Automatic archiving of Gmail's emails which are labeled with 'autoarchive' or 'autoarchiveX' where 0 < X < 10.

gmailAutoarchive.js

function gmailAutoarchive() {

  // Get all the labels
  var labels = GmailApp.getUserLabels();
  // Filter out the ones not containinig autoarchive
  var autoarchive = labels.filter(function (label) {
    var labelName = label.getName();
    return labelName.indexOf("autoarchive") !== -1;
  });
  
  //helper function to archive threads given to it
  function archiveThreads(threads) {
    var batch_size = 100;
    while (threads.length) {
      var this_batch_size = Math.min(threads.length, batch_size);
      var this_batch = threads.splice(0, this_batch_size);
      GmailApp.moveThreadsToArchive(this_batch);
    }
  }
  
  // helper function to extract the last number, otherwise return 1
  // This allows you to have different autoarchive labels in gmail,
  // for example autoarchive, autoarchive4, autoarchive8.
  // Limit is 1 digit number.
  
  function getNumberFromLabel(label) {
    if (label == null || label == undefined) {
      return 1
    }
    
    // Get name returns String representation of the label
    var n = label.getName().slice(-1);
    var delayDays = 1;

    // If it's just autoarchive for example,
    // we can skip
    if (!isNaN(n)) {
      delayDays = Number(n);
    }
    
    return delayDays
  }
  
  // Main loop, autoarchive contains all labels that have
  // the keyword "autoarchive" in it. We loop through it and 
  // handle each labels' threads.
  for (var i = 0 ; i < autoarchive.length ; i++) {
    var label = autoarchive[i];
    //-->                                                           ex. autoarchive3
    var query = "in:inbox label:autoarchive older_than:" + getNumberFromLabel(label) + "d"

    // Use Googles own api to search the above query.
    var threads = GmailApp.search(query);
    
    // Archive the threads
    archiveThreads(threads)
  
}

Modification allows to have different autoarchivement labels for specific amount of day/s.