Initial Problem

Start: f3
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: f0, f3, f4
Transitions:
1:f0(Arg_0,Arg_1) -> f0(Arg_0,Arg_1-1):|:1<=Arg_1
3:f0(Arg_0,Arg_1) -> f4(-1,Arg_1):|:Arg_1<=0
0:f3(Arg_0,Arg_1) -> f0(0,Arg_1)
2:f4(Arg_0,Arg_1) -> f4(Arg_0,Arg_1)

Preprocessing

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

Found invariant Arg_1<=0 for location f4

Problem after Preprocessing

Start: f3
Program_Vars: Arg_1
Temp_Vars:
Locations: f0, f3, f4
Transitions:
9:f0(Arg_1) -> f0(Arg_1-1):|:1<=Arg_1
10:f0(Arg_1) -> f4(Arg_1):|:Arg_1<=0
11:f3(Arg_1) -> f0(Arg_1)
12:f4(Arg_1) -> f4(Arg_1):|:Arg_1<=0

MPRF for transition 9:f0(Arg_1) -> f0(Arg_1-1):|:1<=Arg_1 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

f0 [Arg_1 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
9: f0->f0: Arg_1 {O(n)}
10: f0->f4: 1 {O(1)}
11: f3->f0: 1 {O(1)}
12: f4->f4: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
9: f0->f0: Arg_1 {O(n)}
10: f0->f4: 1 {O(1)}
11: f3->f0: 1 {O(1)}
12: f4->f4: inf {Infinity}

Sizebounds

9: f0->f0, Arg_1: Arg_1 {O(n)}
10: f0->f4, Arg_1: 2*Arg_1 {O(n)}
11: f3->f0, Arg_1: Arg_1 {O(n)}
12: f4->f4, Arg_1: 2*Arg_1 {O(n)}