Initial Problem

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6
Temp_Vars: H
Locations: f0, f10, f16, f28, f9
Transitions:
0:f0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f9(0,0,H,Arg_3,Arg_4,Arg_5,Arg_6)
8:f10(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f16(0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:10<=Arg_0
3:f10(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f9(Arg_0+1,Arg_0+1,H,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_0<=9
5:f16(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f16(Arg_0+1,Arg_1,Arg_2,Arg_3,Arg_0,H,H):|:Arg_0<=9 && H+1<=0
6:f16(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f16(Arg_0+1,Arg_1,Arg_2,Arg_3,Arg_0,H,H):|:Arg_0<=9 && 1<=H
4:f16(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f28(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:10<=Arg_0
7:f16(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f28(Arg_0,Arg_1,Arg_2,Arg_3,Arg_0,0,0):|:Arg_0<=9
1:f9(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f10(Arg_0,Arg_1,Arg_2,Arg_2,Arg_4,Arg_5,Arg_6):|:Arg_2+1<=0
2:f9(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f10(Arg_0,Arg_1,Arg_2,Arg_2,Arg_4,Arg_5,Arg_6):|:1<=Arg_2
9:f9(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> f16(0,Arg_1,0,0,Arg_4,Arg_5,Arg_6):|:Arg_2<=0 && 0<=Arg_2

Preprocessing

Eliminate variables {Arg_1,Arg_3,Arg_4,Arg_5,Arg_6} that do not contribute to the problem

Found invariant Arg_0<=10 && 0<=Arg_0 for location f28

Found invariant 0<=Arg_0 for location f10

Found invariant Arg_0<=10 && 0<=Arg_0 for location f16

Found invariant Arg_0<=10 && 0<=Arg_0 for location f9

Problem after Preprocessing

Start: f0
Program_Vars: Arg_0, Arg_2
Temp_Vars: H
Locations: f0, f10, f16, f28, f9
Transitions:
21:f0(Arg_0,Arg_2) -> f9(0,H)
23:f10(Arg_0,Arg_2) -> f16(0,Arg_2):|:0<=Arg_0 && 10<=Arg_0
22:f10(Arg_0,Arg_2) -> f9(Arg_0+1,H):|:0<=Arg_0 && Arg_0<=9
25:f16(Arg_0,Arg_2) -> f16(Arg_0+1,Arg_2):|:Arg_0<=10 && 0<=Arg_0 && Arg_0<=9 && H+1<=0
26:f16(Arg_0,Arg_2) -> f16(Arg_0+1,Arg_2):|:Arg_0<=10 && 0<=Arg_0 && Arg_0<=9 && 1<=H
24:f16(Arg_0,Arg_2) -> f28(Arg_0,Arg_2):|:Arg_0<=10 && 0<=Arg_0 && 10<=Arg_0
27:f16(Arg_0,Arg_2) -> f28(Arg_0,Arg_2):|:Arg_0<=10 && 0<=Arg_0 && Arg_0<=9
28:f9(Arg_0,Arg_2) -> f10(Arg_0,Arg_2):|:Arg_0<=10 && 0<=Arg_0 && Arg_2+1<=0
29:f9(Arg_0,Arg_2) -> f10(Arg_0,Arg_2):|:Arg_0<=10 && 0<=Arg_0 && 1<=Arg_2
30:f9(Arg_0,Arg_2) -> f16(0,0):|:Arg_0<=10 && 0<=Arg_0 && Arg_2<=0 && 0<=Arg_2

MPRF for transition 22:f10(Arg_0,Arg_2) -> f9(Arg_0+1,H):|:0<=Arg_0 && Arg_0<=9 of depth 1:

new bound:

10 {O(1)}

MPRF:

f9 [10-Arg_0 ]
f10 [10-Arg_0 ]

MPRF for transition 28:f9(Arg_0,Arg_2) -> f10(Arg_0,Arg_2):|:Arg_0<=10 && 0<=Arg_0 && Arg_2+1<=0 of depth 1:

new bound:

11 {O(1)}

MPRF:

f9 [11-Arg_0 ]
f10 [10-Arg_0 ]

MPRF for transition 29:f9(Arg_0,Arg_2) -> f10(Arg_0,Arg_2):|:Arg_0<=10 && 0<=Arg_0 && 1<=Arg_2 of depth 1:

new bound:

11 {O(1)}

MPRF:

f9 [11-Arg_0 ]
f10 [10-Arg_0 ]

MPRF for transition 25:f16(Arg_0,Arg_2) -> f16(Arg_0+1,Arg_2):|:Arg_0<=10 && 0<=Arg_0 && Arg_0<=9 && H+1<=0 of depth 1:

new bound:

20 {O(1)}

MPRF:

f16 [10-Arg_0 ]

MPRF for transition 26:f16(Arg_0,Arg_2) -> f16(Arg_0+1,Arg_2):|:Arg_0<=10 && 0<=Arg_0 && Arg_0<=9 && 1<=H of depth 1:

new bound:

20 {O(1)}

MPRF:

f16 [10-Arg_0 ]

All Bounds

Timebounds

Overall timebound:77 {O(1)}
21: f0->f9: 1 {O(1)}
22: f10->f9: 10 {O(1)}
23: f10->f16: 1 {O(1)}
24: f16->f28: 1 {O(1)}
25: f16->f16: 20 {O(1)}
26: f16->f16: 20 {O(1)}
27: f16->f28: 1 {O(1)}
28: f9->f10: 11 {O(1)}
29: f9->f10: 11 {O(1)}
30: f9->f16: 1 {O(1)}

Costbounds

Overall costbound: 77 {O(1)}
21: f0->f9: 1 {O(1)}
22: f10->f9: 10 {O(1)}
23: f10->f16: 1 {O(1)}
24: f16->f28: 1 {O(1)}
25: f16->f16: 20 {O(1)}
26: f16->f16: 20 {O(1)}
27: f16->f28: 1 {O(1)}
28: f9->f10: 11 {O(1)}
29: f9->f10: 11 {O(1)}
30: f9->f16: 1 {O(1)}

Sizebounds

21: f0->f9, Arg_0: 0 {O(1)}
22: f10->f9, Arg_0: 10 {O(1)}
23: f10->f16, Arg_0: 0 {O(1)}
24: f16->f28, Arg_0: 10 {O(1)}
25: f16->f16, Arg_0: 10 {O(1)}
26: f16->f16, Arg_0: 10 {O(1)}
27: f16->f28, Arg_0: 9 {O(1)}
28: f9->f10, Arg_0: 10 {O(1)}
29: f9->f10, Arg_0: 10 {O(1)}
30: f9->f16, Arg_0: 0 {O(1)}
30: f9->f16, Arg_2: 0 {O(1)}