Initial Problem

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: f0, f4
Transitions:
2:f0(Arg_0,Arg_1,Arg_2) -> f4(0,0,Arg_2):|:1<=Arg_2
0:f4(Arg_0,Arg_1,Arg_2) -> f4(Arg_0,Arg_1+1,Arg_2):|:Arg_1+1<=Arg_0
1:f4(Arg_0,Arg_1,Arg_2) -> f4(Arg_0+1,0,Arg_2):|:Arg_0+2<=Arg_2 && Arg_0<=Arg_1

Preprocessing

Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location f4

Problem after Preprocessing

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: f0, f4
Transitions:
2:f0(Arg_0,Arg_1,Arg_2) -> f4(0,0,Arg_2):|:1<=Arg_2
0:f4(Arg_0,Arg_1,Arg_2) -> f4(Arg_0,Arg_1+1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1+1<=Arg_0
1:f4(Arg_0,Arg_1,Arg_2) -> f4(Arg_0+1,0,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0+2<=Arg_2 && Arg_0<=Arg_1

MPRF for transition 1:f4(Arg_0,Arg_1,Arg_2) -> f4(Arg_0+1,0,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_0+2<=Arg_2 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_2 {O(n)}

MPRF:

f4 [Arg_2-Arg_0 ]

MPRF for transition 0:f4(Arg_0,Arg_1,Arg_2) -> f4(Arg_0,Arg_1+1,Arg_2):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_1+1<=Arg_0 of depth 1:

new bound:

Arg_2*Arg_2+Arg_2 {O(n^2)}

MPRF:

f4 [Arg_0+1-Arg_1 ]

All Bounds

Timebounds

Overall timebound:Arg_2*Arg_2+2*Arg_2+1 {O(n^2)}
2: f0->f4: 1 {O(1)}
0: f4->f4: Arg_2*Arg_2+Arg_2 {O(n^2)}
1: f4->f4: Arg_2 {O(n)}

Costbounds

Overall costbound: Arg_2*Arg_2+2*Arg_2+1 {O(n^2)}
2: f0->f4: 1 {O(1)}
0: f4->f4: Arg_2*Arg_2+Arg_2 {O(n^2)}
1: f4->f4: Arg_2 {O(n)}

Sizebounds

2: f0->f4, Arg_0: 0 {O(1)}
2: f0->f4, Arg_1: 0 {O(1)}
2: f0->f4, Arg_2: Arg_2 {O(n)}
0: f4->f4, Arg_0: Arg_2 {O(n)}
0: f4->f4, Arg_1: Arg_2*Arg_2+Arg_2 {O(n^2)}
0: f4->f4, Arg_2: Arg_2 {O(n)}
1: f4->f4, Arg_0: Arg_2 {O(n)}
1: f4->f4, Arg_1: 0 {O(1)}
1: f4->f4, Arg_2: Arg_2 {O(n)}