Longest path $\equiv$ Linear Program

• State of program in each step of longest path is current value

  Each function in path changes value

• Initial $\mbox{state}_0 =$ value of deepest leaf (y)
• Determine value of other argument (3)

  Treat function (/) as having one argument, (i.e. /3)

• next $\mbox{state}_1 = y/3 = \mbox{state}_0 M$

  Transformation matrix $M \equiv /3$

• N.B. process is not Markov as M depends upon position in path to the root