  We study the problem of causal effect identification from observational
distribution given the causal graph and some context-specific independence
(CSI) relations. It was recently shown that this problem is NP-hard, and while
a sound algorithm to learn the causal effects is proposed in Tikka et al.
(2019), no complete algorithm for the task exists. In this work, we propose a
sound and complete algorithm for the setting when the CSI relations are limited
to observed nodes with no parents in the causal graph. One limitation of the
state of the art in terms of its applicability is that the CSI relations among
all variables, even unobserved ones, must be given (as opposed to learned).
Instead, We introduce a set of graphical constraints under which the CSI
relations can be learned from mere observational distribution. This expands the
set of identifiable causal effects beyond the state of the art.
