# Inferring Expected Runtimes Using Sizes

KoAT2 Proof WORST_CASE( ?, 296/3+74/15*Arg_1 {O(n)})

### Initial Complexity Problem (after preprocessing)

Start:f
Program_Vars:Arg_0, Arg_1
Temp_Vars:
Locations:f, g
Transitions:
f(Arg_0,Arg_1) -{0}> g(10,Arg_1)
g(Arg_0,Arg_1) -> 6/37:g(Uniform (3, 6),Arg_1) :+: 6/37:g(Uniform (1, 2),Arg_1) :+: 4/37:g(Uniform (3, 6),Arg_1) :+: 8/37:g(Uniform (1, 2),Arg_1) :+: 8/37:g(Uniform (-6, -3),Arg_1) :+: 4/37:g(Uniform (-10, -5),Arg_1) :+: 1/37:g(Uniform (-10, -5),Arg_1) :|: Arg_1<=Arg_0

### Timebounds:

Overall timebound:inf {Infinity}
0,0: f->g: 1 {O(1)}
1,1: g->g: inf {Infinity}
2,1: g->g: inf {Infinity}
3,1: g->g: inf {Infinity}
4,1: g->g: inf {Infinity}
5,1: g->g: inf {Infinity}
6,1: g->g: inf {Infinity}
7,1: g->g: inf {Infinity}

### Expected Timebounds:

Overall expected timebound: 299/3+74/15*Arg_1 {O(n)}
0: f->[1:g]: 1 {O(1)}
1: g->[6/37:g; 6/37:g; 4/37:g; 8/37:g; 8/37:g; 4/37:g; 1/37:g]: 296/3+74/15*Arg_1 {O(n)}

### Costbounds:

Overall costbound: inf {Infinity}
0,0: f->g: inf {Infinity}
1,1: g->g: inf {Infinity}
2,1: g->g: inf {Infinity}
3,1: g->g: inf {Infinity}
4,1: g->g: inf {Infinity}
5,1: g->g: inf {Infinity}
6,1: g->g: inf {Infinity}
7,1: g->g: inf {Infinity}

### Expected Costbounds:

Overall expected costbound: 296/3+74/15*Arg_1 {O(n)}
0: f->[1:g]: 0 {O(1)}
1: g->[6/37:g; 6/37:g; 4/37:g; 8/37:g; 8/37:g; 4/37:g; 1/37:g]: 296/3+74/15*Arg_1 {O(n)}

### Sizebounds:

0,0: f->g, Arg_0: 10 {O(1)}
0,0: f->g, Arg_1: Arg_1 {O(n)}
1,1: g->g, Arg_1: Arg_1 {O(n)}
2,1: g->g, Arg_1: Arg_1 {O(n)}
3,1: g->g, Arg_1: Arg_1 {O(n)}
4,1: g->g, Arg_1: Arg_1 {O(n)}
5,1: g->g, Arg_1: Arg_1 {O(n)}
6,1: g->g, Arg_1: Arg_1 {O(n)}
7,1: g->g, Arg_1: Arg_1 {O(n)}

### ExpSizeBounds:

(0: f->[1:g], g), Arg_0: 10 {O(1)}
(0: f->[1:g], g), Arg_1: Arg_1 {O(n)}
(1: g->[6/37:g; 6/37:g; 4/37:g; 8/37:g; 8/37:g; 4/37:g; 1/37:g], g), Arg_0: 10+279/74*(296/3+74/15*Arg_1) {O(n)}
(1: g->[6/37:g; 6/37:g; 4/37:g; 8/37:g; 8/37:g; 4/37:g; 1/37:g], g), Arg_1: Arg_1 {O(n)}