I'm pretty sure part of the contract with gzip (and compression in general) is that applying it N times is undone by decompressing N times.

The size definitely gets bigger with each iteration:

  $ echo text >0.txt
  $ for i in {0..9}; do                             
  gzip <$i.txt >$((i + 1)).txt
  done
  $ ls | sort -n | xargs -n1 wc -c
       5 0.txt
      25 1.txt
      46 2.txt
      69 3.txt
      82 4.txt
     105 5.txt
     120 6.txt
     143 7.txt
     161 8.txt
     184 9.txt
     207 10.txt

He doesn't have the results, yet. He's running it in an infinite number of times.

Without actually checking, the result is going to be that the output size increases slightly over time.