User blog comment:B1mb0w/Deeply Nested Ackermann/@comment-25337554-20150602100224

I read your changes, but how about

d(m,0)=d(m-1,d(m-1,m)) ?

This comes from applying generalized formula to two arguments.

Or, should d(1,0,0)=d(0,1,1)?

For the previous interpretion, you should change

DNA(x,y,z,0,0, ... ,0) is substituted for DNA(x,y,z-1,z,z, ... ,z) in all cases

into

DNA(x,y,z,0,0, ... ,-1) is substituted for DNA(x,y,z-1,z,z, ... ,z) in all cases

because you want to use the rule when you try to subtract one from zero.