A$ s.t. $a$ has an acyclic pd–evaluation $ace^a = ((a_0,...,a_n), B) $ in $A$. We say that a two–valued interpretation $v$ **blocks** $ace^a$ iff $\exists b\in B$ s.t. $v(b) = {\mathbf{t}}$ or $\exists a_i \in  \{a_0,...,a_n\}$ s.t. $v(a_i) = {\mathbf{f}}$.

Let us now show on an example why we require minimality on the chosen interpretations and why do we store the blocking set:

Let us assume an ADF $(\{a,b,c\}, \{C_a:\neg c \lor b, C_b:a, C_c:c\})$ depicted in Figure \[fig:cf\]. For argument $a$ there exist the following decisively in interpretations: $v_1 = \{c:{\mathbf{f}}\},v_2 = \{b:{\mathbf{t}}\},v_3 = \{b:{\mathbf{t}}, c:{\mathbf{f}}\},v_4= \{b:{\mathbf{t}}, c:{\mathbf{t}}\},
v_5 = \{b:{\mathbf{f}}, c:{\mathbf{f}}\}$. Only the first two are minimal. Considering $v_4$ would give us a wrong view that $a$ requires $c$ for acceptance, which is not a desirable reading. The interpretations for $b$ and $c$ are respectively $w_1 = \{a:{\mathbf{t}}\}$ and $z_1 = \{c:{\mathbf{t}}\}$. Consequently, we have two pd–functions on $\{a,b,c\}$, namely $pd_1 = \{a:v_1, b:w_1, c:z_1\}$ and $pd_2 = \{a:v_2, b:w_1, c:z_1\}$. From them we obtain one acyclic pd–evaluation for $a$: $((a),\{c\})$, one for $b$: $((a,b),\{c\})$ and none for $c$.

Let us look closer at a set $E=\{a,b,c\}$. We can see that $c$ is not pd–acyclic in $E$. However, 