Initial Problem

Start: f0
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: f0, f2, f3
Transitions:
1:f0(Arg_0,Arg_1) -> f2(Arg_0,0)
2:f2(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1):|:1<=Arg_0
0:f2(Arg_0,Arg_1) -> f3(Arg_0,1):|:Arg_0<=0

Preprocessing

Eliminate variables {Arg_1} that do not contribute to the problem

Found invariant Arg_0<=0 for location f3

Problem after Preprocessing

Start: f0
Program_Vars: Arg_0
Temp_Vars:
Locations: f0, f2, f3
Transitions:
7:f0(Arg_0) -> f2(Arg_0)
9:f2(Arg_0) -> f2(Arg_0-1):|:1<=Arg_0
8:f2(Arg_0) -> f3(Arg_0):|:Arg_0<=0

MPRF for transition 9:f2(Arg_0) -> f2(Arg_0-1):|:1<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

f2 [Arg_0 ]

All Bounds

Timebounds

Overall timebound:Arg_0+2 {O(n)}
7: f0->f2: 1 {O(1)}
8: f2->f3: 1 {O(1)}
9: f2->f2: Arg_0 {O(n)}

Costbounds

Overall costbound: Arg_0+2 {O(n)}
7: f0->f2: 1 {O(1)}
8: f2->f3: 1 {O(1)}
9: f2->f2: Arg_0 {O(n)}

Sizebounds

7: f0->f2, Arg_0: Arg_0 {O(n)}
8: f2->f3, Arg_0: 2*Arg_0 {O(n)}
9: f2->f2, Arg_0: Arg_0 {O(n)}