Initial Problem

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

Preprocessing

Found invariant Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location f3

Problem after Preprocessing

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

MPRF for transition 2:f3(Arg_0,Arg_1) -> f3(Arg_0-1,Arg_0-1):|:Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<=0 && 2<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

f3 [Arg_0 ]

MPRF for transition 1:f3(Arg_0,Arg_1) -> f3(Arg_0,Arg_1-1):|:Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

Arg_0*Arg_0+2*Arg_0+1 {O(n^2)}

MPRF:

f3 [Arg_1+1 ]

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

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