@NP04; @H06] and analytical [@JvWOT04] studies. The answer seems to be one of two possibilities: The PCPD belongs to the DP class with a long transient, or forms a new universality class distinct from known universality classes to date. As an attempt to resolve the issue, the present authors suggested two different approaches to the PCPD.

First, introducing the dynamic perturbation which is implemented by the biased hopping, we showed that the one-dimensional PCPD with biased diffusion (driven PCPD or DPCPD), exhibits critical scaling distinct from the unbiased PCPD, but instead shares the critical behavior with the two-dimensional PCPD without bias (dimensional reduction) [@PP05a; @PP05b]. Since all known DP models are robust against the biased diffusion [@PP05a], a DPCPD-type variant can serve as a litmus test for the PCPD scaling [@P06]. Second, we studied the crossover behavior from the PCPD to the DP by introducing single-particle annihilation/branching reactions and showed that there are diverging crossover scales with the universal nontrivial crossover exponent [@PP06]. These results provided another evidence that the PCPD is distinct from the DP.

In this paper, we study the crossover behavior from the DP${}_\textrm{IM}$ to the DP in order to understand better the difference between these two 