Multiple rack applications mounted inside each other

app1.ru

require 'rack'

use Rack::ContentLength
use Rack::ContentType

run proc { |env| [200, {}, '<p>First application</p><p><a href="/bar">Go to Second Application</a></p>'] }

app2.ru

require 'rack'

use Rack::ContentLength
use Rack::ContentType

run proc { |env| [200, {}, '<p>Second application</p><p><a href="/">Go to First Application</a></p>'] }

config.ru

require 'rack'

run Rack::URLMap.new \
  "/" => Rack::Builder.parse_file('app1.ru').first,
  "/bar" => Rack::Builder.parse_file('app2.ru').first