import scala.concurrent._

import scala.concurrent.duration._

import ExecutionContext.Implicits.global

import scala.language.postfixOps 

val EVIL_urban = SEQ(STAR(STAR(CHAR('a'))), CHAR('b'))

def nullable_urban (r: Rexp) : Boolean = r match {

  case ZERO => false

  case ONE => true

  case CHAR(_) => false

  case ALT(r1, r2) => nullable_urban(r1) || nullable_urban(r2)

  case SEQ(r1, r2) => nullable_urban(r1) && nullable_urban(r2)

  case STAR(_) => true

}

def der_urban (c: Char, r: Rexp) : Rexp = r match {

  case ZERO => ZERO

  case ONE => ZERO

  case CHAR(d) => if (c == d) ONE else ZERO

  case ALT(r1, r2) => ALT(der_urban(c, r1), der_urban(c, r2))

  case SEQ(r1, r2) => 

    if (nullable_urban(r1)) ALT(SEQ(der_urban(c, r1), r2), der_urban(c, r2))

    else SEQ(der_urban(c, r1), r2)

  case STAR(r1) => SEQ(der_urban(c, r1), STAR(r1))

}

def simp_urban(r: Rexp) : Rexp = r match {

  case ALT(r1, r2) => (simp_urban(r1), simp_urban(r2)) match {

    case (ZERO, r2s) => r2s

    case (r1s, ZERO) => r1s

    case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s)

  }

  case SEQ(r1, r2) =>  (simp_urban(r1), simp_urban(r2)) match {

    case (ZERO, _) => ZERO

    case (_, ZERO) => ZERO

    case (ONE, r2s) => r2s

    case (r1s, ONE) => r1s

    case (r1s, r2s) => SEQ(r1s, r2s)

  }

  case r => r

}

import scala.annotation.tailrec

@tailrec

def iterT_urban[A](n: Int, f: A => A, x: A): A = 

  if (n == 0) x else iterT_urban(n - 1, f, f(x)) 

lazy val f = Future {

  assert(size(iterT_urban(20, (r: Rexp) => der_urban('a', r), EVIL_urban)) == 7340068) 

  assert(size(iterT_urban(20, (r: Rexp) => simp_urban(der_urban('a', r)), EVIL_urban)) == 8) 

}

Await.result(f, 90 second)