Initial Problem

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

Preprocessing

Cut unsatisfiable transition 4: f1->f300

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

Found invariant 1+Arg_1<=Arg_0 for location f300

Problem after Preprocessing

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

MPRF for transition 12:f1(Arg_0,Arg_1) -> f1(1+Arg_0,Arg_1):|:1+Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0+Arg_1 {O(n)}

MPRF:

f1 [Arg_1-Arg_0 ]

MPRF for transition 13:f1(Arg_0,Arg_1) -> f1(1+Arg_0,Arg_0):|:D<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 of depth 1:

new bound:

Arg_0+Arg_1+1 {O(n)}

MPRF:

f1 [Arg_1+1-Arg_0 ]

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

12: f1->f1, Arg_0: 2*Arg_0+Arg_1 {O(n)}
12: f1->f1, Arg_1: Arg_1 {O(n)}
13: f1->f1, Arg_0: 3*Arg_0+Arg_1+2 {O(n)}
13: f1->f1, Arg_1: 3*Arg_0+Arg_1 {O(n)}
14: f1->f300, Arg_0: 4*Arg_0+Arg_1+2 {O(n)}
14: f1->f300, Arg_1: 2*Arg_1+3*Arg_0 {O(n)}
15: f2->f1, Arg_0: Arg_0 {O(n)}
15: f2->f1, Arg_1: Arg_1 {O(n)}