ExecutionLog | `- Expected Cost | +- [f] | 0 | +- [Program] | 0:If(m 0) Then | Skip | Else | Abort | 1:While(n 1) | h :~ {1 : 0} | t :~ {1 : m} | 2:While(t h) | Choice | 3/4: sample :~ {1/3 : 1;1/3 : 2;1/3 : 3} | h :~ {1 : h + sample} | 1/4: Skip | t :~ {1 : 1 + t} | Tick(1) | n :~ {1 : -1 + n} | +- While.step | | | +- [Problem] | | 1:While(n 1) | | h :~ {1 : 0} | | t :~ {1 : m} | | 2:While(t h) | | Choice | | 3/4: sample :~ {1/3 : 1;1/3 : 2;1/3 : 3} | | h :~ {1 : h + sample} | | 1/4: Skip | | t :~ {1 : 1 + t} | | Tick(1) | | n :~ {1 : -1 + n} | | | +- [f] | | 0 | | | +- Expected Cost Body | | | | | +- Expected Cost | | | | | | | +- [f] | | | | 0 | | | | | | | +- [Program] | | | | 2:While(t h) | | | | Choice | | | | 3/4: sample :~ {1/3 : 1;1/3 : 2;1/3 : 3} | | | | h :~ {1 : h + sample} | | | | 1/4: Skip | | | | t :~ {1 : 1 + t} | | | | Tick(1) | | | | | | | +- While.step | | | | | | | | | +- [Problem] | | | | | 2:While(t h) | | | | | Choice | | | | | 3/4: sample :~ {1/3 : 1;1/3 : 2;1/3 : 3} | | | | | h :~ {1 : h + sample} | | | | | 1/4: Skip | | | | | t :~ {1 : 1 + t} | | | | | Tick(1) | | | | | | | | | +- [f] | | | | | 0 | | | | | | | | | +- Expected Cost Body | | | | | | | | | | | `- [1 | ] | | | | | | | | | +- linear-template | | | | | | | | | | | `- 1 + [1 + -h + t | 1 + -h + t 0] | | | | | | | | | +- [Norms] | | | | | [[1 | ],[1 + -h + t | 1 + -h + t 0]] | | | | | | | | | +- [Invariant] | | | | | t h ==> [1 | ] + h([1 | ],1/4[1 + -h + t | 1 + -h + t 0] + 1/4[-h + t | -h + t 0] + 1/4[-1 + -h + t | -1 + -h + t 0] + 1/4[2 + -h + t | 2 + -h + t 0]) h([1 | ],[1 + -h + t | 1 + -h + t 0]) | | | | | h 1 + t ==> 0 h([1 | ],[1 + -h + t | 1 + -h + t 0]) | | | | | | | | | `- 4[1 + -h + t | 1 + -h + t 0] | | | | | | | `- 4[1 + -h + t | 1 + -h + t 0] | | | | | +- Expected Cost | | | | | | | +- [f] | | | | 0 | | | | | | | +- [Program] | | | | n :~ {1 : -1 + n} | | | | | | | `- 0 | | | | | +- Expected Cost | | | | | | | +- [f] | | | | 0 | | | | | | | +- [Program] | | | | 2:While(t h) | | | | Choice | | | | 3/4: sample :~ {1/3 : 1;1/3 : 2;1/3 : 3} | | | | h :~ {1 : h + sample} | | | | 1/4: Skip | | | | t :~ {1 : 1 + t} | | | | Tick(1) | | | | | | | `- 0 | | | | | `- 4[1 + m | 1 + m 0] | | | +- mixed-lin-template | | | | | `- 1 + [1 + m | 1 + m 0] + [1 + m | 1 + m 0][n | n 0] + 2([n | n 0]) + [n | n 0]^2 | | | +- [Norms] | | [[1 | ],[1 + m | 1 + m 0],[mn + n | 1 + m 0 n 0],[n | n 0],[n^2 | n 0]] | | | +- [Invariant] | | n 1 ==> 4[1 + m | 1 + m 0] + h([1 | ],[1 + m | 1 + m 0],[-1 + -m + mn + n | -1 + n 0 1 + m 0],[-1 + n | -1 + n 0],[1 + -2(n) + n^2 | -1 + n 0]) h([1 | ],[1 + m | 1 + m 0],[mn + n | 1 + m 0 n 0],[n | n 0],[n^2 | n 0]) | | 1 1 + n ==> 0 h([1 | ],[1 + m | 1 + m 0],[mn + n | 1 + m 0 n 0],[n | n 0],[n^2 | n 0]) | | | `- 4[mn + n | 1 + m 0 n 0] | `- [m 0] 4[mn + n | 1 + m 0 n 0] [Success] [m 0] 4[mn + n | 1 + m 0 n 0] Degree: 2