User blog comment:Mh314159/new YIP notation/@comment-39585023-20190705220451/@comment-39585023-20190705233450

Yes, {0}(x) is never reached and not defined, it should have been {0}0{x) = [[x,b-1],b-1].  The idea is to terminate all expressions of the type {m}y(x)  by recursing y down to zero which them decreases m, and eventually m goes down to zero and then so does y and we can evaluate in terms of the next lower b number.  I hope this terminates.  It wasn't easy for me.