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_0,1+Arg_1,Arg_2):|:Arg_0<=1
1:f2(Arg_0,Arg_1,Arg_2) -> f2(1+Arg_0,1+Arg_1,Arg_2):|:Arg_1<=2 && 2<=Arg_0
2:f2(Arg_0,Arg_1,Arg_2) -> f300(Arg_0,Arg_1,D):|:3<=Arg_1 && 2<=Arg_0

Preprocessing

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

Found invariant 3<=Arg_1 && 5<=Arg_0+Arg_1 && 2<=Arg_0 for location f300

Problem after Preprocessing

Start: f1
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: f1, f2, f300
Transitions:
11:f1(Arg_0,Arg_1) -> f2(Arg_0,Arg_1)
12:f2(Arg_0,Arg_1) -> f2(1+Arg_0,1+Arg_1):|:Arg_0<=1
13:f2(Arg_0,Arg_1) -> f2(1+Arg_0,1+Arg_1):|:Arg_1<=2 && 2<=Arg_0
14:f2(Arg_0,Arg_1) -> f300(Arg_0,Arg_1):|:3<=Arg_1 && 2<=Arg_0

MPRF for transition 12:f2(Arg_0,Arg_1) -> f2(1+Arg_0,1+Arg_1):|:Arg_0<=1 of depth 1:

new bound:

Arg_0+2 {O(n)}

MPRF:

f2 [2-Arg_0 ]

MPRF for transition 13:f2(Arg_0,Arg_1) -> f2(1+Arg_0,1+Arg_1):|:Arg_1<=2 && 2<=Arg_0 of depth 1:

new bound:

Arg_1+3 {O(n)}

MPRF:

f2 [3-Arg_1 ]

All Bounds

Timebounds

Overall timebound:Arg_0+Arg_1+7 {O(n)}
11: f1->f2: 1 {O(1)}
12: f2->f2: Arg_0+2 {O(n)}
13: f2->f2: Arg_1+3 {O(n)}
14: f2->f300: 1 {O(1)}

Costbounds

Overall costbound: Arg_0+Arg_1+7 {O(n)}
11: f1->f2: 1 {O(1)}
12: f2->f2: Arg_0+2 {O(n)}
13: f2->f2: Arg_1+3 {O(n)}
14: f2->f300: 1 {O(1)}

Sizebounds

11: f1->f2, Arg_0: Arg_0 {O(n)}
11: f1->f2, Arg_1: Arg_1 {O(n)}
12: f2->f2, Arg_0: 2*Arg_0+2 {O(n)}
12: f2->f2, Arg_1: Arg_0+Arg_1+2 {O(n)}
13: f2->f2, Arg_0: 3*Arg_0+Arg_1+5 {O(n)}
13: f2->f2, Arg_1: 3*Arg_1+Arg_0+5 {O(n)}
14: f2->f300, Arg_0: 6*Arg_0+Arg_1+7 {O(n)}
14: f2->f300, Arg_1: 2*Arg_0+5*Arg_1+7 {O(n)}