Initial Problem

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: f0, f14, f6
Transitions:
0:f0(Arg_0,Arg_1,Arg_2,Arg_3) -> f6(Arg_1,Arg_1,Arg_3,Arg_3)
3:f6(Arg_0,Arg_1,Arg_2,Arg_3) -> f14(0,Arg_1,Arg_2,Arg_3):|:Arg_1+1<=Arg_3 && Arg_0<=0 && 0<=Arg_0
4:f6(Arg_0,Arg_1,Arg_2,Arg_3) -> f14(0,Arg_1,Arg_2,Arg_3):|:1+Arg_3<=Arg_1 && Arg_0<=0 && 0<=Arg_0
5:f6(Arg_0,Arg_1,Arg_2,Arg_3) -> f14(0,Arg_1,Arg_2,Arg_1):|:Arg_0<=0 && 0<=Arg_0 && Arg_1<=Arg_3 && Arg_3<=Arg_1
1:f6(Arg_0,Arg_1,Arg_2,Arg_3) -> f6(Arg_0-1,Arg_1,Arg_2-1,Arg_3):|:Arg_0+1<=0
2:f6(Arg_0,Arg_1,Arg_2,Arg_3) -> f6(Arg_0-1,Arg_1,Arg_2-1,Arg_3):|:1<=Arg_0

Preprocessing

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

Found invariant Arg_0<=Arg_1 for location f6

Found invariant 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location f14

Problem after Preprocessing

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_3
Temp_Vars:
Locations: f0, f14, f6
Transitions:
16:f0(Arg_0,Arg_1,Arg_3) -> f6(Arg_1,Arg_1,Arg_3)
19:f6(Arg_0,Arg_1,Arg_3) -> f14(0,Arg_1,Arg_3):|:Arg_0<=Arg_1 && Arg_1+1<=Arg_3 && Arg_0<=0 && 0<=Arg_0
20:f6(Arg_0,Arg_1,Arg_3) -> f14(0,Arg_1,Arg_3):|:Arg_0<=Arg_1 && 1+Arg_3<=Arg_1 && Arg_0<=0 && 0<=Arg_0
21:f6(Arg_0,Arg_1,Arg_3) -> f14(0,Arg_1,Arg_1):|:Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=Arg_3 && Arg_3<=Arg_1
17:f6(Arg_0,Arg_1,Arg_3) -> f6(Arg_0-1,Arg_1,Arg_3):|:Arg_0<=Arg_1 && Arg_0+1<=0
18:f6(Arg_0,Arg_1,Arg_3) -> f6(Arg_0-1,Arg_1,Arg_3):|:Arg_0<=Arg_1 && 1<=Arg_0

MPRF for transition 18:f6(Arg_0,Arg_1,Arg_3) -> f6(Arg_0-1,Arg_1,Arg_3):|:Arg_0<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

f6 [Arg_0 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
16: f0->f6: 1 {O(1)}
17: f6->f6: inf {Infinity}
18: f6->f6: Arg_1 {O(n)}
19: f6->f14: 1 {O(1)}
20: f6->f14: 1 {O(1)}
21: f6->f14: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
16: f0->f6: 1 {O(1)}
17: f6->f6: inf {Infinity}
18: f6->f6: Arg_1 {O(n)}
19: f6->f14: 1 {O(1)}
20: f6->f14: 1 {O(1)}
21: f6->f14: 1 {O(1)}

Sizebounds

16: f0->f6, Arg_0: Arg_1 {O(n)}
16: f0->f6, Arg_1: Arg_1 {O(n)}
16: f0->f6, Arg_3: Arg_3 {O(n)}
17: f6->f6, Arg_1: Arg_1 {O(n)}
17: f6->f6, Arg_3: Arg_3 {O(n)}
18: f6->f6, Arg_0: Arg_1 {O(n)}
18: f6->f6, Arg_1: Arg_1 {O(n)}
18: f6->f6, Arg_3: Arg_3 {O(n)}
19: f6->f14, Arg_0: 0 {O(1)}
19: f6->f14, Arg_1: 2*Arg_1 {O(n)}
19: f6->f14, Arg_3: 2*Arg_3 {O(n)}
20: f6->f14, Arg_0: 0 {O(1)}
20: f6->f14, Arg_1: 2*Arg_1 {O(n)}
20: f6->f14, Arg_3: 2*Arg_3 {O(n)}
21: f6->f14, Arg_0: 0 {O(1)}
21: f6->f14, Arg_1: 2*Arg_1 {O(n)}
21: f6->f14, Arg_3: 2*Arg_1 {O(n)}