MAYBE
Time: 0.048208
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(and(), x), app(app(or(), y), z)) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
          app(app(and(), app(app(or(), y), z)), x) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
       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(not(), app(app(and(), x), y)) -> app(app(or(), app(not(), x)), app(not(), y)),
                  app(not(), app(app(or(), x), y)) -> app(app(and(), app(not(), x)), app(not(), y)),
                         app(not(), app(not(), x)) -> x}
 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(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y),
            app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z),
            app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
            app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)),
            app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y),
            app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z),
            app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
            app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x),
            app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), 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#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)),
                   app#(not(), app(app(and(), x), y)) -> app#(not(), x),
                   app#(not(), app(app(and(), x), y)) -> app#(not(), y),
                   app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)),
                    app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)),
                    app#(not(), app(app(or(), x), y)) -> app#(not(), x),
                    app#(not(), app(app(or(), x), y)) -> app#(not(), y),
                    app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), 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(and(), x), app(app(or(), y), z)) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
           app(app(and(), app(app(or(), y), z)), x) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
        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(not(), app(app(and(), x), y)) -> app(app(or(), app(not(), x)), app(not(), y)),
                   app(not(), app(app(or(), x), y)) -> app(app(and(), app(not(), x)), app(not(), y)),
                          app(not(), app(not(), x)) -> x}
  UR:
   { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
    app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
            app(app(and(), x), app(app(or(), y), z)) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
            app(app(and(), app(app(or(), y), z)), x) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
         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(not(), app(app(and(), x), y)) -> app(app(or(), app(not(), x)), app(not(), y)),
                    app(not(), app(app(or(), x), y)) -> app(app(and(), app(not(), x)), app(not(), y)),
                           app(not(), app(not(), x)) -> x,
                                             a(w, v) -> w,
                                             a(w, v) -> v}
   EDG:
    {
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (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(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), 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#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), 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#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), 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(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (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(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), 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#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
    }
    STATUS:
     arrows: 0.842773
     SCCS (3):
      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#(not(), app(app(and(), x), y)) -> app#(not(), x),
        app#(not(), app(app(and(), x), y)) -> app#(not(), y),
         app#(not(), app(app(or(), x), y)) -> app#(not(), x),
         app#(not(), app(app(or(), x), y)) -> app#(not(), y)}
      Scc:
       {app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y),
        app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z),
        app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y),
        app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z)}
      
      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(and(), x), app(app(or(), y), z)) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
                app(app(and(), app(app(or(), y), z)), x) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
             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(not(), app(app(and(), x), y)) -> app(app(or(), app(not(), x)), app(not(), y)),
                        app(not(), app(app(or(), x), y)) -> app(app(and(), app(not(), x)), app(not(), y)),
                               app(not(), app(not(), x)) -> x}
       Open
      SCC (4):
       Strict:
        {app#(not(), app(app(and(), x), y)) -> app#(not(), x),
         app#(not(), app(app(and(), x), y)) -> app#(not(), y),
          app#(not(), app(app(or(), x), y)) -> app#(not(), x),
          app#(not(), app(app(or(), x), y)) -> app#(not(), 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(and(), x), app(app(or(), y), z)) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
                app(app(and(), app(app(or(), y), z)), x) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
             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(not(), app(app(and(), x), y)) -> app(app(or(), app(not(), x)), app(not(), y)),
                        app(not(), app(app(or(), x), y)) -> app(app(and(), app(not(), x)), app(not(), y)),
                               app(not(), app(not(), x)) -> x}
       Open
      
      
      
      
      
      
      SCC (4):
       Strict:
        {app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y),
         app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z),
         app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y),
         app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z)}
       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(and(), x), app(app(or(), y), z)) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
                app(app(and(), app(app(or(), y), z)), x) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
             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(not(), app(app(and(), x), y)) -> app(app(or(), app(not(), x)), app(not(), y)),
                        app(not(), app(app(or(), x), y)) -> app(app(and(), app(not(), x)), app(not(), y)),
                               app(not(), app(not(), x)) -> x}
       Open