User blog comment:Billicusp/Extending ExE to absurd heights/@comment-5529393-20160222033533/@comment-5529393-20160222221513

but the thing is that { {1 { { 1 } } 1 } } = { { 1 {#{#...{#}...#}#} 1 } } will eventually resolve to { {n} } for some positive integer n greater than 1, so it's going to expand into something even bigger, and your expression will never terminate.

In order for your notation to be well-defined, the resolutions must terminate, so your notations must be ordered by some well-founded relation. In your notation, { {2} } resolves to something bigger, so it never terminates.