Initial Problem

Start: f0
Program_Vars: Arg_0
Temp_Vars: B
Locations: f0, f12, f5
Transitions:
2:f0(Arg_0) -> f12(B):|:B<=0
0:f0(Arg_0) -> f5(B):|:1<=B
3:f5(Arg_0) -> f12(Arg_0):|:20<=Arg_0
1:f5(Arg_0) -> f5(Arg_0+1):|:Arg_0<=19

Preprocessing

Found invariant 1<=Arg_0 for location f5

Problem after Preprocessing

Start: f0
Program_Vars: Arg_0
Temp_Vars: B
Locations: f0, f12, f5
Transitions:
2:f0(Arg_0) -> f12(B):|:B<=0
0:f0(Arg_0) -> f5(B):|:1<=B
3:f5(Arg_0) -> f12(Arg_0):|:1<=Arg_0 && 20<=Arg_0
1:f5(Arg_0) -> f5(Arg_0+1):|:1<=Arg_0 && Arg_0<=19

Analysing control-flow refined program

Found invariant 1<=Arg_0 for location f5

Found invariant Arg_0<=20 && 2<=Arg_0 for location n_f5___1

MPRF for transition 25:n_f5___1(Arg_0) -> n_f5___1(Arg_0+1):|:Arg_0<=20 && 2<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && Arg_0<=20 && 1<=Arg_0 && Arg_0<=19 of depth 1:

new bound:

40 {O(1)}

MPRF:

n_f5___1 [20-Arg_0 ]

CFR: Improvement to new bound with the following program:

new bound:

40 {O(1)}

cfr-program:

Start: f0
Program_Vars: Arg_0
Temp_Vars: B
Locations: f0, f12, f5, n_f5___1
Transitions:
2:f0(Arg_0) -> f12(B):|:B<=0
0:f0(Arg_0) -> f5(B):|:1<=B
3:f5(Arg_0) -> f12(Arg_0):|:1<=Arg_0 && 1<=Arg_0 && 20<=Arg_0
26:f5(Arg_0) -> n_f5___1(Arg_0+1):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_0<=19
29:n_f5___1(Arg_0) -> f12(Arg_0):|:Arg_0<=20 && 2<=Arg_0 && 1<=Arg_0 && 20<=Arg_0
25:n_f5___1(Arg_0) -> n_f5___1(Arg_0+1):|:Arg_0<=20 && 2<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && Arg_0<=20 && 1<=Arg_0 && Arg_0<=19

All Bounds

Timebounds

Overall timebound:45 {O(1)}
0: f0->f5: 1 {O(1)}
2: f0->f12: 1 {O(1)}
3: f5->f12: 1 {O(1)}
26: f5->n_f5___1: 1 {O(1)}
25: n_f5___1->n_f5___1: 40 {O(1)}
29: n_f5___1->f12: 1 {O(1)}

Costbounds

Overall costbound: 45 {O(1)}
0: f0->f5: 1 {O(1)}
2: f0->f12: 1 {O(1)}
3: f5->f12: 1 {O(1)}
26: f5->n_f5___1: 1 {O(1)}
25: n_f5___1->n_f5___1: 40 {O(1)}
29: n_f5___1->f12: 1 {O(1)}

Sizebounds

26: f5->n_f5___1, Arg_0: 20 {O(1)}
25: n_f5___1->n_f5___1, Arg_0: 20 {O(1)}
29: n_f5___1->f12, Arg_0: 20 {O(1)}