Summarizing I would say that your sexp is not the same as Walkers, because
your \( T_b \) satisfies: \( T_b(x+1)=x+1+b^{T_b(x)} \)
while Walker's \( T_b \) satisfies \( T_b(x+1)=e^{T_b(x)}-1 \) (at least in the case b=e).
your \( T_b \) satisfies: \( T_b(x+1)=x+1+b^{T_b(x)} \)
while Walker's \( T_b \) satisfies \( T_b(x+1)=e^{T_b(x)}-1 \) (at least in the case b=e).