YES
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:
  Strict:
   { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f),
    app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
    app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f),
            app#(app(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))}
  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}
  EDG:
   {
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(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#(f, x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(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#(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(), 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#(app(filter(), f), xs))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
    (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(and(), 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#(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(and(), x), y)) -> app#(or(), 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#(not(), x))
    (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#(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#(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#(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#(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), 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#(or(), 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(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#(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), 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)))
    (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#(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(and(), x), y)) -> app#(or(), 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#(not(), 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#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(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#(f, x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(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#(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#(f, 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(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#(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#(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(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#(or(), 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(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#(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(and(), x), y))
    (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(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(), true()), f), x), xs) -> app#(filter(), f))
    (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#(app(filter(), f), xs))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
    (app#(app(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#(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#(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#(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), 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#(or(), 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(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#(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), y))
    (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(and(), 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#(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(and(), x), y)) -> app#(or(), 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#(not(), x))
    (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(and(), 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(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#(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(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(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(), y))
    (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
    (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#(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(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#(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#(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), 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(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#(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#(or(), app(app(and(), x), y)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(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#(cons(), x))
    (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(), false()), f), x), xs) -> app#(app(filter(), f), xs))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
    (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(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(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#(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#(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#(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(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#(and(), 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(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#(app(map(), f), xs))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
    (app#(app(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(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#(app(app(app(filter2(), app(f, x)), f), x), xs))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(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(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#(filter2(), app(f, 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#(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#(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(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(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#(not(), y))
    (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#(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#(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(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#(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#(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#(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(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#(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#(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(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), 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(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#(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#(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), 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(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#(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#(or(), app(app(and(), x), y)))
    (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#(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#(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(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(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(), y))
    (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), 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#(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(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#(cons(), 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#(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(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(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#(filter2(), app(f, x)))
   }
   SCCS:
    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:
     { 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:
     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}
     SPSC:
      Simple Projection:
       pi(app#) = 1
      Strict:
       {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)}
      EDG:
       {(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#(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(), 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(), 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(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(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(), y))}
       SCCS:
        Scc:
         {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:
         Strict:
          {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}
         SPSC:
          Simple Projection:
           pi(app#) = 1
          Strict:
           {app#(not(), app(app(or(), x), y)) -> app#(not(), x),
            app#(not(), app(app(or(), x), y)) -> app#(not(), y)}
          EDG:
           {(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#(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#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), y))}
           SCCS:
            Scc:
             {app#(not(), app(app(or(), x), y)) -> app#(not(), x),
              app#(not(), app(app(or(), x), y)) -> app#(not(), y)}
            SCC:
             Strict:
              {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}
             SPSC:
              Simple Projection:
               pi(app#) = 1
              Strict:
               {app#(not(), app(app(or(), x), y)) -> app#(not(), y)}
              EDG:
               {(app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), y))}
               SCCS:
                Scc:
                 {app#(not(), app(app(or(), x), y)) -> app#(not(), y)}
                SCC:
                 Strict:
                  {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}
                 SPSC:
                  Simple Projection:
                   pi(app#) = 1
                  Strict:
                   {}
                  Qed
    SCC:
     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}
     UR:
      {}
      BOUND:
       Bound: match(-raise)-bounded by 1
       Automaton:
        {      or_0() -> 2*
              and_1() -> 3*
              and_0() -> 1*
         app#_1(4, 2) -> 1*
         app#_1(4, 1) -> 1*
         app#_0(2, 2) -> 1*
         app#_0(2, 1) -> 1*
         app#_0(1, 2) -> 1*
         app#_0(1, 1) -> 1*
          app_1(3, 2) -> 4*
          app_1(3, 1) -> 4*
          app_0(2, 2) -> 1*
          app_0(2, 1) -> 1*
          app_0(1, 2) -> 1*
          app_0(1, 1) -> 1*}
       Strict:
        {}
       Qed
    SCC:
     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}
     SPSC:
      Simple Projection:
       pi(app#) = 1
      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#(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)}
      EDG:
       {(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#(app(map(), f), xs))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(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(), false()), f), x), xs) -> app#(app(filter(), f), xs))
        (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(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(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(), false()), 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(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))}
       SCCS:
        Scc:
         {app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)}
        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(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:
         Strict:
          {app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), 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}
         SPSC:
          Simple Projection:
           pi(app#) = 1
          Strict:
           {}
          Qed
        SCC:
         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(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}
         SPSC:
          Simple Projection:
           pi(app#) = 1
          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(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)}
          EDG:
           {(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(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(), false()), f), x), xs) -> app#(app(filter(), f), xs))
            (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))}
           SCCS:
            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(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)}
            SCC:
             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(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}
             SPSC:
              Simple Projection:
               pi(app#) = 1
              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)}
              EDG:
               {}
               SCCS:
                
                Qed