Initial Problem

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: f0, f1
Transitions:
0:f0(Arg_0,Arg_1,Arg_2,Arg_3) -> f1(Arg_0,Arg_1,2,Arg_3):|:0<=Arg_0 && Arg_0<=3 && Arg_1<=3 && 0<=Arg_1
1:f1(Arg_0,Arg_1,Arg_2,Arg_3) -> f1(Arg_0,Arg_1+1,Arg_2,Arg_1+1):|:2*Arg_1+1<=Arg_2+Arg_0 && 2<=0
2:f1(Arg_0,Arg_1,Arg_2,Arg_3) -> f1(Arg_0,Arg_1+1,Arg_2,Arg_1+1):|:2*Arg_1+1<=Arg_2+Arg_0
3:f1(Arg_0,Arg_1,Arg_2,Arg_3) -> f1(Arg_0,Arg_1-1,Arg_2,Arg_1-1):|:2+Arg_2+Arg_0<=2*Arg_1
4:f1(Arg_0,Arg_1,Arg_2,Arg_3) -> f1(Arg_0,Arg_1-1,Arg_2,Arg_1-1):|:2+Arg_2+Arg_0<=2*Arg_1 && 2<=0
5:f1(Arg_0,Arg_1,Arg_2,Arg_3) -> f1(Arg_0,Arg_1,Arg_2,Arg_1):|:1<=0 && Arg_2+Arg_0<=2*Arg_1 && 2*Arg_1<=Arg_2+Arg_0+1
6:f1(Arg_0,Arg_1,Arg_2,Arg_3) -> f1(Arg_0,Arg_1,Arg_2,Arg_1):|:1<=0 && Arg_2+Arg_0<=2*Arg_1 && 2*Arg_1<=Arg_2+Arg_0+1

Preprocessing

Cut unsatisfiable transition 1: f1->f1

Cut unsatisfiable transition 4: f1->f1

Cut unsatisfiable transition 5: f1->f1

Cut unsatisfiable transition 6: f1->f1

Eliminate variables {Arg_3} that do not contribute to the problem

Found invariant Arg_2<=2 && Arg_2<=2+Arg_1 && Arg_1+Arg_2<=5 && Arg_2<=2+Arg_0 && Arg_0+Arg_2<=5 && 2<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && Arg_1<=3 && Arg_1<=3+Arg_0 && Arg_0+Arg_1<=6 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=3+Arg_1 && Arg_0<=3 && 0<=Arg_0 for location f1

Problem after Preprocessing

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: f0, f1
Transitions:
50:f0(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1,2):|:0<=Arg_0 && Arg_0<=3 && Arg_1<=3 && 0<=Arg_1
51:f1(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1+1,Arg_2):|:Arg_2<=2 && Arg_2<=2+Arg_1 && Arg_1+Arg_2<=5 && Arg_2<=2+Arg_0 && Arg_0+Arg_2<=5 && 2<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && Arg_1<=3 && Arg_1<=3+Arg_0 && Arg_0+Arg_1<=6 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=3+Arg_1 && Arg_0<=3 && 0<=Arg_0 && 2*Arg_1+1<=Arg_2+Arg_0
52:f1(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=2 && Arg_2<=2+Arg_1 && Arg_1+Arg_2<=5 && Arg_2<=2+Arg_0 && Arg_0+Arg_2<=5 && 2<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && Arg_1<=3 && Arg_1<=3+Arg_0 && Arg_0+Arg_1<=6 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=3+Arg_1 && Arg_0<=3 && 0<=Arg_0 && 2+Arg_2+Arg_0<=2*Arg_1

MPRF for transition 51:f1(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1+1,Arg_2):|:Arg_2<=2 && Arg_2<=2+Arg_1 && Arg_1+Arg_2<=5 && Arg_2<=2+Arg_0 && Arg_0+Arg_2<=5 && 2<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && Arg_1<=3 && Arg_1<=3+Arg_0 && Arg_0+Arg_1<=6 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=3+Arg_1 && Arg_0<=3 && 0<=Arg_0 && 2*Arg_1+1<=Arg_2+Arg_0 of depth 1:

new bound:

7 {O(1)}

MPRF:

f1 [4-Arg_1 ]

MPRF for transition 52:f1(Arg_0,Arg_1,Arg_2) -> f1(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=2 && Arg_2<=2+Arg_1 && Arg_1+Arg_2<=5 && Arg_2<=2+Arg_0 && Arg_0+Arg_2<=5 && 2<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && Arg_1<=3 && Arg_1<=3+Arg_0 && Arg_0+Arg_1<=6 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=3+Arg_1 && Arg_0<=3 && 0<=Arg_0 && 2+Arg_2+Arg_0<=2*Arg_1 of depth 1:

new bound:

4 {O(1)}

MPRF:

f1 [Arg_1+1 ]

All Bounds

Timebounds

Overall timebound:12 {O(1)}
50: f0->f1: 1 {O(1)}
51: f1->f1: 7 {O(1)}
52: f1->f1: 4 {O(1)}

Costbounds

Overall costbound: 12 {O(1)}
50: f0->f1: 1 {O(1)}
51: f1->f1: 7 {O(1)}
52: f1->f1: 4 {O(1)}

Sizebounds

50: f0->f1, Arg_0: 3 {O(1)}
50: f0->f1, Arg_1: 3 {O(1)}
50: f0->f1, Arg_2: 2 {O(1)}
51: f1->f1, Arg_0: 3 {O(1)}
51: f1->f1, Arg_1: 3 {O(1)}
51: f1->f1, Arg_2: 2 {O(1)}
52: f1->f1, Arg_0: 2 {O(1)}
52: f1->f1, Arg_1: 2 {O(1)}
52: f1->f1, Arg_2: 2 {O(1)}