# 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
	# tick(0.707 * (x-y))
        tick(x-y)