Initial Problem

Start: n_eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: n_eval_foo_bb0_in___15, n_eval_foo_bb1_in___10, n_eval_foo_bb1_in___12, n_eval_foo_bb1_in___14, n_eval_foo_bb2_in___11, n_eval_foo_bb2_in___13, n_eval_foo_bb2_in___9, n_eval_foo_bb3_in___4, n_eval_foo_bb3_in___6, n_eval_foo_bb3_in___8, n_eval_foo_bb4_in___3, n_eval_foo_bb4_in___5, n_eval_foo_bb4_in___7, n_eval_foo_bb5_in___2, n_eval_foo_start, n_eval_foo_stop___1
Transitions:
0:n_eval_foo_bb0_in___15(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___14(0,Arg_1,Arg_2,Arg_3)
1:n_eval_foo_bb1_in___10(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___9(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<100
2:n_eval_foo_bb1_in___10(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb3_in___8(Arg_0,5,Arg_2,Arg_3):|:100<=Arg_0
3:n_eval_foo_bb1_in___12(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___11(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<100 && Arg_0<=99 && Arg_0<100
4:n_eval_foo_bb1_in___14(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___13(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<100 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=99 && Arg_0<100
5:n_eval_foo_bb2_in___11(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___10(Arg_0+1,Arg_1,Arg_2,Arg_3):|:Arg_0<=99
6:n_eval_foo_bb2_in___13(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___12(Arg_0+1,Arg_1,Arg_2,Arg_3):|:Arg_0<=0 && 0<=Arg_0
7:n_eval_foo_bb2_in___9(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___10(Arg_0+1,Arg_1,Arg_2,Arg_3):|:Arg_0<100
8:n_eval_foo_bb3_in___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb4_in___3(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<21
9:n_eval_foo_bb3_in___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb5_in___2(Arg_0,Arg_1,Arg_2,Arg_3):|:21<=Arg_1
10:n_eval_foo_bb3_in___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb4_in___5(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<21 && Arg_1<=20 && Arg_1<21
11:n_eval_foo_bb3_in___8(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb4_in___7(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<21 && Arg_1<=5 && 5<=Arg_1 && 100<=Arg_0 && Arg_1<=20 && Arg_1<21
12:n_eval_foo_bb4_in___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb3_in___4(Arg_0,Arg_1+3,Arg_2,Arg_3):|:Arg_1<21
13:n_eval_foo_bb4_in___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb3_in___4(Arg_0,Arg_1+3,Arg_2,Arg_3):|:Arg_1<=20
14:n_eval_foo_bb4_in___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb3_in___6(Arg_0,Arg_1+3,Arg_2,Arg_3):|:100<=Arg_0 && Arg_1<=5 && 5<=Arg_1
15:n_eval_foo_bb5_in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_stop___1(Arg_0,Arg_1,Arg_2,Arg_3):|:21<=Arg_1
16:n_eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb0_in___15(Arg_0,Arg_1,Arg_2,Arg_3)

Preprocessing

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

Found invariant Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb1_in___14

Found invariant Arg_1<=5 && 95+Arg_1<=Arg_0 && Arg_0+Arg_1<=105 && 5<=Arg_1 && 105<=Arg_0+Arg_1 && Arg_0<=95+Arg_1 && Arg_0<=100 && 100<=Arg_0 for location n_eval_foo_bb4_in___7

Found invariant Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb2_in___13

Found invariant Arg_1<=8 && 92+Arg_1<=Arg_0 && Arg_0+Arg_1<=108 && 8<=Arg_1 && 108<=Arg_0+Arg_1 && Arg_0<=92+Arg_1 && Arg_0<=100 && 100<=Arg_0 for location n_eval_foo_bb3_in___6

Found invariant Arg_1<=23 && 77+Arg_1<=Arg_0 && Arg_0+Arg_1<=123 && 21<=Arg_1 && 121<=Arg_0+Arg_1 && Arg_0<=79+Arg_1 && Arg_0<=100 && 100<=Arg_0 for location n_eval_foo_bb5_in___2

Found invariant Arg_0<=100 && 2<=Arg_0 for location n_eval_foo_bb1_in___10

Found invariant Arg_0<=1 && 1<=Arg_0 for location n_eval_foo_bb2_in___11

Found invariant Arg_1<=23 && 77+Arg_1<=Arg_0 && Arg_0+Arg_1<=123 && 21<=Arg_1 && 121<=Arg_0+Arg_1 && Arg_0<=79+Arg_1 && Arg_0<=100 && 100<=Arg_0 for location n_eval_foo_stop___1

Found invariant Arg_1<=5 && 95+Arg_1<=Arg_0 && Arg_0+Arg_1<=105 && 5<=Arg_1 && 105<=Arg_0+Arg_1 && Arg_0<=95+Arg_1 && Arg_0<=100 && 100<=Arg_0 for location n_eval_foo_bb3_in___8

Found invariant Arg_1<=20 && 80+Arg_1<=Arg_0 && Arg_0+Arg_1<=120 && 11<=Arg_1 && 111<=Arg_0+Arg_1 && Arg_0<=89+Arg_1 && Arg_0<=100 && 100<=Arg_0 for location n_eval_foo_bb4_in___3

Found invariant Arg_0<=1 && 1<=Arg_0 for location n_eval_foo_bb1_in___12

Found invariant Arg_0<=99 && 2<=Arg_0 for location n_eval_foo_bb2_in___9

Found invariant Arg_1<=8 && 92+Arg_1<=Arg_0 && Arg_0+Arg_1<=108 && 8<=Arg_1 && 108<=Arg_0+Arg_1 && Arg_0<=92+Arg_1 && Arg_0<=100 && 100<=Arg_0 for location n_eval_foo_bb4_in___5

Found invariant Arg_1<=23 && 77+Arg_1<=Arg_0 && Arg_0+Arg_1<=123 && 11<=Arg_1 && 111<=Arg_0+Arg_1 && Arg_0<=89+Arg_1 && Arg_0<=100 && 100<=Arg_0 for location n_eval_foo_bb3_in___4

Problem after Preprocessing

Start: n_eval_foo_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_eval_foo_bb0_in___15, n_eval_foo_bb1_in___10, n_eval_foo_bb1_in___12, n_eval_foo_bb1_in___14, n_eval_foo_bb2_in___11, n_eval_foo_bb2_in___13, n_eval_foo_bb2_in___9, n_eval_foo_bb3_in___4, n_eval_foo_bb3_in___6, n_eval_foo_bb3_in___8, n_eval_foo_bb4_in___3, n_eval_foo_bb4_in___5, n_eval_foo_bb4_in___7, n_eval_foo_bb5_in___2, n_eval_foo_start, n_eval_foo_stop___1
Transitions:
34:n_eval_foo_bb0_in___15(Arg_0,Arg_1) -> n_eval_foo_bb1_in___14(0,Arg_1)
35:n_eval_foo_bb1_in___10(Arg_0,Arg_1) -> n_eval_foo_bb2_in___9(Arg_0,Arg_1):|:Arg_0<=100 && 2<=Arg_0 && Arg_0<100
36:n_eval_foo_bb1_in___10(Arg_0,Arg_1) -> n_eval_foo_bb3_in___8(Arg_0,5):|:Arg_0<=100 && 2<=Arg_0 && 100<=Arg_0
37:n_eval_foo_bb1_in___12(Arg_0,Arg_1) -> n_eval_foo_bb2_in___11(Arg_0,Arg_1):|:Arg_0<=1 && 1<=Arg_0 && Arg_0<100 && Arg_0<=99 && Arg_0<100
38:n_eval_foo_bb1_in___14(Arg_0,Arg_1) -> n_eval_foo_bb2_in___13(Arg_0,Arg_1):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<100 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=99 && Arg_0<100
39:n_eval_foo_bb2_in___11(Arg_0,Arg_1) -> n_eval_foo_bb1_in___10(Arg_0+1,Arg_1):|:Arg_0<=1 && 1<=Arg_0 && Arg_0<=99
40:n_eval_foo_bb2_in___13(Arg_0,Arg_1) -> n_eval_foo_bb1_in___12(Arg_0+1,Arg_1):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0
41:n_eval_foo_bb2_in___9(Arg_0,Arg_1) -> n_eval_foo_bb1_in___10(Arg_0+1,Arg_1):|:Arg_0<=99 && 2<=Arg_0 && Arg_0<100
42:n_eval_foo_bb3_in___4(Arg_0,Arg_1) -> n_eval_foo_bb4_in___3(Arg_0,Arg_1):|:Arg_1<=23 && 77+Arg_1<=Arg_0 && Arg_0+Arg_1<=123 && 11<=Arg_1 && 111<=Arg_0+Arg_1 && Arg_0<=89+Arg_1 && Arg_0<=100 && 100<=Arg_0 && Arg_1<21
43:n_eval_foo_bb3_in___4(Arg_0,Arg_1) -> n_eval_foo_bb5_in___2(Arg_0,Arg_1):|:Arg_1<=23 && 77+Arg_1<=Arg_0 && Arg_0+Arg_1<=123 && 11<=Arg_1 && 111<=Arg_0+Arg_1 && Arg_0<=89+Arg_1 && Arg_0<=100 && 100<=Arg_0 && 21<=Arg_1
44:n_eval_foo_bb3_in___6(Arg_0,Arg_1) -> n_eval_foo_bb4_in___5(Arg_0,Arg_1):|:Arg_1<=8 && 92+Arg_1<=Arg_0 && Arg_0+Arg_1<=108 && 8<=Arg_1 && 108<=Arg_0+Arg_1 && Arg_0<=92+Arg_1 && Arg_0<=100 && 100<=Arg_0 && Arg_1<21 && Arg_1<=20 && Arg_1<21
45:n_eval_foo_bb3_in___8(Arg_0,Arg_1) -> n_eval_foo_bb4_in___7(Arg_0,Arg_1):|:Arg_1<=5 && 95+Arg_1<=Arg_0 && Arg_0+Arg_1<=105 && 5<=Arg_1 && 105<=Arg_0+Arg_1 && Arg_0<=95+Arg_1 && Arg_0<=100 && 100<=Arg_0 && Arg_1<21 && Arg_1<=5 && 5<=Arg_1 && 100<=Arg_0 && Arg_1<=20 && Arg_1<21
46:n_eval_foo_bb4_in___3(Arg_0,Arg_1) -> n_eval_foo_bb3_in___4(Arg_0,Arg_1+3):|:Arg_1<=20 && 80+Arg_1<=Arg_0 && Arg_0+Arg_1<=120 && 11<=Arg_1 && 111<=Arg_0+Arg_1 && Arg_0<=89+Arg_1 && Arg_0<=100 && 100<=Arg_0 && Arg_1<21
47:n_eval_foo_bb4_in___5(Arg_0,Arg_1) -> n_eval_foo_bb3_in___4(Arg_0,Arg_1+3):|:Arg_1<=8 && 92+Arg_1<=Arg_0 && Arg_0+Arg_1<=108 && 8<=Arg_1 && 108<=Arg_0+Arg_1 && Arg_0<=92+Arg_1 && Arg_0<=100 && 100<=Arg_0 && Arg_1<=20
48:n_eval_foo_bb4_in___7(Arg_0,Arg_1) -> n_eval_foo_bb3_in___6(Arg_0,Arg_1+3):|:Arg_1<=5 && 95+Arg_1<=Arg_0 && Arg_0+Arg_1<=105 && 5<=Arg_1 && 105<=Arg_0+Arg_1 && Arg_0<=95+Arg_1 && Arg_0<=100 && 100<=Arg_0 && 100<=Arg_0 && Arg_1<=5 && 5<=Arg_1
49:n_eval_foo_bb5_in___2(Arg_0,Arg_1) -> n_eval_foo_stop___1(Arg_0,Arg_1):|:Arg_1<=23 && 77+Arg_1<=Arg_0 && Arg_0+Arg_1<=123 && 21<=Arg_1 && 121<=Arg_0+Arg_1 && Arg_0<=79+Arg_1 && Arg_0<=100 && 100<=Arg_0 && 21<=Arg_1
50:n_eval_foo_start(Arg_0,Arg_1) -> n_eval_foo_bb0_in___15(Arg_0,Arg_1)

MPRF for transition 35:n_eval_foo_bb1_in___10(Arg_0,Arg_1) -> n_eval_foo_bb2_in___9(Arg_0,Arg_1):|:Arg_0<=100 && 2<=Arg_0 && Arg_0<100 of depth 1:

new bound:

102 {O(1)}

MPRF:

n_eval_foo_bb2_in___9 [99-Arg_0 ]
n_eval_foo_bb1_in___10 [100-Arg_0 ]

MPRF for transition 41:n_eval_foo_bb2_in___9(Arg_0,Arg_1) -> n_eval_foo_bb1_in___10(Arg_0+1,Arg_1):|:Arg_0<=99 && 2<=Arg_0 && Arg_0<100 of depth 1:

new bound:

102 {O(1)}

MPRF:

n_eval_foo_bb2_in___9 [100-Arg_0 ]
n_eval_foo_bb1_in___10 [100-Arg_0 ]

MPRF for transition 42:n_eval_foo_bb3_in___4(Arg_0,Arg_1) -> n_eval_foo_bb4_in___3(Arg_0,Arg_1):|:Arg_1<=23 && 77+Arg_1<=Arg_0 && Arg_0+Arg_1<=123 && 11<=Arg_1 && 111<=Arg_0+Arg_1 && Arg_0<=89+Arg_1 && Arg_0<=100 && 100<=Arg_0 && Arg_1<21 of depth 1:

new bound:

32 {O(1)}

MPRF:

n_eval_foo_bb4_in___3 [18-Arg_1 ]
n_eval_foo_bb3_in___4 [21-Arg_1 ]

MPRF for transition 46:n_eval_foo_bb4_in___3(Arg_0,Arg_1) -> n_eval_foo_bb3_in___4(Arg_0,Arg_1+3):|:Arg_1<=20 && 80+Arg_1<=Arg_0 && Arg_0+Arg_1<=120 && 11<=Arg_1 && 111<=Arg_0+Arg_1 && Arg_0<=89+Arg_1 && Arg_0<=100 && 100<=Arg_0 && Arg_1<21 of depth 1:

new bound:

32 {O(1)}

MPRF:

n_eval_foo_bb4_in___3 [21-Arg_1 ]
n_eval_foo_bb3_in___4 [21-Arg_1 ]

All Bounds

Timebounds

Overall timebound:281 {O(1)}
34: n_eval_foo_bb0_in___15->n_eval_foo_bb1_in___14: 1 {O(1)}
35: n_eval_foo_bb1_in___10->n_eval_foo_bb2_in___9: 102 {O(1)}
36: n_eval_foo_bb1_in___10->n_eval_foo_bb3_in___8: 1 {O(1)}
37: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___11: 1 {O(1)}
38: n_eval_foo_bb1_in___14->n_eval_foo_bb2_in___13: 1 {O(1)}
39: n_eval_foo_bb2_in___11->n_eval_foo_bb1_in___10: 1 {O(1)}
40: n_eval_foo_bb2_in___13->n_eval_foo_bb1_in___12: 1 {O(1)}
41: n_eval_foo_bb2_in___9->n_eval_foo_bb1_in___10: 102 {O(1)}
42: n_eval_foo_bb3_in___4->n_eval_foo_bb4_in___3: 32 {O(1)}
43: n_eval_foo_bb3_in___4->n_eval_foo_bb5_in___2: 1 {O(1)}
44: n_eval_foo_bb3_in___6->n_eval_foo_bb4_in___5: 1 {O(1)}
45: n_eval_foo_bb3_in___8->n_eval_foo_bb4_in___7: 1 {O(1)}
46: n_eval_foo_bb4_in___3->n_eval_foo_bb3_in___4: 32 {O(1)}
47: n_eval_foo_bb4_in___5->n_eval_foo_bb3_in___4: 1 {O(1)}
48: n_eval_foo_bb4_in___7->n_eval_foo_bb3_in___6: 1 {O(1)}
49: n_eval_foo_bb5_in___2->n_eval_foo_stop___1: 1 {O(1)}
50: n_eval_foo_start->n_eval_foo_bb0_in___15: 1 {O(1)}

Costbounds

Overall costbound: 281 {O(1)}
34: n_eval_foo_bb0_in___15->n_eval_foo_bb1_in___14: 1 {O(1)}
35: n_eval_foo_bb1_in___10->n_eval_foo_bb2_in___9: 102 {O(1)}
36: n_eval_foo_bb1_in___10->n_eval_foo_bb3_in___8: 1 {O(1)}
37: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___11: 1 {O(1)}
38: n_eval_foo_bb1_in___14->n_eval_foo_bb2_in___13: 1 {O(1)}
39: n_eval_foo_bb2_in___11->n_eval_foo_bb1_in___10: 1 {O(1)}
40: n_eval_foo_bb2_in___13->n_eval_foo_bb1_in___12: 1 {O(1)}
41: n_eval_foo_bb2_in___9->n_eval_foo_bb1_in___10: 102 {O(1)}
42: n_eval_foo_bb3_in___4->n_eval_foo_bb4_in___3: 32 {O(1)}
43: n_eval_foo_bb3_in___4->n_eval_foo_bb5_in___2: 1 {O(1)}
44: n_eval_foo_bb3_in___6->n_eval_foo_bb4_in___5: 1 {O(1)}
45: n_eval_foo_bb3_in___8->n_eval_foo_bb4_in___7: 1 {O(1)}
46: n_eval_foo_bb4_in___3->n_eval_foo_bb3_in___4: 32 {O(1)}
47: n_eval_foo_bb4_in___5->n_eval_foo_bb3_in___4: 1 {O(1)}
48: n_eval_foo_bb4_in___7->n_eval_foo_bb3_in___6: 1 {O(1)}
49: n_eval_foo_bb5_in___2->n_eval_foo_stop___1: 1 {O(1)}
50: n_eval_foo_start->n_eval_foo_bb0_in___15: 1 {O(1)}

Sizebounds

34: n_eval_foo_bb0_in___15->n_eval_foo_bb1_in___14, Arg_0: 0 {O(1)}
34: n_eval_foo_bb0_in___15->n_eval_foo_bb1_in___14, Arg_1: Arg_1 {O(n)}
35: n_eval_foo_bb1_in___10->n_eval_foo_bb2_in___9, Arg_0: 99 {O(1)}
35: n_eval_foo_bb1_in___10->n_eval_foo_bb2_in___9, Arg_1: Arg_1 {O(n)}
36: n_eval_foo_bb1_in___10->n_eval_foo_bb3_in___8, Arg_0: 100 {O(1)}
36: n_eval_foo_bb1_in___10->n_eval_foo_bb3_in___8, Arg_1: 5 {O(1)}
37: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___11, Arg_0: 1 {O(1)}
37: n_eval_foo_bb1_in___12->n_eval_foo_bb2_in___11, Arg_1: Arg_1 {O(n)}
38: n_eval_foo_bb1_in___14->n_eval_foo_bb2_in___13, Arg_0: 0 {O(1)}
38: n_eval_foo_bb1_in___14->n_eval_foo_bb2_in___13, Arg_1: Arg_1 {O(n)}
39: n_eval_foo_bb2_in___11->n_eval_foo_bb1_in___10, Arg_0: 2 {O(1)}
39: n_eval_foo_bb2_in___11->n_eval_foo_bb1_in___10, Arg_1: Arg_1 {O(n)}
40: n_eval_foo_bb2_in___13->n_eval_foo_bb1_in___12, Arg_0: 1 {O(1)}
40: n_eval_foo_bb2_in___13->n_eval_foo_bb1_in___12, Arg_1: Arg_1 {O(n)}
41: n_eval_foo_bb2_in___9->n_eval_foo_bb1_in___10, Arg_0: 100 {O(1)}
41: n_eval_foo_bb2_in___9->n_eval_foo_bb1_in___10, Arg_1: Arg_1 {O(n)}
42: n_eval_foo_bb3_in___4->n_eval_foo_bb4_in___3, Arg_0: 100 {O(1)}
42: n_eval_foo_bb3_in___4->n_eval_foo_bb4_in___3, Arg_1: 20 {O(1)}
43: n_eval_foo_bb3_in___4->n_eval_foo_bb5_in___2, Arg_0: 100 {O(1)}
43: n_eval_foo_bb3_in___4->n_eval_foo_bb5_in___2, Arg_1: 23 {O(1)}
44: n_eval_foo_bb3_in___6->n_eval_foo_bb4_in___5, Arg_0: 100 {O(1)}
44: n_eval_foo_bb3_in___6->n_eval_foo_bb4_in___5, Arg_1: 8 {O(1)}
45: n_eval_foo_bb3_in___8->n_eval_foo_bb4_in___7, Arg_0: 100 {O(1)}
45: n_eval_foo_bb3_in___8->n_eval_foo_bb4_in___7, Arg_1: 5 {O(1)}
46: n_eval_foo_bb4_in___3->n_eval_foo_bb3_in___4, Arg_0: 100 {O(1)}
46: n_eval_foo_bb4_in___3->n_eval_foo_bb3_in___4, Arg_1: 23 {O(1)}
47: n_eval_foo_bb4_in___5->n_eval_foo_bb3_in___4, Arg_0: 100 {O(1)}
47: n_eval_foo_bb4_in___5->n_eval_foo_bb3_in___4, Arg_1: 11 {O(1)}
48: n_eval_foo_bb4_in___7->n_eval_foo_bb3_in___6, Arg_0: 100 {O(1)}
48: n_eval_foo_bb4_in___7->n_eval_foo_bb3_in___6, Arg_1: 8 {O(1)}
49: n_eval_foo_bb5_in___2->n_eval_foo_stop___1, Arg_0: 100 {O(1)}
49: n_eval_foo_bb5_in___2->n_eval_foo_stop___1, Arg_1: 23 {O(1)}
50: n_eval_foo_start->n_eval_foo_bb0_in___15, Arg_0: Arg_0 {O(n)}
50: n_eval_foo_start->n_eval_foo_bb0_in___15, Arg_1: Arg_1 {O(n)}