0 + 1fun + 1xs
          app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs))
          0 + 1x + 1fun + 1xs >= 0 + 1x + 1fun + 1xs
        SCCS (0):