add (variation) of 2drobot as imp

examples/2drobot.imp

+# 2D Robot 
+# Chatterjee et al., Cost Analysis of Nondeterministic Programs
+#
+# **2D Robot** We consider a robot walking in a plane. Suppose
+# that the robot is initially located below the line y = x and
+# we want it to cross this line, i.e. the program continues until
+# the robot crosses the line. At each iteration, the robot prob-
+# abilistically chooses one of the following 9 directions and
+# moves in that direction: {0: North, 1: South, 2: East, 3: West, 4:
+# Northeast, 5: Southeast, 6: Northwest, 7: Southwest, 8: Stay}.
+# Moreover, the robot’s step size is a uniformly random vari-
+# able between 1 and 3. At the end of each iteration, a cost is
+# incurred, which is dependent on the distance between the
+# robot and the line y = x.
+
+# Note: use approximation `tick(x-y)` instead of `tick(0.707 * (x-y))`
+
+def f():
+  var x, y, r, a, b
+
+  x = a
+  y = b
+
+  while y <= x:
+    prob(1,4):
+      r = unif(1,3)
+      y = y + r
+    else:
+      prob(1,7):
+        r = unif(1,3)
+        y = y - r
+      else:
+        prob(1,6):
+          r = unif(1,3)
+          x = x + r
+        else:
+          prob(1,5):
+            r = unif(1,3)
+            x = x - r
+          else:
+            prob(1,4):
+              r = unif(1,3)
+              x = x + r
+              r = unif(1,3)
+              y = y + r
+            else:
+              prob(1,3):
+                r = unif(1,3)
+                x = x + r
+                r = unif(1,3)
+                y = y - r
+              else:
+                prob(1,2):
+                  r = unif(1,3)
+                  x = x - r
+                  r = unif(1,3)
+                  y = y + r
+                else:
+                  prob(1,1):
+                    r = unif(1,3)
+                    x = x - r
+                    r = unif(1,3)
+                    y = y - r
+                  else:
+                    skip
+
+		# tick(0.707 * (x-y))
+    tick(x-y)
+