Initial Problem

Start: eval0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: end, eval0, eval1, eval11, eval3, eval5, eval7, eval9
Transitions:
0:eval0(Arg_0,Arg_1,Arg_2,Arg_3) -> eval1(Arg_1,Arg_1,1,Arg_3)
1:eval1(Arg_0,Arg_1,Arg_2,Arg_3) -> end(Arg_0,Arg_1,Arg_2,Arg_3):|:101<=Arg_0
2:eval1(Arg_0,Arg_1,Arg_2,Arg_3) -> eval3(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=100
12:eval11(Arg_0,Arg_1,Arg_2,Arg_3) -> eval5(Arg_0+11,Arg_1,Arg_2+1,Arg_3)
3:eval3(Arg_0,Arg_1,Arg_2,Arg_3) -> eval3(Arg_0+11,Arg_1,Arg_2+1,Arg_3):|:Arg_0<=100
4:eval3(Arg_0,Arg_1,Arg_2,Arg_3) -> eval5(Arg_0,Arg_1,Arg_2,Arg_3):|:101<=Arg_0
5:eval5(Arg_0,Arg_1,Arg_2,Arg_3) -> eval7(Arg_0-10,Arg_1,Arg_2-1,Arg_3):|:2<=Arg_2
6:eval7(Arg_0,Arg_1,Arg_2,Arg_3) -> eval5(Arg_0,Arg_1,Arg_2,Arg_0-10):|:101<=Arg_0 && Arg_2<=1 && 1<=Arg_2
7:eval7(Arg_0,Arg_1,Arg_2,Arg_3) -> eval9(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=100
8:eval7(Arg_0,Arg_1,Arg_2,Arg_3) -> eval9(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=2
9:eval7(Arg_0,Arg_1,Arg_2,Arg_3) -> eval9(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_2
10:eval9(Arg_0,Arg_1,Arg_2,Arg_3) -> eval11(Arg_0-10,Arg_1,Arg_2-1,Arg_3):|:101<=Arg_0
11:eval9(Arg_0,Arg_1,Arg_2,Arg_3) -> eval11(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=100

Preprocessing

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

Found invariant 0<=Arg_2 && Arg_1<=100+Arg_2 && 91<=Arg_0+Arg_2 && Arg_0<=99+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=200 && Arg_0<=100 && 91<=Arg_0 for location eval11

Found invariant 1<=Arg_2 && Arg_1<=99+Arg_2 && 102<=Arg_0+Arg_2 && Arg_0<=109+Arg_2 && Arg_1<=100 && 1+Arg_1<=Arg_0 && Arg_0+Arg_1<=211 && Arg_0<=111 && 101<=Arg_0 for location eval5

Found invariant Arg_2<=1 && 1<=Arg_2 && Arg_1<=Arg_0 && Arg_0<=Arg_1 for location eval1

Found invariant Arg_2<=1 && 100+Arg_2<=Arg_1 && 100+Arg_2<=Arg_0 && 1<=Arg_2 && 102<=Arg_1+Arg_2 && 102<=Arg_0+Arg_2 && Arg_1<=Arg_0 && 101<=Arg_1 && 202<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 101<=Arg_0 for location end

Found invariant 1<=Arg_2 && Arg_1<=99+Arg_2 && Arg_0<=109+Arg_2 && Arg_1<=100 && Arg_1<=Arg_0 && Arg_0+Arg_1<=211 && Arg_0<=111 for location eval3

Found invariant 1<=Arg_2 && Arg_1<=99+Arg_2 && 92<=Arg_0+Arg_2 && Arg_0<=100+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=201 && Arg_0<=101 && 91<=Arg_0 for location eval7

Found invariant 1<=Arg_2 && Arg_1<=99+Arg_2 && 92<=Arg_0+Arg_2 && Arg_0<=100+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=201 && Arg_0<=101 && 91<=Arg_0 for location eval9

Problem after Preprocessing

Start: eval0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: end, eval0, eval1, eval11, eval3, eval5, eval7, eval9
Transitions:
28:eval0(Arg_0,Arg_1,Arg_2) -> eval1(Arg_1,Arg_1,1)
29:eval1(Arg_0,Arg_1,Arg_2) -> end(Arg_0,Arg_1,Arg_2):|:Arg_2<=1 && 1<=Arg_2 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && 101<=Arg_0
30:eval1(Arg_0,Arg_1,Arg_2) -> eval3(Arg_0,Arg_1,Arg_2):|:Arg_2<=1 && 1<=Arg_2 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=100
31:eval11(Arg_0,Arg_1,Arg_2) -> eval5(Arg_0+11,Arg_1,Arg_2+1):|:0<=Arg_2 && Arg_1<=100+Arg_2 && 91<=Arg_0+Arg_2 && Arg_0<=99+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=200 && Arg_0<=100 && 91<=Arg_0
32:eval3(Arg_0,Arg_1,Arg_2) -> eval3(Arg_0+11,Arg_1,Arg_2+1):|:1<=Arg_2 && Arg_1<=99+Arg_2 && Arg_0<=109+Arg_2 && Arg_1<=100 && Arg_1<=Arg_0 && Arg_0+Arg_1<=211 && Arg_0<=111 && Arg_0<=100
33:eval3(Arg_0,Arg_1,Arg_2) -> eval5(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && Arg_1<=99+Arg_2 && Arg_0<=109+Arg_2 && Arg_1<=100 && Arg_1<=Arg_0 && Arg_0+Arg_1<=211 && Arg_0<=111 && 101<=Arg_0
34:eval5(Arg_0,Arg_1,Arg_2) -> eval7(Arg_0-10,Arg_1,Arg_2-1):|:1<=Arg_2 && Arg_1<=99+Arg_2 && 102<=Arg_0+Arg_2 && Arg_0<=109+Arg_2 && Arg_1<=100 && 1+Arg_1<=Arg_0 && Arg_0+Arg_1<=211 && Arg_0<=111 && 101<=Arg_0 && 2<=Arg_2
35:eval7(Arg_0,Arg_1,Arg_2) -> eval5(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && Arg_1<=99+Arg_2 && 92<=Arg_0+Arg_2 && Arg_0<=100+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=201 && Arg_0<=101 && 91<=Arg_0 && 101<=Arg_0 && Arg_2<=1 && 1<=Arg_2
36:eval7(Arg_0,Arg_1,Arg_2) -> eval9(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && Arg_1<=99+Arg_2 && 92<=Arg_0+Arg_2 && Arg_0<=100+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=201 && Arg_0<=101 && 91<=Arg_0 && Arg_0<=100
37:eval7(Arg_0,Arg_1,Arg_2) -> eval9(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && Arg_1<=99+Arg_2 && 92<=Arg_0+Arg_2 && Arg_0<=100+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=201 && Arg_0<=101 && 91<=Arg_0 && Arg_2<=2
38:eval7(Arg_0,Arg_1,Arg_2) -> eval9(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && Arg_1<=99+Arg_2 && 92<=Arg_0+Arg_2 && Arg_0<=100+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=201 && Arg_0<=101 && 91<=Arg_0 && 0<=Arg_2
39:eval9(Arg_0,Arg_1,Arg_2) -> eval11(Arg_0-10,Arg_1,Arg_2-1):|:1<=Arg_2 && Arg_1<=99+Arg_2 && 92<=Arg_0+Arg_2 && Arg_0<=100+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=201 && Arg_0<=101 && 91<=Arg_0 && 101<=Arg_0
40:eval9(Arg_0,Arg_1,Arg_2) -> eval11(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && Arg_1<=99+Arg_2 && 92<=Arg_0+Arg_2 && Arg_0<=100+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=201 && Arg_0<=101 && 91<=Arg_0 && Arg_0<=100

MPRF for transition 32:eval3(Arg_0,Arg_1,Arg_2) -> eval3(Arg_0+11,Arg_1,Arg_2+1):|:1<=Arg_2 && Arg_1<=99+Arg_2 && Arg_0<=109+Arg_2 && Arg_1<=100 && Arg_1<=Arg_0 && Arg_0+Arg_1<=211 && Arg_0<=111 && Arg_0<=100 of depth 1:

new bound:

Arg_1+101 {O(n)}

MPRF:

eval3 [101-Arg_0 ]

MPRF for transition 31:eval11(Arg_0,Arg_1,Arg_2) -> eval5(Arg_0+11,Arg_1,Arg_2+1):|:0<=Arg_2 && Arg_1<=100+Arg_2 && 91<=Arg_0+Arg_2 && Arg_0<=99+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=200 && Arg_0<=100 && 91<=Arg_0 of depth 1:

new bound:

10*Arg_1+1232 {O(n)}

MPRF:

eval5 [10*Arg_2+101-Arg_0 ]
eval7 [10*Arg_2+101-Arg_0 ]
eval9 [10*Arg_2+101-Arg_0 ]
eval11 [10*Arg_2+101-Arg_0 ]

MPRF for transition 34:eval5(Arg_0,Arg_1,Arg_2) -> eval7(Arg_0-10,Arg_1,Arg_2-1):|:1<=Arg_2 && Arg_1<=99+Arg_2 && 102<=Arg_0+Arg_2 && Arg_0<=109+Arg_2 && Arg_1<=100 && 1+Arg_1<=Arg_0 && Arg_0+Arg_1<=211 && Arg_0<=111 && 101<=Arg_0 && 2<=Arg_2 of depth 1:

new bound:

11*Arg_1+1323 {O(n)}

MPRF:

eval5 [11*Arg_2+90-Arg_0 ]
eval7 [11*Arg_2+90-Arg_0 ]
eval9 [11*Arg_2+90-Arg_0 ]
eval11 [11*Arg_2+90-Arg_0 ]

MPRF for transition 35:eval7(Arg_0,Arg_1,Arg_2) -> eval5(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && Arg_1<=99+Arg_2 && 92<=Arg_0+Arg_2 && Arg_0<=100+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=201 && Arg_0<=101 && 91<=Arg_0 && 101<=Arg_0 && Arg_2<=1 && 1<=Arg_2 of depth 1:

new bound:

Arg_1+103 {O(n)}

MPRF:

eval5 [Arg_2-1 ]
eval7 [Arg_2 ]
eval9 [Arg_2 ]
eval11 [Arg_2 ]

MPRF for transition 36:eval7(Arg_0,Arg_1,Arg_2) -> eval9(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && Arg_1<=99+Arg_2 && 92<=Arg_0+Arg_2 && Arg_0<=100+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=201 && Arg_0<=101 && 91<=Arg_0 && Arg_0<=100 of depth 1:

new bound:

901*Arg_1+93712 {O(n)}

MPRF:

eval5 [901*Arg_2-9*Arg_0-811 ]
eval7 [901*Arg_2-9*Arg_0 ]
eval9 [901*Arg_2-9*Arg_0-9 ]
eval11 [901*Arg_2-9*Arg_0-9 ]

MPRF for transition 37:eval7(Arg_0,Arg_1,Arg_2) -> eval9(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && Arg_1<=99+Arg_2 && 92<=Arg_0+Arg_2 && Arg_0<=100+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=201 && Arg_0<=101 && 91<=Arg_0 && Arg_2<=2 of depth 1:

new bound:

10*Arg_1+1224 {O(n)}

MPRF:

eval5 [10*Arg_2+93-Arg_0 ]
eval7 [10*Arg_2+93-Arg_0 ]
eval9 [10*Arg_2+92-Arg_0 ]
eval11 [10*Arg_2+92-Arg_0 ]

MPRF for transition 38:eval7(Arg_0,Arg_1,Arg_2) -> eval9(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && Arg_1<=99+Arg_2 && 92<=Arg_0+Arg_2 && Arg_0<=100+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=201 && Arg_0<=101 && 91<=Arg_0 && 0<=Arg_2 of depth 1:

new bound:

10*Arg_1+1234 {O(n)}

MPRF:

eval5 [10*Arg_2+103-Arg_0 ]
eval7 [10*Arg_2+103-Arg_0 ]
eval9 [10*Arg_2+102-Arg_0 ]
eval11 [10*Arg_2+102-Arg_0 ]

MPRF for transition 39:eval9(Arg_0,Arg_1,Arg_2) -> eval11(Arg_0-10,Arg_1,Arg_2-1):|:1<=Arg_2 && Arg_1<=99+Arg_2 && 92<=Arg_0+Arg_2 && Arg_0<=100+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=201 && Arg_0<=101 && 91<=Arg_0 && 101<=Arg_0 of depth 1:

new bound:

Arg_1+103 {O(n)}

MPRF:

eval5 [Arg_2-1 ]
eval7 [Arg_2 ]
eval9 [Arg_2 ]
eval11 [Arg_2 ]

MPRF for transition 40:eval9(Arg_0,Arg_1,Arg_2) -> eval11(Arg_0,Arg_1,Arg_2):|:1<=Arg_2 && Arg_1<=99+Arg_2 && 92<=Arg_0+Arg_2 && Arg_0<=100+Arg_2 && Arg_1<=100 && Arg_1<=9+Arg_0 && Arg_0+Arg_1<=201 && Arg_0<=101 && 91<=Arg_0 && Arg_0<=100 of depth 1:

new bound:

10*Arg_1+1231 {O(n)}

MPRF:

eval5 [10*Arg_2+100-Arg_0 ]
eval7 [10*Arg_2+100-Arg_0 ]
eval9 [10*Arg_2+100-Arg_0 ]
eval11 [10*Arg_2+99-Arg_0 ]

All Bounds

Timebounds

Overall timebound:955*Arg_1+100267 {O(n)}
28: eval0->eval1: 1 {O(1)}
29: eval1->end: 1 {O(1)}
30: eval1->eval3: 1 {O(1)}
31: eval11->eval5: 10*Arg_1+1232 {O(n)}
32: eval3->eval3: Arg_1+101 {O(n)}
33: eval3->eval5: 1 {O(1)}
34: eval5->eval7: 11*Arg_1+1323 {O(n)}
35: eval7->eval5: Arg_1+103 {O(n)}
36: eval7->eval9: 901*Arg_1+93712 {O(n)}
37: eval7->eval9: 10*Arg_1+1224 {O(n)}
38: eval7->eval9: 10*Arg_1+1234 {O(n)}
39: eval9->eval11: Arg_1+103 {O(n)}
40: eval9->eval11: 10*Arg_1+1231 {O(n)}

Costbounds

Overall costbound: 955*Arg_1+100267 {O(n)}
28: eval0->eval1: 1 {O(1)}
29: eval1->end: 1 {O(1)}
30: eval1->eval3: 1 {O(1)}
31: eval11->eval5: 10*Arg_1+1232 {O(n)}
32: eval3->eval3: Arg_1+101 {O(n)}
33: eval3->eval5: 1 {O(1)}
34: eval5->eval7: 11*Arg_1+1323 {O(n)}
35: eval7->eval5: Arg_1+103 {O(n)}
36: eval7->eval9: 901*Arg_1+93712 {O(n)}
37: eval7->eval9: 10*Arg_1+1224 {O(n)}
38: eval7->eval9: 10*Arg_1+1234 {O(n)}
39: eval9->eval11: Arg_1+103 {O(n)}
40: eval9->eval11: 10*Arg_1+1231 {O(n)}

Sizebounds

28: eval0->eval1, Arg_0: Arg_1 {O(n)}
28: eval0->eval1, Arg_1: Arg_1 {O(n)}
28: eval0->eval1, Arg_2: 1 {O(1)}
29: eval1->end, Arg_0: Arg_1 {O(n)}
29: eval1->end, Arg_1: Arg_1 {O(n)}
29: eval1->end, Arg_2: 1 {O(1)}
30: eval1->eval3, Arg_0: Arg_1 {O(n)}
30: eval1->eval3, Arg_1: Arg_1 {O(n)}
30: eval1->eval3, Arg_2: 1 {O(1)}
31: eval11->eval5, Arg_0: 111 {O(1)}
31: eval11->eval5, Arg_1: Arg_1 {O(n)}
31: eval11->eval5, Arg_2: 11*Arg_1+1338 {O(n)}
32: eval3->eval3, Arg_0: 12*Arg_1+1111 {O(n)}
32: eval3->eval3, Arg_1: Arg_1 {O(n)}
32: eval3->eval3, Arg_2: Arg_1+102 {O(n)}
33: eval3->eval5, Arg_0: 111 {O(1)}
33: eval3->eval5, Arg_1: Arg_1 {O(n)}
33: eval3->eval5, Arg_2: Arg_1+102 {O(n)}
34: eval5->eval7, Arg_0: 101 {O(1)}
34: eval5->eval7, Arg_1: Arg_1 {O(n)}
34: eval5->eval7, Arg_2: 11*Arg_1+1338 {O(n)}
35: eval7->eval5, Arg_0: 101 {O(1)}
35: eval7->eval5, Arg_1: Arg_1 {O(n)}
35: eval7->eval5, Arg_2: 1 {O(1)}
36: eval7->eval9, Arg_0: 100 {O(1)}
36: eval7->eval9, Arg_1: Arg_1 {O(n)}
36: eval7->eval9, Arg_2: 11*Arg_1+1338 {O(n)}
37: eval7->eval9, Arg_0: 101 {O(1)}
37: eval7->eval9, Arg_1: Arg_1 {O(n)}
37: eval7->eval9, Arg_2: 2 {O(1)}
38: eval7->eval9, Arg_0: 101 {O(1)}
38: eval7->eval9, Arg_1: Arg_1 {O(n)}
38: eval7->eval9, Arg_2: 11*Arg_1+1338 {O(n)}
39: eval9->eval11, Arg_0: 91 {O(1)}
39: eval9->eval11, Arg_1: Arg_1 {O(n)}
39: eval9->eval11, Arg_2: 11*Arg_1+1338 {O(n)}
40: eval9->eval11, Arg_0: 100 {O(1)}
40: eval9->eval11, Arg_1: Arg_1 {O(n)}
40: eval9->eval11, Arg_2: 11*Arg_1+1338 {O(n)}