(VAR x y z xs f)
(RULES
  app(app(., 1), x) -> x
  app(app(., x), 1) -> x
  app(app(., app(i, x)), x) -> 1
  app(app(., x), app(i, x)) -> 1
  app(app(., app(i, y)), app(app(., y), z)) -> z
  app(app(., y), app(app(., app(i, y)), z)) -> z
  app(app(., app(app(., x), y)), z) -> app(app(., x), app(app(., y), z))
  app(i, 1) -> 1
  app(i, app(i, x)) -> x
  app(i, app(app(., x), y)) -> app(app(., app(i, y)), app(i, x))

  app(app(map,f),nil) -> nil
  app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs))

  app(app(filter,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(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)

)