  We have generalized the idea of backbend in a nearest-neighbor oriented bond
percolation process by considering a backbend sequence $\beta : \mathbb{Z}_+
\to \mathbb{Z}_+ \cup \{\infty\}$, and defining a $\beta$-backbend path from
the origin as a path that never retreats further than $\beta(h)$ levels back
from its record level $h$. We study the relationship between the critical
probabilities of different percolation processes based on different backbend
sequences on half-space, full-space, and half-slabs of the $d$-dimensional ($d
\geq 2$) body-centered cubic (BCC) lattice. We also give sufficient conditions
on the backbend sequences such that there will be no percolation at the
critical probabilities of the corresponding percolation processes on half-space
and full-space of the BCC lattice.
