# Upper bound for runtime complexity of LOOP programs

Recently I learned about LOOP programs, which always terminate and have the same computational power as primitive recursive functions. Furthermore primitve recursive functions can (as far as I understood) compute anything that isn't growing faster than $$Ack(n)$$.

Is this implying that the upper bound runtime complexity for LOOP programs is $$O(Ack(n))$$? And are there functions similar to Ackermann's function, which can't be computed by primitive recursive functions, but grow slower than $$Ack(n)$$?

(sorry for spelling and grammar)