Initial Problem

Start: f0
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: f0, f2
Transitions:
0:f0(Arg_0,Arg_1) -> f2(Arg_0,Arg_1):|:1<=Arg_0 && 1<=Arg_1
1:f0(Arg_0,Arg_1) -> f2(Arg_0,Arg_1):|:1<=Arg_0 && Arg_1+1<=0
2:f0(Arg_0,Arg_1) -> f2(Arg_0,Arg_1):|:Arg_0+1<=0 && 1<=Arg_1
3:f0(Arg_0,Arg_1) -> f2(Arg_0,Arg_1):|:Arg_0+1<=0 && Arg_1+1<=0
4:f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1-1):|:Arg_1<=Arg_0 && 2<=Arg_1 && 1<=Arg_0 && 2<=Arg_0+Arg_1
5:f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1-1):|:Arg_1<=Arg_0 && 2<=Arg_1 && Arg_0+1<=0 && 2<=Arg_0+Arg_1
6:f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1-1):|:Arg_1<=Arg_0 && Arg_1<=0 && 1<=Arg_0 && 2<=Arg_0+Arg_1
7:f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1-1):|:Arg_1<=Arg_0 && Arg_1<=0 && Arg_0+1<=0 && 2<=Arg_0+Arg_1
8:f2(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1):|:Arg_0+Arg_1<=1 && Arg_1+1<=Arg_0 && 2<=Arg_0 && 1<=Arg_1
9:f2(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1):|:Arg_0+Arg_1<=1 && Arg_1+1<=Arg_0 && 2<=Arg_0 && Arg_1+1<=0
10:f2(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1):|:Arg_0+Arg_1<=1 && Arg_1+1<=Arg_0 && Arg_0<=0 && 1<=Arg_1
11:f2(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1):|:Arg_0+Arg_1<=1 && Arg_1+1<=Arg_0 && Arg_0<=0 && Arg_1+1<=0
12:f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1+1):|:Arg_0<=Arg_1 && 0<=Arg_1 && 1<=Arg_0 && Arg_1+Arg_0+1<=0
13:f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1+1):|:Arg_0<=Arg_1 && 0<=Arg_1 && Arg_0+1<=0 && Arg_1+Arg_0+1<=0
14:f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1+1):|:Arg_0<=Arg_1 && Arg_1+2<=0 && 1<=Arg_0 && Arg_1+Arg_0+1<=0
15:f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1+1):|:Arg_0<=Arg_1 && Arg_1+2<=0 && Arg_0+1<=0 && Arg_1+Arg_0+1<=0
16:f2(Arg_0,Arg_1) -> f2(Arg_0+1,Arg_1):|:0<=Arg_1+Arg_0 && Arg_0+1<=Arg_1 && 0<=Arg_0 && 1<=Arg_1
17:f2(Arg_0,Arg_1) -> f2(Arg_0+1,Arg_1):|:0<=Arg_1+Arg_0 && Arg_0+1<=Arg_1 && 0<=Arg_0 && Arg_1+1<=0
18:f2(Arg_0,Arg_1) -> f2(Arg_0+1,Arg_1):|:0<=Arg_1+Arg_0 && Arg_0+1<=Arg_1 && Arg_0+2<=0 && 1<=Arg_1
19:f2(Arg_0,Arg_1) -> f2(Arg_0+1,Arg_1):|:0<=Arg_1+Arg_0 && Arg_0+1<=Arg_1 && Arg_0+2<=0 && Arg_1+1<=0

Preprocessing

Cut unsatisfiable transition 5: f2->f2

Cut unsatisfiable transition 7: f2->f2

Cut unsatisfiable transition 8: f2->f2

Cut unsatisfiable transition 10: f2->f2

Cut unsatisfiable transition 12: f2->f2

Cut unsatisfiable transition 14: f2->f2

Cut unsatisfiable transition 17: f2->f2

Cut unsatisfiable transition 19: f2->f2

Problem after Preprocessing

Start: f0
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: f0, f2
Transitions:
0:f0(Arg_0,Arg_1) -> f2(Arg_0,Arg_1):|:1<=Arg_0 && 1<=Arg_1
1:f0(Arg_0,Arg_1) -> f2(Arg_0,Arg_1):|:1<=Arg_0 && Arg_1+1<=0
2:f0(Arg_0,Arg_1) -> f2(Arg_0,Arg_1):|:Arg_0+1<=0 && 1<=Arg_1
3:f0(Arg_0,Arg_1) -> f2(Arg_0,Arg_1):|:Arg_0+1<=0 && Arg_1+1<=0
4:f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1-1):|:Arg_1<=Arg_0 && 2<=Arg_1 && 1<=Arg_0 && 2<=Arg_0+Arg_1
6:f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1-1):|:Arg_1<=Arg_0 && Arg_1<=0 && 1<=Arg_0 && 2<=Arg_0+Arg_1
9:f2(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1):|:Arg_0+Arg_1<=1 && Arg_1+1<=Arg_0 && 2<=Arg_0 && Arg_1+1<=0
11:f2(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1):|:Arg_0+Arg_1<=1 && Arg_1+1<=Arg_0 && Arg_0<=0 && Arg_1+1<=0
13:f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1+1):|:Arg_0<=Arg_1 && 0<=Arg_1 && Arg_0+1<=0 && Arg_1+Arg_0+1<=0
15:f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1+1):|:Arg_0<=Arg_1 && Arg_1+2<=0 && Arg_0+1<=0 && Arg_1+Arg_0+1<=0
16:f2(Arg_0,Arg_1) -> f2(Arg_0+1,Arg_1):|:0<=Arg_1+Arg_0 && Arg_0+1<=Arg_1 && 0<=Arg_0 && 1<=Arg_1
18:f2(Arg_0,Arg_1) -> f2(Arg_0+1,Arg_1):|:0<=Arg_1+Arg_0 && Arg_0+1<=Arg_1 && Arg_0+2<=0 && 1<=Arg_1

MPRF for transition 4:f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1-1):|:Arg_1<=Arg_0 && 2<=Arg_1 && 1<=Arg_0 && 2<=Arg_0+Arg_1 of depth 1:

new bound:

3*Arg_1 {O(n)}

MPRF:

f2 [Arg_1 ]

MPRF for transition 6:f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1-1):|:Arg_1<=Arg_0 && Arg_1<=0 && 1<=Arg_0 && 2<=Arg_0+Arg_1 of depth 1:

new bound:

2*Arg_0+2*Arg_1 {O(n)}

MPRF:

f2 [Arg_0+Arg_1 ]

MPRF for transition 9:f2(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1):|:Arg_0+Arg_1<=1 && Arg_1+1<=Arg_0 && 2<=Arg_0 && Arg_1+1<=0 of depth 1:

new bound:

3*Arg_0 {O(n)}

MPRF:

f2 [Arg_0 ]

MPRF for transition 11:f2(Arg_0,Arg_1) -> f2(Arg_0-1,Arg_1):|:Arg_0+Arg_1<=1 && Arg_1+1<=Arg_0 && Arg_0<=0 && Arg_1+1<=0 of depth 1:

new bound:

2*Arg_0+2*Arg_1 {O(n)}

MPRF:

f2 [Arg_0-Arg_1 ]

MPRF for transition 13:f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1+1):|:Arg_0<=Arg_1 && 0<=Arg_1 && Arg_0+1<=0 && Arg_1+Arg_0+1<=0 of depth 1:

new bound:

2*Arg_0+2*Arg_1 {O(n)}

MPRF:

f2 [-Arg_0-Arg_1 ]

MPRF for transition 15:f2(Arg_0,Arg_1) -> f2(Arg_0,Arg_1+1):|:Arg_0<=Arg_1 && Arg_1+2<=0 && Arg_0+1<=0 && Arg_1+Arg_0+1<=0 of depth 1:

new bound:

3*Arg_1 {O(n)}

MPRF:

f2 [-Arg_1 ]

MPRF for transition 16:f2(Arg_0,Arg_1) -> f2(Arg_0+1,Arg_1):|:0<=Arg_1+Arg_0 && Arg_0+1<=Arg_1 && 0<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

2*Arg_0+2*Arg_1 {O(n)}

MPRF:

f2 [Arg_1-Arg_0 ]

MPRF for transition 18:f2(Arg_0,Arg_1) -> f2(Arg_0+1,Arg_1):|:0<=Arg_1+Arg_0 && Arg_0+1<=Arg_1 && Arg_0+2<=0 && 1<=Arg_1 of depth 1:

new bound:

3*Arg_0 {O(n)}

MPRF:

f2 [-Arg_0 ]

All Bounds

Timebounds

Overall timebound:14*Arg_0+14*Arg_1+4 {O(n)}
0: f0->f2: 1 {O(1)}
1: f0->f2: 1 {O(1)}
2: f0->f2: 1 {O(1)}
3: f0->f2: 1 {O(1)}
4: f2->f2: 3*Arg_1 {O(n)}
6: f2->f2: 2*Arg_0+2*Arg_1 {O(n)}
9: f2->f2: 3*Arg_0 {O(n)}
11: f2->f2: 2*Arg_0+2*Arg_1 {O(n)}
13: f2->f2: 2*Arg_0+2*Arg_1 {O(n)}
15: f2->f2: 3*Arg_1 {O(n)}
16: f2->f2: 2*Arg_0+2*Arg_1 {O(n)}
18: f2->f2: 3*Arg_0 {O(n)}

Costbounds

Overall costbound: 14*Arg_0+14*Arg_1+4 {O(n)}
0: f0->f2: 1 {O(1)}
1: f0->f2: 1 {O(1)}
2: f0->f2: 1 {O(1)}
3: f0->f2: 1 {O(1)}
4: f2->f2: 3*Arg_1 {O(n)}
6: f2->f2: 2*Arg_0+2*Arg_1 {O(n)}
9: f2->f2: 3*Arg_0 {O(n)}
11: f2->f2: 2*Arg_0+2*Arg_1 {O(n)}
13: f2->f2: 2*Arg_0+2*Arg_1 {O(n)}
15: f2->f2: 3*Arg_1 {O(n)}
16: f2->f2: 2*Arg_0+2*Arg_1 {O(n)}
18: f2->f2: 3*Arg_0 {O(n)}

Sizebounds

0: f0->f2, Arg_0: Arg_0 {O(n)}
0: f0->f2, Arg_1: Arg_1 {O(n)}
1: f0->f2, Arg_0: Arg_0 {O(n)}
1: f0->f2, Arg_1: Arg_1 {O(n)}
2: f0->f2, Arg_0: Arg_0 {O(n)}
2: f0->f2, Arg_1: Arg_1 {O(n)}
3: f0->f2, Arg_0: Arg_0 {O(n)}
3: f0->f2, Arg_1: Arg_1 {O(n)}
4: f2->f2, Arg_0: 2*Arg_1+4*Arg_0 {O(n)}
4: f2->f2, Arg_1: 2*Arg_1 {O(n)}
6: f2->f2, Arg_0: Arg_0 {O(n)}
6: f2->f2, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
9: f2->f2, Arg_0: 2*Arg_0 {O(n)}
9: f2->f2, Arg_1: 2*Arg_0+4*Arg_1 {O(n)}
11: f2->f2, Arg_0: 2*Arg_1+3*Arg_0 {O(n)}
11: f2->f2, Arg_1: Arg_1 {O(n)}
13: f2->f2, Arg_0: Arg_0 {O(n)}
13: f2->f2, Arg_1: 2*Arg_0+3*Arg_1 {O(n)}
15: f2->f2, Arg_0: 2*Arg_1+4*Arg_0 {O(n)}
15: f2->f2, Arg_1: 2*Arg_1 {O(n)}
16: f2->f2, Arg_0: 2*Arg_1+3*Arg_0 {O(n)}
16: f2->f2, Arg_1: Arg_1 {O(n)}
18: f2->f2, Arg_0: 2*Arg_0 {O(n)}
18: f2->f2, Arg_1: 2*Arg_0+4*Arg_1 {O(n)}