Initial Problem

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: F
Locations: f0, f10, f20, f22, f25
Transitions:
5:f0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f10(8,F,0,Arg_3,8):|:1<=F
0:f10(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f10(Arg_0-1,Arg_1-1,Arg_2+1,F,Arg_4):|:1<=Arg_0 && 1<=F
1:f10(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f10(Arg_0-1,Arg_1,Arg_2,F,Arg_4):|:F<=0 && 1<=Arg_0 && Arg_1+1<=Arg_0
4:f10(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f20(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_0<=0
2:f20(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f20(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)
3:f22(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> f25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

Preprocessing

Cut unreachable locations [f22; f25] from the program graph

Eliminate variables {Arg_2,Arg_3,Arg_4} that do not contribute to the problem

Found invariant 0<=7+Arg_1 && 0<=7+Arg_0+Arg_1 && Arg_0<=7+Arg_1 && Arg_0<=8 && 0<=Arg_0 for location f10

Found invariant 0<=7+Arg_1 && 0<=7+Arg_0+Arg_1 && Arg_0<=7+Arg_1 && Arg_0<=0 && 0<=Arg_0 for location f20

Problem after Preprocessing

Start: f0
Program_Vars: Arg_0, Arg_1
Temp_Vars: F
Locations: f0, f10, f20
Transitions:
13:f0(Arg_0,Arg_1) -> f10(8,F):|:1<=F
14:f10(Arg_0,Arg_1) -> f10(Arg_0-1,Arg_1-1):|:0<=7+Arg_1 && 0<=7+Arg_0+Arg_1 && Arg_0<=7+Arg_1 && Arg_0<=8 && 0<=Arg_0 && 1<=Arg_0 && 1<=F
15:f10(Arg_0,Arg_1) -> f10(Arg_0-1,Arg_1):|:0<=7+Arg_1 && 0<=7+Arg_0+Arg_1 && Arg_0<=7+Arg_1 && Arg_0<=8 && 0<=Arg_0 && F<=0 && 1<=Arg_0 && Arg_1+1<=Arg_0
16:f10(Arg_0,Arg_1) -> f20(Arg_0,Arg_1):|:0<=7+Arg_1 && 0<=7+Arg_0+Arg_1 && Arg_0<=7+Arg_1 && Arg_0<=8 && 0<=Arg_0 && Arg_0<=0
17:f20(Arg_0,Arg_1) -> f20(Arg_0,Arg_1):|:0<=7+Arg_1 && 0<=7+Arg_0+Arg_1 && Arg_0<=7+Arg_1 && Arg_0<=0 && 0<=Arg_0

MPRF for transition 14:f10(Arg_0,Arg_1) -> f10(Arg_0-1,Arg_1-1):|:0<=7+Arg_1 && 0<=7+Arg_0+Arg_1 && Arg_0<=7+Arg_1 && Arg_0<=8 && 0<=Arg_0 && 1<=Arg_0 && 1<=F of depth 1:

new bound:

9 {O(1)}

MPRF:

f10 [Arg_0+1 ]

MPRF for transition 15:f10(Arg_0,Arg_1) -> f10(Arg_0-1,Arg_1):|:0<=7+Arg_1 && 0<=7+Arg_0+Arg_1 && Arg_0<=7+Arg_1 && Arg_0<=8 && 0<=Arg_0 && F<=0 && 1<=Arg_0 && Arg_1+1<=Arg_0 of depth 1:

new bound:

9 {O(1)}

MPRF:

f10 [Arg_0+1 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
13: f0->f10: 1 {O(1)}
14: f10->f10: 9 {O(1)}
15: f10->f10: 9 {O(1)}
16: f10->f20: 1 {O(1)}
17: f20->f20: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
13: f0->f10: 1 {O(1)}
14: f10->f10: 9 {O(1)}
15: f10->f10: 9 {O(1)}
16: f10->f20: 1 {O(1)}
17: f20->f20: inf {Infinity}

Sizebounds

13: f0->f10, Arg_0: 8 {O(1)}
14: f10->f10, Arg_0: 7 {O(1)}
15: f10->f10, Arg_0: 7 {O(1)}
15: f10->f10, Arg_1: 7 {O(1)}
16: f10->f20, Arg_0: 0 {O(1)}
17: f20->f20, Arg_0: 0 {O(1)}