Initial Problem

Start: f0
Program_Vars: Arg_0, Arg_1
Temp_Vars: C
Locations: f0, f15, f6
Transitions:
0:f0(Arg_0,Arg_1) -> f6(C,0)
2:f6(Arg_0,Arg_1) -> f15(Arg_0,Arg_1):|:10<=Arg_1
1:f6(Arg_0,Arg_1) -> f6(Arg_0,Arg_1+1):|:Arg_1<=9

Preprocessing

Eliminate variables {C,Arg_0} that do not contribute to the problem

Found invariant Arg_1<=10 && 0<=Arg_1 for location f6

Found invariant Arg_1<=10 && 10<=Arg_1 for location f15

Problem after Preprocessing

Start: f0
Program_Vars: Arg_1
Temp_Vars:
Locations: f0, f15, f6
Transitions:
7:f0(Arg_1) -> f6(0)
9:f6(Arg_1) -> f15(Arg_1):|:Arg_1<=10 && 0<=Arg_1 && 10<=Arg_1
8:f6(Arg_1) -> f6(Arg_1+1):|:Arg_1<=10 && 0<=Arg_1 && Arg_1<=9

MPRF for transition 8:f6(Arg_1) -> f6(Arg_1+1):|:Arg_1<=10 && 0<=Arg_1 && Arg_1<=9 of depth 1:

new bound:

10 {O(1)}

MPRF:

f6 [10-Arg_1 ]

All Bounds

Timebounds

Overall timebound:12 {O(1)}
7: f0->f6: 1 {O(1)}
8: f6->f6: 10 {O(1)}
9: f6->f15: 1 {O(1)}

Costbounds

Overall costbound: 12 {O(1)}
7: f0->f6: 1 {O(1)}
8: f6->f6: 10 {O(1)}
9: f6->f15: 1 {O(1)}

Sizebounds

7: f0->f6, Arg_1: 0 {O(1)}
8: f6->f6, Arg_1: 10 {O(1)}
9: f6->f15, Arg_1: 10 {O(1)}