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