def simp(r: Rexp): Rexp = r match {+
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  case ALT(r1, r2) => {+
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    val r1s = simp(r1)+
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    val r2s = simp(r2)+
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    (r1s, r2s) match {+
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      case (NULL, _) => r2s+
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      case (_, NULL) => r1s+
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      case _ => if (r1s == r2s) r1s else ALT(r1s, r2s)+
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    }+
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  }+
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  case SEQ(r1, r2) => {+
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    val r1s = simp(r1)+
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    val r2s = simp(r2)+
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    (r1s, r2s) match {+
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      case (NULL, _) => NULL+
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      case (_, NULL) => NULL+
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      case (EMPTY, _) => r2s+
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      case (_, EMPTY) => r1s+
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      case _ => SEQ(r1s, r2s)+
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    }+
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  }+
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  case NTIMES(r, n) => NTIMES(simp(r), n)    +
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  case r => r+
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}+
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+
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def ders (s: List[Char], r: Rexp) : Rexp = s match {+
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  case Nil => r+
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  case c::s => ders(s, simp(der(c, r)))+
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}+
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+
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