Initial Problem

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7
Temp_Vars: I, J
Locations: f0, f15, f25, f41, f48
Transitions:
0:f0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f15(10,35,285,I,I,0,Arg_6,Arg_7)
1:f15(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,I,1):|:Arg_5+1<=Arg_0
8:f15(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f48(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_0<=Arg_5
7:f25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f15(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4-1,Arg_5+1,Arg_6,Arg_7):|:Arg_4<=Arg_7
2:f25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,I,Arg_7+1):|:Arg_7+1<=Arg_4
5:f25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f41(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_4<=Arg_7 && J+1<=I
6:f25(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f41(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7):|:Arg_4<=Arg_7
3:f41(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f15(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5+1,Arg_6,Arg_7):|:Arg_1<=Arg_4
4:f41(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6,Arg_7) -> f15(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4+1,Arg_5+1,Arg_6,Arg_7):|:Arg_4+1<=Arg_1

Preprocessing

Eliminate variables {Arg_2,Arg_3,Arg_6} that do not contribute to the problem

Found invariant 10<=Arg_5 && 45<=Arg_1+Arg_5 && Arg_1<=25+Arg_5 && 20<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 for location f48

Found invariant 1<=Arg_7 && 1<=Arg_5+Arg_7 && Arg_4<=Arg_7 && 36<=Arg_1+Arg_7 && Arg_1<=34+Arg_7 && 11<=Arg_0+Arg_7 && Arg_0<=9+Arg_7 && 0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 for location f41

Found invariant 0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 for location f15

Found invariant 1<=Arg_7 && 1<=Arg_5+Arg_7 && 36<=Arg_1+Arg_7 && Arg_1<=34+Arg_7 && 11<=Arg_0+Arg_7 && Arg_0<=9+Arg_7 && 0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 for location f25

Problem after Preprocessing

Start: f0
Program_Vars: Arg_0, Arg_1, Arg_4, Arg_5, Arg_7
Temp_Vars: I, J
Locations: f0, f15, f25, f41, f48
Transitions:
19:f0(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7) -> f15(10,35,I,0,Arg_7)
20:f15(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7) -> f25(Arg_0,Arg_1,Arg_4,Arg_5,1):|:0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 && Arg_5+1<=Arg_0
21:f15(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7) -> f48(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7):|:0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 && Arg_0<=Arg_5
25:f25(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7) -> f15(Arg_0,Arg_1,Arg_4-1,Arg_5+1,Arg_7):|:1<=Arg_7 && 1<=Arg_5+Arg_7 && 36<=Arg_1+Arg_7 && Arg_1<=34+Arg_7 && 11<=Arg_0+Arg_7 && Arg_0<=9+Arg_7 && 0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 && Arg_4<=Arg_7
22:f25(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7) -> f25(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7+1):|:1<=Arg_7 && 1<=Arg_5+Arg_7 && 36<=Arg_1+Arg_7 && Arg_1<=34+Arg_7 && 11<=Arg_0+Arg_7 && Arg_0<=9+Arg_7 && 0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 && Arg_7+1<=Arg_4
23:f25(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7) -> f41(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7):|:1<=Arg_7 && 1<=Arg_5+Arg_7 && 36<=Arg_1+Arg_7 && Arg_1<=34+Arg_7 && 11<=Arg_0+Arg_7 && Arg_0<=9+Arg_7 && 0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 && Arg_4<=Arg_7 && J+1<=I
24:f25(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7) -> f41(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7):|:1<=Arg_7 && 1<=Arg_5+Arg_7 && 36<=Arg_1+Arg_7 && Arg_1<=34+Arg_7 && 11<=Arg_0+Arg_7 && Arg_0<=9+Arg_7 && 0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 && Arg_4<=Arg_7
26:f41(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7) -> f15(Arg_0,Arg_1,Arg_4,Arg_5+1,Arg_7):|:1<=Arg_7 && 1<=Arg_5+Arg_7 && Arg_4<=Arg_7 && 36<=Arg_1+Arg_7 && Arg_1<=34+Arg_7 && 11<=Arg_0+Arg_7 && Arg_0<=9+Arg_7 && 0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 && Arg_1<=Arg_4
27:f41(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7) -> f15(Arg_0,Arg_1,Arg_4+1,Arg_5+1,Arg_7):|:1<=Arg_7 && 1<=Arg_5+Arg_7 && Arg_4<=Arg_7 && 36<=Arg_1+Arg_7 && Arg_1<=34+Arg_7 && 11<=Arg_0+Arg_7 && Arg_0<=9+Arg_7 && 0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 && Arg_4+1<=Arg_1

MPRF for transition 20:f15(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7) -> f25(Arg_0,Arg_1,Arg_4,Arg_5,1):|:0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 && Arg_5+1<=Arg_0 of depth 1:

new bound:

11 {O(1)}

MPRF:

f25 [Arg_0-Arg_5 ]
f41 [Arg_0-Arg_5 ]
f15 [Arg_0+1-Arg_5 ]

MPRF for transition 23:f25(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7) -> f41(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7):|:1<=Arg_7 && 1<=Arg_5+Arg_7 && 36<=Arg_1+Arg_7 && Arg_1<=34+Arg_7 && 11<=Arg_0+Arg_7 && Arg_0<=9+Arg_7 && 0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 && Arg_4<=Arg_7 && J+1<=I of depth 1:

new bound:

11 {O(1)}

MPRF:

f25 [1 ]
f41 [0 ]
f15 [0 ]

MPRF for transition 24:f25(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7) -> f41(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7):|:1<=Arg_7 && 1<=Arg_5+Arg_7 && 36<=Arg_1+Arg_7 && Arg_1<=34+Arg_7 && 11<=Arg_0+Arg_7 && Arg_0<=9+Arg_7 && 0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 && Arg_4<=Arg_7 of depth 1:

new bound:

11 {O(1)}

MPRF:

f25 [1 ]
f41 [0 ]
f15 [0 ]

MPRF for transition 25:f25(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7) -> f15(Arg_0,Arg_1,Arg_4-1,Arg_5+1,Arg_7):|:1<=Arg_7 && 1<=Arg_5+Arg_7 && 36<=Arg_1+Arg_7 && Arg_1<=34+Arg_7 && 11<=Arg_0+Arg_7 && Arg_0<=9+Arg_7 && 0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 && Arg_4<=Arg_7 of depth 1:

new bound:

11 {O(1)}

MPRF:

f25 [1 ]
f41 [0 ]
f15 [1-Arg_5 ]

MPRF for transition 26:f41(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7) -> f15(Arg_0,Arg_1,Arg_4,Arg_5+1,Arg_7):|:1<=Arg_7 && 1<=Arg_5+Arg_7 && Arg_4<=Arg_7 && 36<=Arg_1+Arg_7 && Arg_1<=34+Arg_7 && 11<=Arg_0+Arg_7 && Arg_0<=9+Arg_7 && 0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 && Arg_1<=Arg_4 of depth 1:

new bound:

880 {O(1)}

MPRF:

f25 [Arg_5+36-Arg_1 ]
f41 [Arg_1+Arg_5-34 ]
f15 [Arg_1-35*Arg_5 ]

MPRF for transition 27:f41(Arg_0,Arg_1,Arg_4,Arg_5,Arg_7) -> f15(Arg_0,Arg_1,Arg_4+1,Arg_5+1,Arg_7):|:1<=Arg_7 && 1<=Arg_5+Arg_7 && Arg_4<=Arg_7 && 36<=Arg_1+Arg_7 && Arg_1<=34+Arg_7 && 11<=Arg_0+Arg_7 && Arg_0<=9+Arg_7 && 0<=Arg_5 && 35<=Arg_1+Arg_5 && Arg_1<=35+Arg_5 && 10<=Arg_0+Arg_5 && Arg_0<=10+Arg_5 && Arg_1<=35 && Arg_1<=25+Arg_0 && Arg_0+Arg_1<=45 && 35<=Arg_1 && 45<=Arg_0+Arg_1 && 25+Arg_0<=Arg_1 && Arg_0<=10 && 10<=Arg_0 && Arg_4+1<=Arg_1 of depth 1:

new bound:

11 {O(1)}

MPRF:

f25 [1 ]
f41 [1 ]
f15 [-1 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
19: f0->f15: 1 {O(1)}
20: f15->f25: 11 {O(1)}
21: f15->f48: 1 {O(1)}
22: f25->f25: inf {Infinity}
23: f25->f41: 11 {O(1)}
24: f25->f41: 11 {O(1)}
25: f25->f15: 11 {O(1)}
26: f41->f15: 880 {O(1)}
27: f41->f15: 11 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
19: f0->f15: 1 {O(1)}
20: f15->f25: 11 {O(1)}
21: f15->f48: 1 {O(1)}
22: f25->f25: inf {Infinity}
23: f25->f41: 11 {O(1)}
24: f25->f41: 11 {O(1)}
25: f25->f15: 11 {O(1)}
26: f41->f15: 880 {O(1)}
27: f41->f15: 11 {O(1)}

Sizebounds

19: f0->f15, Arg_0: 10 {O(1)}
19: f0->f15, Arg_1: 35 {O(1)}
19: f0->f15, Arg_5: 0 {O(1)}
19: f0->f15, Arg_7: Arg_7 {O(n)}
20: f15->f25, Arg_0: 10 {O(1)}
20: f15->f25, Arg_1: 35 {O(1)}
20: f15->f25, Arg_5: 9 {O(1)}
20: f15->f25, Arg_7: 1 {O(1)}
21: f15->f48, Arg_0: 10 {O(1)}
21: f15->f48, Arg_1: 35 {O(1)}
21: f15->f48, Arg_5: 96 {O(1)}
22: f25->f25, Arg_0: 10 {O(1)}
22: f25->f25, Arg_1: 35 {O(1)}
22: f25->f25, Arg_5: 9 {O(1)}
23: f25->f41, Arg_0: 10 {O(1)}
23: f25->f41, Arg_1: 35 {O(1)}
23: f25->f41, Arg_5: 18 {O(1)}
24: f25->f41, Arg_0: 10 {O(1)}
24: f25->f41, Arg_1: 35 {O(1)}
24: f25->f41, Arg_5: 18 {O(1)}
25: f25->f15, Arg_0: 10 {O(1)}
25: f25->f15, Arg_1: 35 {O(1)}
25: f25->f15, Arg_5: 20 {O(1)}
26: f41->f15, Arg_0: 10 {O(1)}
26: f41->f15, Arg_1: 35 {O(1)}
26: f41->f15, Arg_5: 38 {O(1)}
27: f41->f15, Arg_0: 10 {O(1)}
27: f41->f15, Arg_1: 35 {O(1)}
27: f41->f15, Arg_5: 38 {O(1)}