Initial Problem

Start: f3
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: f1, f3
Transitions:
0:f1(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1+1,Arg_2):|:Arg_1+1<=Arg_0
2:f1(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1,Arg_2+1):|:Arg_2+2<=Arg_1 && Arg_0<=Arg_1
1:f3(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1,Arg_2):|:Arg_2+1<=Arg_1

Preprocessing

Found invariant 1+Arg_2<=Arg_1 for location f1

Problem after Preprocessing

Start: f3
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: f1, f3
Transitions:
0:f1(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1+1,Arg_2):|:1+Arg_2<=Arg_1 && Arg_1+1<=Arg_0
2:f1(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && Arg_2+2<=Arg_1 && Arg_0<=Arg_1
1:f3(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1,Arg_2):|:Arg_2+1<=Arg_1

MPRF for transition 0:f1(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1+1,Arg_2):|:1+Arg_2<=Arg_1 && Arg_1+1<=Arg_0 of depth 1:

new bound:

Arg_0+Arg_1 {O(n)}

MPRF:

f1 [Arg_0-Arg_1 ]

MPRF for transition 2:f1(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && Arg_2+2<=Arg_1 && Arg_0<=Arg_1 of depth 1:

new bound:

2*Arg_1*Arg_1+3*Arg_0*Arg_1+Arg_0*Arg_0+Arg_0*Arg_2+Arg_1*Arg_2+Arg_1+Arg_2 {O(n^2)}

MPRF:

f1 [Arg_1-Arg_2 ]

All Bounds

Timebounds

Overall timebound:2*Arg_1*Arg_1+3*Arg_0*Arg_1+Arg_0*Arg_0+Arg_0*Arg_2+Arg_1*Arg_2+2*Arg_1+Arg_0+Arg_2+1 {O(n^2)}
0: f1->f1: Arg_0+Arg_1 {O(n)}
2: f1->f1: 2*Arg_1*Arg_1+3*Arg_0*Arg_1+Arg_0*Arg_0+Arg_0*Arg_2+Arg_1*Arg_2+Arg_1+Arg_2 {O(n^2)}
1: f3->f1: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_1*Arg_1+3*Arg_0*Arg_1+Arg_0*Arg_0+Arg_0*Arg_2+Arg_1*Arg_2+2*Arg_1+Arg_0+Arg_2+1 {O(n^2)}
0: f1->f1: Arg_0+Arg_1 {O(n)}
2: f1->f1: 2*Arg_1*Arg_1+3*Arg_0*Arg_1+Arg_0*Arg_0+Arg_0*Arg_2+Arg_1*Arg_2+Arg_1+Arg_2 {O(n^2)}
1: f3->f1: 1 {O(1)}

Sizebounds

0: f1->f1, Arg_0: Arg_0 {O(n)}
0: f1->f1, Arg_1: 2*Arg_1+Arg_0 {O(n)}
0: f1->f1, Arg_2: Arg_2 {O(n)}
2: f1->f1, Arg_0: 2*Arg_0 {O(n)}
2: f1->f1, Arg_1: 3*Arg_1+Arg_0 {O(n)}
2: f1->f1, Arg_2: 2*Arg_1*Arg_1+3*Arg_0*Arg_1+Arg_0*Arg_0+Arg_0*Arg_2+Arg_1*Arg_2+3*Arg_2+Arg_1 {O(n^2)}
1: f3->f1, Arg_0: Arg_0 {O(n)}
1: f3->f1, Arg_1: Arg_1 {O(n)}
1: f3->f1, Arg_2: Arg_2 {O(n)}