User blog comment:B1mb0w/The Quantum Function/@comment-35470197-20180926050834/@comment-10262436-20181001100815

PS.the third eample you gave needed a rule. Thanks for spotting this. I have added:

t_d(a + 1,0_[y + 1],c + 1) = t_d^C(a,0_*,0_[y],C)

so

t_d(2,0_[y + 1],1) = t_d^C(1,0_*,0_[y],C)

where C is the decremented function defined in my Notation Explained blog.

C = t_d(2,0_[y + 1],0)