Add two small examples

examples/3col.md

@@ -0,0 +1,72 @@
+# The *3-Coloring Problem*
+
+The *3-Coloring Problem* is a decision problem: Given a *graph*, consisting of
+*nodes* and *edges* that connect two nodes each, can we find a solution, i.e.
+an assignment of one of three colors (here we call them red, green, and blue)
+to every node, such that no nodes that are connected are assigned the same
+color?
+
+## Instance
+
+We will be looking at ten nodes
+
+    node(0..9).
+
+that are connected as follows:
+
+    connected(0,2).
+    connected(0,3).
+    connected(0,4).
+    connected(1,3).
+    connected(1,5).
+    connected(1,7).
+    connected(1,8).
+    connected(2,3).
+    connected(2,6).
+    connected(2,7).
+    connected(2,9).
+    connected(3,6).
+    connected(3,8).
+    connected(4,5).
+    connected(5,8).
+    connected(5,9).
+    connected(6,7).
+    connected(7,8).
+
+To ensure undirectedness of connections, we add the following rule
+that establishes symmetry:
+
+    connected(N,M) :- connected(M,N).
+
+## Guess
+
+We will use the predicates `red`, `green` and `blue` to mark vertices of the
+respective color. Note that we enforce two conditions here:
+  1. A node that is not of two colors, must be of the third color.
+  2. A node cannot be colored by two colors at the same time.
+  3. Following from (1.) and (2.) every node is assigned exactly one color.
+
+    red(N)   :- node(N), not green(N), not blue(N).
+    green(N) :- node(N), not red(N), not blue(N).
+    blue(N)  :- node(N), not red(N), not green(N).
+
+## Check
+
+Additionally we need to impose restrictions such that two connected nodes
+are not assigned the same color.
+
+    :- connected(N1,N2), blue(N1), blue(N2).
+    :- connected(N1,N2), red(N1), red(N2).
+    :- connected(N1,N2), green(N1), green(N2).
+
+## Evaluating the Program in this File
+
+Run the following command, substituting the name of the JAR file and the path
+to this file as required:
+
+```sh
+java -jar alpha-bundled.jar -l -i .../3col.md
+```
+
+Note that the flag `-l` indicates that the input is written in "literate"
+style, i.e. that code is indented by four spaces.

examples/innocence.asp

@@ -0,0 +1,6 @@
+motive(a).
+motive(b).
+guilty(b).
+
+% ei incumbit probatio qui dicit, non qui negat
+innocent(S) :- motive(S), not guilty(S).