Inferring Expected Runtimes Using Sizes

KoAT2 Proof WORST_CASE( ?, 50 {O(1)})

Initial Complexity Problem (after preprocessing)

Start:f
Program_Vars:Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations:f, g, h, i
Transitions:
f(Arg_0,Arg_1,Arg_2) -> 1/3:g(1,Arg_1,Arg_2) :+: 1/3:g(2,Arg_1,Arg_2) :+: 1/3:g(3,Arg_1,Arg_2)
g(Arg_0,Arg_1,Arg_2) -> h(Arg_0,Arg_1,Arg_0) :|: Arg_0<=3 && 1<=Arg_0
h(Arg_0,Arg_1,Arg_2) -> i(Arg_0,Arg_2,Arg_2) :|: 0<Arg_0 && Arg_2<=3 && Arg_2<=3+Arg_0 && Arg_0+Arg_2<=6 && 1<=Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_0<=3 && 0<=Arg_0
i(Arg_0,Arg_1,Arg_2) -> i(Arg_0,Arg_1-1,Arg_2) :|: 0<Arg_1 && Arg_2<=3 && Arg_2<=3+Arg_1 && Arg_1+Arg_2<=6 && Arg_2<=2+Arg_0 && Arg_0+Arg_2<=6 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=3 && Arg_1<=2+Arg_0 && Arg_0+Arg_1<=6 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=3+Arg_1 && Arg_0<=3 && 1<=Arg_0
i(Arg_0,Arg_1,Arg_2) -> h(Arg_0-1,Arg_1,Arg_2) :|: Arg_1<=0 && Arg_2<=3 && Arg_2<=3+Arg_1 && Arg_1+Arg_2<=6 && Arg_2<=2+Arg_0 && Arg_0+Arg_2<=6 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=3 && Arg_1<=2+Arg_0 && Arg_0+Arg_1<=6 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=3+Arg_1 && Arg_0<=3 && 1<=Arg_0

Timebounds:

Overall timebound:52 {O(1)}
0,0: f->g: 1 {O(1)}
1,0: f->g: 1 {O(1)}
2,0: f->g: 1 {O(1)}
3,1: g->h: 1 {O(1)}
4,2: h->i: 9 {O(1)}
5,3: i->i: 36 {O(1)}
6,4: i->h: 3 {O(1)}

Expected Timebounds:

Overall expected timebound: 50 {O(1)}
0: f->[1/3:g; 1/3:g; 1/3:g]: 1 {O(1)}
1: g->[1:h]: 1 {O(1)}
2: h->[1:i]: 9 {O(1)}
3: i->[1:i]: 36 {O(1)}
4: i->[1:h]: 3 {O(1)}

Costbounds:

Overall costbound: inf {Infinity}
0,0: f->g: inf {Infinity}
1,0: f->g: inf {Infinity}
2,0: f->g: inf {Infinity}
3,1: g->h: inf {Infinity}
4,2: h->i: inf {Infinity}
5,3: i->i: inf {Infinity}
6,4: i->h: inf {Infinity}

Expected Costbounds:

Overall expected costbound: 50 {O(1)}
0: f->[1/3:g; 1/3:g; 1/3:g]: 1 {O(1)}
1: g->[1:h]: 1 {O(1)}
2: h->[1:i]: 9 {O(1)}
3: i->[1:i]: 36 {O(1)}
4: i->[1:h]: 3 {O(1)}

Sizebounds:

0,0: f->g, Arg_0: 1 {O(1)}
0,0: f->g, Arg_1: Arg_1 {O(n)}
0,0: f->g, Arg_2: Arg_2 {O(n)}
1,0: f->g, Arg_0: 2 {O(1)}
1,0: f->g, Arg_1: Arg_1 {O(n)}
1,0: f->g, Arg_2: Arg_2 {O(n)}
2,0: f->g, Arg_0: 3 {O(1)}
2,0: f->g, Arg_1: Arg_1 {O(n)}
2,0: f->g, Arg_2: Arg_2 {O(n)}
3,1: g->h, Arg_0: 3 {O(1)}
3,1: g->h, Arg_1: Arg_1 {O(n)}
3,1: g->h, Arg_2: 3 {O(1)}
4,2: h->i, Arg_0: 3 {O(1)}
4,2: h->i, Arg_1: 3 {O(1)}
4,2: h->i, Arg_2: 3 {O(1)}
5,3: i->i, Arg_0: 3 {O(1)}
5,3: i->i, Arg_1: 2 {O(1)}
5,3: i->i, Arg_2: 3 {O(1)}
6,4: i->h, Arg_0: 2 {O(1)}
6,4: i->h, Arg_1: 0 {O(1)}
6,4: i->h, Arg_2: 3 {O(1)}

ExpSizeBounds:

(0: f->[1/3:g; 1/3:g; 1/3:g], g), Arg_0: 3 {O(1)}
(0: f->[1/3:g; 1/3:g; 1/3:g], g), Arg_1: Arg_1 {O(n)}
(0: f->[1/3:g; 1/3:g; 1/3:g], g), Arg_2: Arg_2 {O(n)}
(1: g->[1:h], h), Arg_0: 3 {O(1)}
(1: g->[1:h], h), Arg_1: Arg_1 {O(n)}
(1: g->[1:h], h), Arg_2: 3 {O(1)}
(2: h->[1:i], i), Arg_0: 3 {O(1)}
(2: h->[1:i], i), Arg_1: 3 {O(1)}
(2: h->[1:i], i), Arg_2: 3 {O(1)}
(3: i->[1:i], i), Arg_0: 3 {O(1)}
(3: i->[1:i], i), Arg_1: 2 {O(1)}
(3: i->[1:i], i), Arg_2: 3 {O(1)}
(4: i->[1:h], h), Arg_0: 2 {O(1)}
(4: i->[1:h], h), Arg_1: 0 {O(1)}
(4: i->[1:h], h), Arg_2: 3 {O(1)}