This paper enriches the list of properties of the congruence sequences starting from the universal relation and successively performing the operations of lower $t$ and lower $k$. Three classes of completely regular semigroups, namely semigroups for which $ker{sigma}$ is a cryptogroup, semigroups for which $ker{ u}$ is a cryptogroup and semigroups for which $kappa$ is over rectangular bands, are studied. $((omega_t)_k)_t$, $((mathcal{D}_t)_k)_t$ and $((omega_k)_t)_k$ are found to be the least congruences on $S$ such that the quotient semigroups are semigroups for which $ker{sigma}$ is a cryptogroup, $ker{ u}$ is a cryptogroup and $kappa$ is over rectangular bands, respectively. The results obtained present a response to three problems in Petrich and Reillys textbook textquotelefttextquoteleft Completely Regular Semigroupstextquoterighttextquoteright.
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