Initial Problem

Start: f1
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: D
Locations: f1, f2, f300
Transitions:
3:f1(Arg_0,Arg_1,Arg_2) -> f2(Arg_0,Arg_1,Arg_2)
0:f2(Arg_0,Arg_1,Arg_2) -> f2(1+Arg_0,Arg_1,Arg_2):|:1+Arg_0<=Arg_1
1:f2(Arg_0,Arg_1,Arg_2) -> f2(1+Arg_0,Arg_1,Arg_2):|:1+Arg_1<=Arg_0 && Arg_1<=Arg_0
2:f2(Arg_0,Arg_1,Arg_2) -> f300(Arg_0,Arg_1,D):|:Arg_0<=Arg_1 && Arg_1<=Arg_0

Preprocessing

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

Found invariant Arg_1<=Arg_0 && Arg_0<=Arg_1 for location f300

Problem after Preprocessing

Start: f1
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: f1, f2, f300
Transitions:
13:f1(Arg_0,Arg_1) -> f2(Arg_0,Arg_1)
14:f2(Arg_0,Arg_1) -> f2(1+Arg_0,Arg_1):|:1+Arg_0<=Arg_1
15:f2(Arg_0,Arg_1) -> f2(1+Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && Arg_1<=Arg_0
16:f2(Arg_0,Arg_1) -> f300(Arg_0,Arg_1):|:Arg_0<=Arg_1 && Arg_1<=Arg_0

MPRF for transition 14:f2(Arg_0,Arg_1) -> f2(1+Arg_0,Arg_1):|:1+Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0+Arg_1 {O(n)}

MPRF:

f2 [Arg_1-Arg_0 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
13: f1->f2: 1 {O(1)}
14: f2->f2: Arg_0+Arg_1 {O(n)}
15: f2->f2: inf {Infinity}
16: f2->f300: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
13: f1->f2: 1 {O(1)}
14: f2->f2: Arg_0+Arg_1 {O(n)}
15: f2->f2: inf {Infinity}
16: f2->f300: 1 {O(1)}

Sizebounds

13: f1->f2, Arg_0: Arg_0 {O(n)}
13: f1->f2, Arg_1: Arg_1 {O(n)}
14: f2->f2, Arg_0: 2*Arg_0+Arg_1 {O(n)}
14: f2->f2, Arg_1: Arg_1 {O(n)}
15: f2->f2, Arg_1: Arg_1 {O(n)}
16: f2->f300, Arg_0: 3*Arg_0+Arg_1 {O(n)}
16: f2->f300, Arg_1: 2*Arg_1 {O(n)}