Most limits on the fourth generation heavy top quark (the t) are based on the assumed dominance of t -> Wb, which is expected to be case in the minimal fourth generation framework with a single Higgs (the so called SM4). Here we show, within a variant of a Two Higgs Doublet Model with four generations of fermions, that, in general, a different t detection strategy is required if the physics that underlies the new heavy fermionic degrees of freedom goes beyond the naive SM4. We find that the recent CMS lower bounds: m_{t}< 450 GeV in the semi-leptonic channel pp -> tt -> l u qqbb and m_{t}< 557 GeV in the dilepton channel pp -> tt ->ll u u bb, that were obtained using the customary (SM4-driven) detection strategies, do not apply. In particular, we demonstrate that if the decay t -> ht dominates, then applying the standard CMS search tools leads to a considerably relaxed lower bound: m_{t} >~350 GeV. We, therefore, suggest an alternative search strategy that is more sensitive to beyond SM4 dynamics of the fourth generation fermions.
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