Initial Problem

Start: f0
Program_Vars: Arg_0, Arg_1
Temp_Vars: C
Locations: f0, f10, f18, f4
Transitions:
0:f0(Arg_0,Arg_1) -> f4(0,Arg_1)
2:f10(Arg_0,Arg_1) -> f10(Arg_0,Arg_1+1):|:Arg_1<=1
3:f10(Arg_0,Arg_1) -> f18(Arg_0,Arg_1):|:2<=Arg_1 && C+1<=0
4:f10(Arg_0,Arg_1) -> f18(Arg_0,Arg_1):|:2<=Arg_1
5:f4(Arg_0,Arg_1) -> f10(Arg_0,0):|:2<=Arg_0
1:f4(Arg_0,Arg_1) -> f4(Arg_0+1,Arg_1):|:Arg_0<=1

Preprocessing

Found invariant Arg_1<=2 && Arg_1<=Arg_0 && Arg_0+Arg_1<=4 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=2 && 2<=Arg_0 for location f18

Found invariant Arg_1<=2 && Arg_1<=Arg_0 && Arg_0+Arg_1<=4 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=2+Arg_1 && Arg_0<=2 && 2<=Arg_0 for location f10

Found invariant Arg_0<=2 && 0<=Arg_0 for location f4

Problem after Preprocessing

Start: f0
Program_Vars: Arg_0, Arg_1
Temp_Vars: C
Locations: f0, f10, f18, f4
Transitions:
0:f0(Arg_0,Arg_1) -> f4(0,Arg_1)
2:f10(Arg_0,Arg_1) -> f10(Arg_0,Arg_1+1):|:Arg_1<=2 && Arg_1<=Arg_0 && Arg_0+Arg_1<=4 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=2+Arg_1 && Arg_0<=2 && 2<=Arg_0 && Arg_1<=1
3:f10(Arg_0,Arg_1) -> f18(Arg_0,Arg_1):|:Arg_1<=2 && Arg_1<=Arg_0 && Arg_0+Arg_1<=4 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=2+Arg_1 && Arg_0<=2 && 2<=Arg_0 && 2<=Arg_1 && C+1<=0
4:f10(Arg_0,Arg_1) -> f18(Arg_0,Arg_1):|:Arg_1<=2 && Arg_1<=Arg_0 && Arg_0+Arg_1<=4 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=2+Arg_1 && Arg_0<=2 && 2<=Arg_0 && 2<=Arg_1
5:f4(Arg_0,Arg_1) -> f10(Arg_0,0):|:Arg_0<=2 && 0<=Arg_0 && 2<=Arg_0
1:f4(Arg_0,Arg_1) -> f4(Arg_0+1,Arg_1):|:Arg_0<=2 && 0<=Arg_0 && Arg_0<=1

MPRF for transition 1:f4(Arg_0,Arg_1) -> f4(Arg_0+1,Arg_1):|:Arg_0<=2 && 0<=Arg_0 && Arg_0<=1 of depth 1:

new bound:

2 {O(1)}

MPRF:

f4 [2-Arg_0 ]

MPRF for transition 2:f10(Arg_0,Arg_1) -> f10(Arg_0,Arg_1+1):|:Arg_1<=2 && Arg_1<=Arg_0 && Arg_0+Arg_1<=4 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=2+Arg_1 && Arg_0<=2 && 2<=Arg_0 && Arg_1<=1 of depth 1:

new bound:

3 {O(1)}

MPRF:

f10 [3-Arg_1 ]

All Bounds

Timebounds

Overall timebound:9 {O(1)}
0: f0->f4: 1 {O(1)}
2: f10->f10: 3 {O(1)}
3: f10->f18: 1 {O(1)}
4: f10->f18: 1 {O(1)}
1: f4->f4: 2 {O(1)}
5: f4->f10: 1 {O(1)}

Costbounds

Overall costbound: 9 {O(1)}
0: f0->f4: 1 {O(1)}
2: f10->f10: 3 {O(1)}
3: f10->f18: 1 {O(1)}
4: f10->f18: 1 {O(1)}
1: f4->f4: 2 {O(1)}
5: f4->f10: 1 {O(1)}

Sizebounds

0: f0->f4, Arg_0: 0 {O(1)}
0: f0->f4, Arg_1: Arg_1 {O(n)}
2: f10->f10, Arg_0: 2 {O(1)}
2: f10->f10, Arg_1: 2 {O(1)}
3: f10->f18, Arg_0: 2 {O(1)}
3: f10->f18, Arg_1: 2 {O(1)}
4: f10->f18, Arg_0: 2 {O(1)}
4: f10->f18, Arg_1: 2 {O(1)}
1: f4->f4, Arg_0: 2 {O(1)}
1: f4->f4, Arg_1: Arg_1 {O(n)}
5: f4->f10, Arg_0: 2 {O(1)}
5: f4->f10, Arg_1: 0 {O(1)}