User blog comment:Wythagoras/A far better bound for TREE(3)/@comment-5529393-20140622122929/@comment-10429372-20140622182300

Here is how it works:

[] reduces to [][][]...[][][] with as many [] as possible.

[] reduces to (((...((([])))...))) with as many ('s as possible.

([]) reduces to [][][][]...[][][][]

([][]...[][]) reduces to ([][]...[](((...(())...))))

Here an (((...(())...))) reduces as in the Kirby Paris Hydra, but when we reach, at the ground level:

(#) reduces to (#)(#)...(#)(#)