Expected Cost
|
+- [f]
|    0
|
+- [Program]
|    0:While(x ≥ 1 + y)
|        Tick(1)
|        NonDet
|          {y :~ {1 : 1 + y}}
|          {x :~ {1 : -1 + x}}
|
+- While.step
|  |
|  +- [Problem]
|  |    0:While(x ≥ 1 + y)
|  |        Tick(1)
|  |        NonDet
|  |          {y :~ {1 : 1 + y}}
|  |          {x :~ {1 : -1 + x}}
|  |
|  +- [f]
|  |    0
|  |
|  +- Expected Cost Body
|  |  |
|  |  `- [1 | ⊤]
|  |
|  +- linear-template
|  |  |
|  |  `- 1 + [x + -y | x + -y ≥ 0]
|  |
|  +- [Norms]
|  |    [[1 | ⊤],[x + -y | x + -y ≥ 0]]
|  |
|  +- [Invariant]
|  |    x ≥ 1 + y ==> [1 | ⊤] + h([1 | ⊤],[-1 + x + -y | -1 + x + -y ≥ 0]) ≼ h([1 | ⊤],[x + -y | x + -y ≥ 0])
|  |    1 + y ≥ 1 + x ==> 0 ≼ h([1 | ⊤],[x + -y | x + -y ≥ 0])
|  |
|  `- [x + -y | x + -y ≥ 0]
|
`- [x + -y | x + -y ≥ 0]