Initial Problem

Start: n_eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_eval_foo_bb0_in___13, n_eval_foo_bb1_in___10, n_eval_foo_bb1_in___12, n_eval_foo_bb1_in___4, n_eval_foo_bb1_in___6, n_eval_foo_bb1_in___8, n_eval_foo_bb2_in___11, n_eval_foo_bb2_in___3, n_eval_foo_bb2_in___5, n_eval_foo_bb2_in___7, n_eval_foo_bb2_in___9, n_eval_foo_bb3_in___2, n_eval_foo_start, n_eval_foo_stop___1
Transitions:
0:n_eval_foo_bb0_in___13(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___12(0,Arg_1,Arg_2)
1:n_eval_foo_bb1_in___10(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___9(Arg_0,Arg_1,Arg_2):|:Arg_0<=9 && Arg_0<20 && Arg_0<=19 && Arg_0<=10 && Arg_0<20
2:n_eval_foo_bb1_in___12(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___11(Arg_0,Arg_1,Arg_2):|:Arg_0<=9 && Arg_0<20 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=19 && Arg_0<=10 && Arg_0<20
3:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2):|:9<Arg_0 && Arg_0<20
4:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb3_in___2(Arg_0,Arg_1,Arg_2):|:9<Arg_0 && 20<=Arg_0
5:n_eval_foo_bb1_in___6(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___5(Arg_0,Arg_1,Arg_2):|:Arg_0<20 && 9<Arg_0 && Arg_0<=19 && Arg_0<20
6:n_eval_foo_bb1_in___8(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb2_in___7(Arg_0,Arg_1,Arg_2):|:Arg_0<20 && Arg_0<=19 && Arg_0<=10 && Arg_0<20
7:n_eval_foo_bb2_in___11(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___10(Arg_0+1,Arg_1,Arg_2):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=9
8:n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___4(Arg_0+1,Arg_1,Arg_2):|:Arg_0<20 && 9<Arg_0 && 9<Arg_0
9:n_eval_foo_bb2_in___5(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___4(Arg_0+1,Arg_1,Arg_2):|:Arg_0<=19 && 9<Arg_0 && 9<Arg_0
10:n_eval_foo_bb2_in___7(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___6(Arg_0+1,Arg_1,Arg_2):|:Arg_0<=10 && 9<Arg_0
11:n_eval_foo_bb2_in___7(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___8(Arg_0+1,Arg_1,Arg_2):|:Arg_0<=10 && Arg_0<=9
12:n_eval_foo_bb2_in___9(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb1_in___8(Arg_0+1,Arg_1,Arg_2):|:Arg_0<=9 && Arg_0<=9
13:n_eval_foo_bb3_in___2(Arg_0,Arg_1,Arg_2) -> n_eval_foo_stop___1(Arg_0,Arg_1,Arg_2):|:20<=Arg_0
14:n_eval_foo_start(Arg_0,Arg_1,Arg_2) -> n_eval_foo_bb0_in___13(Arg_0,Arg_1,Arg_2)

Preprocessing

Eliminate variables {Arg_1,Arg_2} that do not contribute to the problem

Found invariant Arg_0<=10 && 2<=Arg_0 for location n_eval_foo_bb2_in___7

Found invariant Arg_0<=20 && 20<=Arg_0 for location n_eval_foo_bb3_in___2

Found invariant Arg_0<=20 && 12<=Arg_0 for location n_eval_foo_bb1_in___4

Found invariant Arg_0<=1 && 1<=Arg_0 for location n_eval_foo_bb1_in___10

Found invariant Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb2_in___11

Found invariant Arg_0<=11 && 11<=Arg_0 for location n_eval_foo_bb2_in___5

Found invariant Arg_0<=20 && 20<=Arg_0 for location n_eval_foo_stop___1

Found invariant Arg_0<=10 && 2<=Arg_0 for location n_eval_foo_bb1_in___8

Found invariant Arg_0<=19 && 12<=Arg_0 for location n_eval_foo_bb2_in___3

Found invariant Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb1_in___12

Found invariant Arg_0<=1 && 1<=Arg_0 for location n_eval_foo_bb2_in___9

Found invariant Arg_0<=11 && 11<=Arg_0 for location n_eval_foo_bb1_in___6

Problem after Preprocessing

Start: n_eval_foo_start
Program_Vars: Arg_0
Temp_Vars:
Locations: n_eval_foo_bb0_in___13, n_eval_foo_bb1_in___10, n_eval_foo_bb1_in___12, n_eval_foo_bb1_in___4, n_eval_foo_bb1_in___6, n_eval_foo_bb1_in___8, n_eval_foo_bb2_in___11, n_eval_foo_bb2_in___3, n_eval_foo_bb2_in___5, n_eval_foo_bb2_in___7, n_eval_foo_bb2_in___9, n_eval_foo_bb3_in___2, n_eval_foo_start, n_eval_foo_stop___1
Transitions:
30:n_eval_foo_bb0_in___13(Arg_0) -> n_eval_foo_bb1_in___12(0)
31:n_eval_foo_bb1_in___10(Arg_0) -> n_eval_foo_bb2_in___9(Arg_0):|:Arg_0<=1 && 1<=Arg_0 && Arg_0<=9 && Arg_0<20 && Arg_0<=19 && Arg_0<=10 && Arg_0<20
32:n_eval_foo_bb1_in___12(Arg_0) -> n_eval_foo_bb2_in___11(Arg_0):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=9 && Arg_0<20 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=19 && Arg_0<=10 && Arg_0<20
33:n_eval_foo_bb1_in___4(Arg_0) -> n_eval_foo_bb2_in___3(Arg_0):|:Arg_0<=20 && 12<=Arg_0 && 9<Arg_0 && Arg_0<20
34:n_eval_foo_bb1_in___4(Arg_0) -> n_eval_foo_bb3_in___2(Arg_0):|:Arg_0<=20 && 12<=Arg_0 && 9<Arg_0 && 20<=Arg_0
35:n_eval_foo_bb1_in___6(Arg_0) -> n_eval_foo_bb2_in___5(Arg_0):|:Arg_0<=11 && 11<=Arg_0 && Arg_0<20 && 9<Arg_0 && Arg_0<=19 && Arg_0<20
36:n_eval_foo_bb1_in___8(Arg_0) -> n_eval_foo_bb2_in___7(Arg_0):|:Arg_0<=10 && 2<=Arg_0 && Arg_0<20 && Arg_0<=19 && Arg_0<=10 && Arg_0<20
37:n_eval_foo_bb2_in___11(Arg_0) -> n_eval_foo_bb1_in___10(Arg_0+1):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=9
38:n_eval_foo_bb2_in___3(Arg_0) -> n_eval_foo_bb1_in___4(Arg_0+1):|:Arg_0<=19 && 12<=Arg_0 && Arg_0<20 && 9<Arg_0 && 9<Arg_0
39:n_eval_foo_bb2_in___5(Arg_0) -> n_eval_foo_bb1_in___4(Arg_0+1):|:Arg_0<=11 && 11<=Arg_0 && Arg_0<=19 && 9<Arg_0 && 9<Arg_0
40:n_eval_foo_bb2_in___7(Arg_0) -> n_eval_foo_bb1_in___6(Arg_0+1):|:Arg_0<=10 && 2<=Arg_0 && Arg_0<=10 && 9<Arg_0
41:n_eval_foo_bb2_in___7(Arg_0) -> n_eval_foo_bb1_in___8(Arg_0+1):|:Arg_0<=10 && 2<=Arg_0 && Arg_0<=10 && Arg_0<=9
42:n_eval_foo_bb2_in___9(Arg_0) -> n_eval_foo_bb1_in___8(Arg_0+1):|:Arg_0<=1 && 1<=Arg_0 && Arg_0<=9 && Arg_0<=9
43:n_eval_foo_bb3_in___2(Arg_0) -> n_eval_foo_stop___1(Arg_0):|:Arg_0<=20 && 20<=Arg_0 && 20<=Arg_0
44:n_eval_foo_start(Arg_0) -> n_eval_foo_bb0_in___13(Arg_0)

MPRF for transition 36:n_eval_foo_bb1_in___8(Arg_0) -> n_eval_foo_bb2_in___7(Arg_0):|:Arg_0<=10 && 2<=Arg_0 && Arg_0<20 && Arg_0<=19 && Arg_0<=10 && Arg_0<20 of depth 1:

new bound:

22 {O(1)}

MPRF:

n_eval_foo_bb2_in___7 [19-Arg_0 ]
n_eval_foo_bb1_in___8 [20-Arg_0 ]

MPRF for transition 41:n_eval_foo_bb2_in___7(Arg_0) -> n_eval_foo_bb1_in___8(Arg_0+1):|:Arg_0<=10 && 2<=Arg_0 && Arg_0<=10 && Arg_0<=9 of depth 1:

new bound:

13 {O(1)}

MPRF:

n_eval_foo_bb2_in___7 [11-Arg_0 ]
n_eval_foo_bb1_in___8 [11-Arg_0 ]

MPRF for transition 33:n_eval_foo_bb1_in___4(Arg_0) -> n_eval_foo_bb2_in___3(Arg_0):|:Arg_0<=20 && 12<=Arg_0 && 9<Arg_0 && Arg_0<20 of depth 1:

new bound:

33 {O(1)}

MPRF:

n_eval_foo_bb2_in___3 [20-Arg_0 ]
n_eval_foo_bb1_in___4 [21-Arg_0 ]

MPRF for transition 38:n_eval_foo_bb2_in___3(Arg_0) -> n_eval_foo_bb1_in___4(Arg_0+1):|:Arg_0<=19 && 12<=Arg_0 && Arg_0<20 && 9<Arg_0 && 9<Arg_0 of depth 1:

new bound:

32 {O(1)}

MPRF:

n_eval_foo_bb2_in___3 [20-Arg_0 ]
n_eval_foo_bb1_in___4 [20-Arg_0 ]

All Bounds

Timebounds

Overall timebound:111 {O(1)}
30: n_eval_foo_bb0_in___13->n_eval_foo_bb1_in___12: 1 {O(1)}
31: n_eval_foo_bb1_in___10->n_eval_foo_bb2_in___9: 1 {O(1)}
32: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___11: 1 {O(1)}
33: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___3: 33 {O(1)}
34: n_eval_foo_bb1_in___4->n_eval_foo_bb3_in___2: 1 {O(1)}
35: n_eval_foo_bb1_in___6->n_eval_foo_bb2_in___5: 1 {O(1)}
36: n_eval_foo_bb1_in___8->n_eval_foo_bb2_in___7: 22 {O(1)}
37: n_eval_foo_bb2_in___11->n_eval_foo_bb1_in___10: 1 {O(1)}
38: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___4: 32 {O(1)}
39: n_eval_foo_bb2_in___5->n_eval_foo_bb1_in___4: 1 {O(1)}
40: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___6: 1 {O(1)}
41: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___8: 13 {O(1)}
42: n_eval_foo_bb2_in___9->n_eval_foo_bb1_in___8: 1 {O(1)}
43: n_eval_foo_bb3_in___2->n_eval_foo_stop___1: 1 {O(1)}
44: n_eval_foo_start->n_eval_foo_bb0_in___13: 1 {O(1)}

Costbounds

Overall costbound: 111 {O(1)}
30: n_eval_foo_bb0_in___13->n_eval_foo_bb1_in___12: 1 {O(1)}
31: n_eval_foo_bb1_in___10->n_eval_foo_bb2_in___9: 1 {O(1)}
32: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___11: 1 {O(1)}
33: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___3: 33 {O(1)}
34: n_eval_foo_bb1_in___4->n_eval_foo_bb3_in___2: 1 {O(1)}
35: n_eval_foo_bb1_in___6->n_eval_foo_bb2_in___5: 1 {O(1)}
36: n_eval_foo_bb1_in___8->n_eval_foo_bb2_in___7: 22 {O(1)}
37: n_eval_foo_bb2_in___11->n_eval_foo_bb1_in___10: 1 {O(1)}
38: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___4: 32 {O(1)}
39: n_eval_foo_bb2_in___5->n_eval_foo_bb1_in___4: 1 {O(1)}
40: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___6: 1 {O(1)}
41: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___8: 13 {O(1)}
42: n_eval_foo_bb2_in___9->n_eval_foo_bb1_in___8: 1 {O(1)}
43: n_eval_foo_bb3_in___2->n_eval_foo_stop___1: 1 {O(1)}
44: n_eval_foo_start->n_eval_foo_bb0_in___13: 1 {O(1)}

Sizebounds

30: n_eval_foo_bb0_in___13->n_eval_foo_bb1_in___12, Arg_0: 0 {O(1)}
31: n_eval_foo_bb1_in___10->n_eval_foo_bb2_in___9, Arg_0: 1 {O(1)}
32: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___11, Arg_0: 0 {O(1)}
33: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___3, Arg_0: 19 {O(1)}
34: n_eval_foo_bb1_in___4->n_eval_foo_bb3_in___2, Arg_0: 20 {O(1)}
35: n_eval_foo_bb1_in___6->n_eval_foo_bb2_in___5, Arg_0: 11 {O(1)}
36: n_eval_foo_bb1_in___8->n_eval_foo_bb2_in___7, Arg_0: 10 {O(1)}
37: n_eval_foo_bb2_in___11->n_eval_foo_bb1_in___10, Arg_0: 1 {O(1)}
38: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___4, Arg_0: 20 {O(1)}
39: n_eval_foo_bb2_in___5->n_eval_foo_bb1_in___4, Arg_0: 12 {O(1)}
40: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___6, Arg_0: 11 {O(1)}
41: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___8, Arg_0: 10 {O(1)}
42: n_eval_foo_bb2_in___9->n_eval_foo_bb1_in___8, Arg_0: 2 {O(1)}
43: n_eval_foo_bb3_in___2->n_eval_foo_stop___1, Arg_0: 20 {O(1)}
44: n_eval_foo_start->n_eval_foo_bb0_in___13, Arg_0: Arg_0 {O(n)}