Initial Problem

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: D
Locations: f0, f1, f4
Transitions:
0:f0(Arg_0,Arg_1,Arg_2) -> f1(0,Arg_1,Arg_2)
1:f1(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1-1,D):|:1<=Arg_1
2:f1(Arg_0,Arg_1,Arg_2) -> f4(Arg_0,Arg_1,D):|:Arg_1<=0
3:f4(Arg_0,Arg_1,Arg_2) -> f4(1,Arg_1,D)

Preprocessing

Eliminate variables {D,Arg_0,Arg_2} that do not contribute to the problem

Found invariant Arg_1<=0 for location f4

Problem after Preprocessing

Start: f0
Program_Vars: Arg_1
Temp_Vars:
Locations: f0, f1, f4
Transitions:
10:f0(Arg_1) -> f1(Arg_1)
11:f1(Arg_1) -> f1(Arg_1-1):|:1<=Arg_1
12:f1(Arg_1) -> f4(Arg_1):|:Arg_1<=0
13:f4(Arg_1) -> f4(Arg_1):|:Arg_1<=0

MPRF for transition 11:f1(Arg_1) -> f1(Arg_1-1):|:1<=Arg_1 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

f1 [Arg_1 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
10: f0->f1: 1 {O(1)}
11: f1->f1: Arg_1 {O(n)}
12: f1->f4: 1 {O(1)}
13: f4->f4: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
10: f0->f1: 1 {O(1)}
11: f1->f1: Arg_1 {O(n)}
12: f1->f4: 1 {O(1)}
13: f4->f4: inf {Infinity}

Sizebounds

10: f0->f1, Arg_1: Arg_1 {O(n)}
11: f1->f1, Arg_1: Arg_1 {O(n)}
12: f1->f4, Arg_1: 2*Arg_1 {O(n)}
13: f4->f4, Arg_1: 2*Arg_1 {O(n)}