Expected Cost | +- [f] | 0 | +- [Program] | flag :~ {1 : 1} | 0:While(flag ≥ 1) | Choice | 1/2: flag :~ {1 : 0} | 1/2: flag :~ {1 : 1} | Tick(1) | +- While.step | | | +- [Problem] | | 0:While(flag ≥ 1) | | Choice | | 1/2: flag :~ {1 : 0} | | 1/2: flag :~ {1 : 1} | | Tick(1) | | | +- [f] | | 0 | | | +- Expected Cost Body | | | | | `- [1 | ⊤] | | | +- linear-template | | | | | `- 1 + [flag | flag ≥ 0] | | | +- [Norms] | | [[1 | ⊤],[flag | flag ≥ 0]] | | | +- [Invariant] | | flag ≥ 1 ==> [1 | ⊤] + h([1 | ⊤],1/2) ≼ h([1 | ⊤],[flag | flag ≥ 0]) | | 1 ≥ 1 + flag ==> 0 ≼ h([1 | ⊤],[flag | flag ≥ 0]) | | | `- 2·[flag | flag ≥ 0] | `- 2