(VAR x y xs f)
(RULES
  app(p, app(s, x)) -> x
  app(fact, 0) -> app(s, 0)
  app(fact, app(s, x)) -> app(app(*, app(s, x)), app(fact, app(p, app(s, x))))
  app(app(*, 0), y) -> 0
  app(app(*, app(s, x)), y) -> app(app(+, app(app(*, x), y)), y)
  app(app(+, x), 0) -> x
  app(app(+, x), app(s, y)) -> app(s, app(app(+, x), 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)

)