ExecutionLog
|
`- Expected Cost
   |
   +- [f]
   |    0
   |
   +- [Program]
   |    0:While(n  1)
   |        j :~ {1 : n}
   |        1:While(j  1)
   |            Choice
   |              1/3: j :~ {1 : -1 + j}
   |                   Tick(1)
   |              2/3: Skip
   |        sample :~ {1/2 : 0;1/2 : 1}
   |        n :~ {1 : n + -sample}
   |
   +- While.step
   |  |
   |  +- [Problem]
   |  |    0:While(n  1)
   |  |        j :~ {1 : n}
   |  |        1:While(j  1)
   |  |            Choice
   |  |              1/3: j :~ {1 : -1 + j}
   |  |                   Tick(1)
   |  |              2/3: Skip
   |  |        sample :~ {1/2 : 0;1/2 : 1}
   |  |        n :~ {1 : n + -sample}
   |  |
   |  +- [f]
   |  |    0
   |  |
   |  +- Expected Cost Body
   |  |  |
   |  |  +- Expected Cost
   |  |  |  |
   |  |  |  +- [f]
   |  |  |  |    0
   |  |  |  |
   |  |  |  +- [Program]
   |  |  |  |    1:While(j  1)
   |  |  |  |        Choice
   |  |  |  |          1/3: j :~ {1 : -1 + j}
   |  |  |  |               Tick(1)
   |  |  |  |          2/3: Skip
   |  |  |  |
   |  |  |  +- While.step
   |  |  |  |  |
   |  |  |  |  +- [Problem]
   |  |  |  |  |    1:While(j  1)
   |  |  |  |  |        Choice
   |  |  |  |  |          1/3: j :~ {1 : -1 + j}
   |  |  |  |  |               Tick(1)
   |  |  |  |  |          2/3: Skip
   |  |  |  |  |
   |  |  |  |  +- [f]
   |  |  |  |  |    0
   |  |  |  |  |
   |  |  |  |  +- Expected Cost Body
   |  |  |  |  |  |
   |  |  |  |  |  `- 1/3
   |  |  |  |  |
   |  |  |  |  +- linear-template
   |  |  |  |  |  |
   |  |  |  |  |  `- 1 + [j | j  0]
   |  |  |  |  |
   |  |  |  |  +- [Norms]
   |  |  |  |  |    [[1 | ],[j | j  0]]
   |  |  |  |  |
   |  |  |  |  +- [Invariant]
   |  |  |  |  |    j  1 ==> 1/3 + h([1 | ],1/3[-1 + j | -1 + j  0] + 2/3[j | j  0])  h([1 | ],[j | j  0])
   |  |  |  |  |    1  1 + j ==> 0  h([1 | ],[j | j  0])
   |  |  |  |  |
   |  |  |  |  `- [j | j  0]
   |  |  |  |
   |  |  |  `- [j | j  0]
   |  |  |
   |  |  +- Expected Cost
   |  |  |  |
   |  |  |  +- [f]
   |  |  |  |    0
   |  |  |  |
   |  |  |  +- [Program]
   |  |  |  |    sample :~ {1/2 : 0;1/2 : 1}
   |  |  |  |    n :~ {1 : n + -sample}
   |  |  |  |
   |  |  |  `- 0
   |  |  |
   |  |  +- Expected Cost
   |  |  |  |
   |  |  |  +- [f]
   |  |  |  |    0
   |  |  |  |
   |  |  |  +- [Program]
   |  |  |  |    1:While(j  1)
   |  |  |  |        Choice
   |  |  |  |          1/3: j :~ {1 : -1 + j}
   |  |  |  |               Tick(1)
   |  |  |  |          2/3: Skip
   |  |  |  |
   |  |  |  `- 0
   |  |  |
   |  |  `- [n | n  0]
   |  |
   |  +- mixed-iteration-template
   |  |  |
   |  |  `- [n | n  0] + [n | n  0]^2
   |  |
   |  +- [Norms]
   |  |    [[n | n  0],[n^2 | n  0]]
   |  |
   |  +- [Invariant]
   |  |    n  1 ==> [n | n  0] + h(1/2[n | n  0] + 1/2[-1 + n | -1 + n  0],1/2[n^2 | n  0] + 1/2[1 + -2(n) + n^2 | -1 + n  0])  h([n | n  0],[n^2 | n  0])
   |  |    1  1 + n ==> 0  h([n | n  0],[n^2 | n  0])
   |  |
   |  `- [n | n  0] + [n^2 | n  0]
   |
   `- [n | n  0] + [n^2 | n  0]

[Success] [n | n  0] + [n^2 | n
                          0]
Degree: 2