(VAR x y f xs)
(RULES
  app(app(minus, x), 0) -> x
  app(app(minus, app(s, x)), app(s, y)) -> app(app(minus, x), y)
  app(double, 0) -> 0
  app(double, app(s, x)) -> app(s, app(s, app(double, x)))
  app(app(plus, 0), y) -> y
  app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))
  app(app(plus, app(s, x)), y) -> app(app(plus, x), app(s, y))
  app(app(plus, app(s, x)), y) -> app(s, app(app(plus, app(app(minus, x), y)), app(double, y)))

  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)

)