ExecutionLog | `- Expected Cost | +- [f] | 0 | +- [Program] | 0:While(x 1) | Choice | 1/4: x :~ {1 : 1 + x} | 3/4: x :~ {1 : -1 + x} | y :~ {1 : -1 + x} | 1:While(y 1) | sample :~ {1/5 : 0;1/5 : 1;1/5 : 2;1/5 : 3;1/5 : 4} | y :~ {1 : -sample + y} | Tick(1) | +- While.step | | | +- [Problem] | | 0:While(x 1) | | Choice | | 1/4: x :~ {1 : 1 + x} | | 3/4: x :~ {1 : -1 + x} | | y :~ {1 : -1 + x} | | 1:While(y 1) | | sample :~ {1/5 : 0;1/5 : 1;1/5 : 2;1/5 : 3;1/5 : 4} | | y :~ {1 : -sample + y} | | Tick(1) | | | +- [f] | | 0 | | | +- Expected Cost Body | | | | | +- While.step | | | | | | | +- [Problem] | | | | 1:While(y 1) | | | | sample :~ {1/5 : 0;1/5 : 1;1/5 : 2;1/5 : 3;1/5 : 4} | | | | y :~ {1 : -sample + y} | | | | Tick(1) | | | | | | | +- [f] | | | | 0 | | | | | | | +- Expected Cost Body | | | | | | | | | `- [1 | ] | | | | | | | +- linear-template | | | | | | | | | `- 1 + [y | y 0] | | | | | | | +- [Norms] | | | | [[1 | ],[y | y 0]] | | | | | | | +- [Invariant] | | | | y 1 ==> [1 | ] + h([1 | ],1/5[y | y 0] + 1/5[-1 + y | -1 + y 0] + 1/5[-2 + y | -2 + y 0] + 1/5[-3 + y | -3 + y 0] + 1/5[-4 + y | -4 + y 0]) h([1 | ],[y | y 0]) | | | | 1 1 + y ==> 0 h([1 | ],[y | y 0]) | | | | | | | `- 5/4[y | y 0] | | | | | `- 5/16[x | x 0] + 15/16[-2 + x | -2 + x 0] | | | +- mixed-iteration-template | | | | | `- [x | x 0] + [x | x 0]^2 | | | +- [Norms] | | [[x | x 0],[x^2 | x 0]] | | | +- [Invariant] | | x 1 ==> 5/16[x | x 0] + 15/16[-2 + x | -2 + x 0] + h(1/4[1 + x | 1 + x 0] + 3/4[-1 + x | -1 + x 0],1/4[1 + 2(x) + x^2 | 1 + x 0] + 3/4[1 + -2(x) + x^2 | -1 + x 0]) h([x | x 0],[x^2 | x 0]) | | 1 1 + x ==> 0 h([x | x 0],[x^2 | x 0]) | | | `- 5/8[x | x 0] + 5/4[x^2 | x 0] | `- 5/8[x | x 0] + 5/4[x^2 | x 0] [Success] 5/8[x | x 0] + 5/4[x^2 | x 0] Degree: 2