  It is well-know that deciding consistency for normal answer set programs
(ASP) is NP-complete, thus, as hard as the satisfaction problem for classical
propositional logic (SAT). The best algorithms to solve these problems take
exponential time in the worst case. The exponential time hypothesis (ETH)
implies that this result is tight for SAT, that is, SAT cannot be solved in
subexponential time. This immediately establishes that the result is also tight
for the consistency problem for ASP. However, accounting for the treewidth of
the problem, the consistency problem for ASP is slightly harder than SAT: while
SAT can be solved by an algorithm that runs in exponential time in the
treewidth k, it was recently shown that ASP requires exponential time in k
\cdot log(k). This extra cost is due checking that there are no self-supported
true atoms due to positive cycles in the program. In this paper, we refine the
above result and show that the consistency problem for ASP can be solved in
exponential time in k \cdot log({\lambda}) where {\lambda} is the minimum
between the treewidth and the size of the largest strongly-connected component
in the positive dependency graph of the program. We provide a dynamic
programming algorithm that solves the problem and a treewidth-aware reduction
from ASP to SAT that adhere to the above limit.
