Initial Problem

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: f0, f10, f13, f21, f24, f27, f39
Transitions:
0:f0(Arg_0,Arg_1,Arg_2) -> f10(1,Arg_1,Arg_2)
1:f10(Arg_0,Arg_1,Arg_2) -> f13(Arg_0,1,Arg_2):|:Arg_0<=5
10:f10(Arg_0,Arg_1,Arg_2) -> f21(1,Arg_1,Arg_2):|:6<=Arg_0
9:f13(Arg_0,Arg_1,Arg_2) -> f10(Arg_0+1,Arg_1,Arg_2):|:6<=Arg_1
2:f13(Arg_0,Arg_1,Arg_2) -> f13(Arg_0,Arg_1+1,Arg_2):|:Arg_1<=5
3:f21(Arg_0,Arg_1,Arg_2) -> f24(Arg_0,1,Arg_2):|:Arg_0<=5
8:f21(Arg_0,Arg_1,Arg_2) -> f39(Arg_0,Arg_1,Arg_2):|:6<=Arg_0
7:f24(Arg_0,Arg_1,Arg_2) -> f21(Arg_0+1,Arg_1,Arg_2):|:6<=Arg_1
4:f24(Arg_0,Arg_1,Arg_2) -> f27(Arg_0,Arg_1,1):|:Arg_1<=5
6:f27(Arg_0,Arg_1,Arg_2) -> f24(Arg_0,Arg_1+1,Arg_2):|:6<=Arg_2
5:f27(Arg_0,Arg_1,Arg_2) -> f27(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=5

Preprocessing

Found invariant Arg_1<=6 && Arg_1<=5+Arg_0 && Arg_0+Arg_1<=11 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=5 && 1<=Arg_0 for location f13

Found invariant Arg_1<=6 && Arg_1<=5+Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location f24

Found invariant Arg_0<=6 && 1<=Arg_0 for location f10

Found invariant Arg_2<=6 && Arg_2<=5+Arg_1 && Arg_1+Arg_2<=11 && Arg_2<=5+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=4+Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=5 && Arg_1<=4+Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location f27

Found invariant 1<=Arg_0 for location f21

Found invariant 6<=Arg_0 for location f39

Problem after Preprocessing

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: f0, f10, f13, f21, f24, f27, f39
Transitions:
0:f0(Arg_0,Arg_1,Arg_2) -> f10(1,Arg_1,Arg_2)
1:f10(Arg_0,Arg_1,Arg_2) -> f13(Arg_0,1,Arg_2):|:Arg_0<=6 && 1<=Arg_0 && Arg_0<=5
10:f10(Arg_0,Arg_1,Arg_2) -> f21(1,Arg_1,Arg_2):|:Arg_0<=6 && 1<=Arg_0 && 6<=Arg_0
9:f13(Arg_0,Arg_1,Arg_2) -> f10(Arg_0+1,Arg_1,Arg_2):|:Arg_1<=6 && Arg_1<=5+Arg_0 && Arg_0+Arg_1<=11 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=5 && 1<=Arg_0 && 6<=Arg_1
2:f13(Arg_0,Arg_1,Arg_2) -> f13(Arg_0,Arg_1+1,Arg_2):|:Arg_1<=6 && Arg_1<=5+Arg_0 && Arg_0+Arg_1<=11 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=5 && 1<=Arg_0 && Arg_1<=5
3:f21(Arg_0,Arg_1,Arg_2) -> f24(Arg_0,1,Arg_2):|:1<=Arg_0 && Arg_0<=5
8:f21(Arg_0,Arg_1,Arg_2) -> f39(Arg_0,Arg_1,Arg_2):|:1<=Arg_0 && 6<=Arg_0
7:f24(Arg_0,Arg_1,Arg_2) -> f21(Arg_0+1,Arg_1,Arg_2):|:Arg_1<=6 && Arg_1<=5+Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 6<=Arg_1
4:f24(Arg_0,Arg_1,Arg_2) -> f27(Arg_0,Arg_1,1):|:Arg_1<=6 && Arg_1<=5+Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<=5
6:f27(Arg_0,Arg_1,Arg_2) -> f24(Arg_0,Arg_1+1,Arg_2):|:Arg_2<=6 && Arg_2<=5+Arg_1 && Arg_1+Arg_2<=11 && Arg_2<=5+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=4+Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=5 && Arg_1<=4+Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 6<=Arg_2
5:f27(Arg_0,Arg_1,Arg_2) -> f27(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=6 && Arg_2<=5+Arg_1 && Arg_1+Arg_2<=11 && Arg_2<=5+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=4+Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=5 && Arg_1<=4+Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<=5

MPRF for transition 1:f10(Arg_0,Arg_1,Arg_2) -> f13(Arg_0,1,Arg_2):|:Arg_0<=6 && 1<=Arg_0 && Arg_0<=5 of depth 1:

new bound:

8 {O(1)}

MPRF:

f13 [6-Arg_0 ]
f10 [7-Arg_0 ]

MPRF for transition 2:f13(Arg_0,Arg_1,Arg_2) -> f13(Arg_0,Arg_1+1,Arg_2):|:Arg_1<=6 && Arg_1<=5+Arg_0 && Arg_0+Arg_1<=11 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=5 && 1<=Arg_0 && Arg_1<=5 of depth 1:

new bound:

36 {O(1)}

MPRF:

f13 [32-5*Arg_0-Arg_1 ]
f10 [31-5*Arg_0 ]

MPRF for transition 9:f13(Arg_0,Arg_1,Arg_2) -> f10(Arg_0+1,Arg_1,Arg_2):|:Arg_1<=6 && Arg_1<=5+Arg_0 && Arg_0+Arg_1<=11 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=4+Arg_1 && Arg_0<=5 && 1<=Arg_0 && 6<=Arg_1 of depth 1:

new bound:

7 {O(1)}

MPRF:

f13 [6-Arg_0 ]
f10 [6-Arg_0 ]

MPRF for transition 3:f21(Arg_0,Arg_1,Arg_2) -> f24(Arg_0,1,Arg_2):|:1<=Arg_0 && Arg_0<=5 of depth 1:

new bound:

7 {O(1)}

MPRF:

f21 [6-Arg_0 ]
f27 [5-Arg_0 ]
f24 [5-Arg_0 ]

MPRF for transition 4:f24(Arg_0,Arg_1,Arg_2) -> f27(Arg_0,Arg_1,1):|:Arg_1<=6 && Arg_1<=5+Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_1<=5 of depth 1:

new bound:

56 {O(1)}

MPRF:

f21 [-Arg_1 ]
f27 [6-Arg_1 ]
f24 [7-Arg_1 ]

MPRF for transition 7:f24(Arg_0,Arg_1,Arg_2) -> f21(Arg_0+1,Arg_1,Arg_2):|:Arg_1<=6 && Arg_1<=5+Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 6<=Arg_1 of depth 1:

new bound:

7 {O(1)}

MPRF:

f21 [4-2*Arg_0 ]
f27 [1 ]
f24 [1 ]

MPRF for transition 5:f27(Arg_0,Arg_1,Arg_2) -> f27(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=6 && Arg_2<=5+Arg_1 && Arg_1+Arg_2<=11 && Arg_2<=5+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=4+Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=5 && Arg_1<=4+Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && Arg_2<=5 of depth 1:

new bound:

252 {O(1)}

MPRF:

f21 [-5*Arg_1 ]
f27 [32-5*Arg_1-Arg_2 ]
f24 [31-5*Arg_1 ]

MPRF for transition 6:f27(Arg_0,Arg_1,Arg_2) -> f24(Arg_0,Arg_1+1,Arg_2):|:Arg_2<=6 && Arg_2<=5+Arg_1 && Arg_1+Arg_2<=11 && Arg_2<=5+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=4+Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=5 && Arg_1<=4+Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 6<=Arg_2 of depth 1:

new bound:

49 {O(1)}

MPRF:

f21 [-Arg_1 ]
f27 [6-Arg_1 ]
f24 [6-Arg_1 ]

All Bounds

Timebounds

Overall timebound:425 {O(1)}
0: f0->f10: 1 {O(1)}
1: f10->f13: 8 {O(1)}
10: f10->f21: 1 {O(1)}
2: f13->f13: 36 {O(1)}
9: f13->f10: 7 {O(1)}
3: f21->f24: 7 {O(1)}
8: f21->f39: 1 {O(1)}
4: f24->f27: 56 {O(1)}
7: f24->f21: 7 {O(1)}
5: f27->f27: 252 {O(1)}
6: f27->f24: 49 {O(1)}

Costbounds

Overall costbound: 425 {O(1)}
0: f0->f10: 1 {O(1)}
1: f10->f13: 8 {O(1)}
10: f10->f21: 1 {O(1)}
2: f13->f13: 36 {O(1)}
9: f13->f10: 7 {O(1)}
3: f21->f24: 7 {O(1)}
8: f21->f39: 1 {O(1)}
4: f24->f27: 56 {O(1)}
7: f24->f21: 7 {O(1)}
5: f27->f27: 252 {O(1)}
6: f27->f24: 49 {O(1)}

Sizebounds

0: f0->f10, Arg_0: 1 {O(1)}
0: f0->f10, Arg_1: Arg_1 {O(n)}
0: f0->f10, Arg_2: Arg_2 {O(n)}
1: f10->f13, Arg_0: 5 {O(1)}
1: f10->f13, Arg_1: 1 {O(1)}
1: f10->f13, Arg_2: Arg_2 {O(n)}
10: f10->f21, Arg_0: 1 {O(1)}
10: f10->f21, Arg_1: 6 {O(1)}
10: f10->f21, Arg_2: Arg_2 {O(n)}
2: f13->f13, Arg_0: 5 {O(1)}
2: f13->f13, Arg_1: 6 {O(1)}
2: f13->f13, Arg_2: Arg_2 {O(n)}
9: f13->f10, Arg_0: 6 {O(1)}
9: f13->f10, Arg_1: 6 {O(1)}
9: f13->f10, Arg_2: Arg_2 {O(n)}
3: f21->f24, Arg_0: 5 {O(1)}
3: f21->f24, Arg_1: 1 {O(1)}
3: f21->f24, Arg_2: Arg_2+6 {O(n)}
8: f21->f39, Arg_0: 6 {O(1)}
8: f21->f39, Arg_1: 6 {O(1)}
8: f21->f39, Arg_2: 6 {O(1)}
4: f24->f27, Arg_0: 5 {O(1)}
4: f24->f27, Arg_1: 5 {O(1)}
4: f24->f27, Arg_2: 1 {O(1)}
7: f24->f21, Arg_0: 6 {O(1)}
7: f24->f21, Arg_1: 6 {O(1)}
7: f24->f21, Arg_2: 6 {O(1)}
5: f27->f27, Arg_0: 5 {O(1)}
5: f27->f27, Arg_1: 5 {O(1)}
5: f27->f27, Arg_2: 6 {O(1)}
6: f27->f24, Arg_0: 5 {O(1)}
6: f27->f24, Arg_1: 6 {O(1)}
6: f27->f24, Arg_2: 6 {O(1)}