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___11, n_eval_foo_bb1_in___10, n_eval_foo_bb1_in___4, n_eval_foo_bb1_in___6, n_eval_foo_bb1_in___8, 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___11(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___10(0,0,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<=50 && 0<=Arg_1 && Arg_1<=0 && 0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && Arg_0<=51 && 0<=Arg_1
2:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3):|:50<Arg_0 && 0<=Arg_1
3:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb3_in___2(Arg_0,Arg_1,Arg_2,Arg_3):|:50<Arg_0 && Arg_1<0
4:n_eval_foo_bb1_in___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___5(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_1 && 0<=Arg_1 && Arg_0<=51 && 0<=Arg_1
5:n_eval_foo_bb1_in___8(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb2_in___7(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=50 && 0<=Arg_1 && 0<=Arg_1 && Arg_0<=51 && 0<=Arg_1
6:n_eval_foo_bb2_in___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___4(Arg_0+1,Arg_1-1,Arg_2,Arg_3):|:0<=Arg_1 && 50<Arg_0 && 50<Arg_0
7:n_eval_foo_bb2_in___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___4(Arg_0+1,Arg_1-1,Arg_2,Arg_3):|:Arg_0<=51 && 0<=Arg_1 && 50<Arg_0
8:n_eval_foo_bb2_in___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___6(Arg_0+1,Arg_1+1,Arg_2,Arg_3):|:Arg_0<=51 && 0<=Arg_1 && Arg_0<=50
9:n_eval_foo_bb2_in___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___6(Arg_0+1,Arg_1+1,Arg_2,Arg_3):|:Arg_0<=50 && 0<=Arg_1 && Arg_0<=50
10:n_eval_foo_bb2_in___9(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb1_in___8(Arg_0+1,Arg_1+1,Arg_2,Arg_3):|:Arg_0<=0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && Arg_0<=50
11:n_eval_foo_bb3_in___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_stop___1(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_1<0 && 50<Arg_0
12:n_eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3) -> n_eval_foo_bb0_in___11(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_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 1<=Arg_0 for location n_eval_foo_bb2_in___7

Found invariant 1+Arg_1<=0 && 104+Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 0<=1+Arg_1 && 102<=Arg_0+Arg_1 && Arg_0<=104+Arg_1 && Arg_0<=103 && 103<=Arg_0 for location n_eval_foo_bb3_in___2

Found invariant Arg_1<=50 && 2+Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 0<=1+Arg_1 && 102<=Arg_0+Arg_1 && Arg_0<=104+Arg_1 && Arg_0<=103 && 52<=Arg_0 for location n_eval_foo_bb1_in___4

Found invariant Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb1_in___10

Found invariant Arg_1<=51 && Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=51 && 2<=Arg_0 for location n_eval_foo_bb2_in___5

Found invariant 1+Arg_1<=0 && 104+Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 0<=1+Arg_1 && 102<=Arg_0+Arg_1 && Arg_0<=104+Arg_1 && Arg_0<=103 && 103<=Arg_0 for location n_eval_foo_stop___1

Found invariant Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 1<=Arg_0 for location n_eval_foo_bb1_in___8

Found invariant Arg_1<=50 && 2+Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 0<=Arg_1 && 102<=Arg_0+Arg_1 && Arg_0<=102+Arg_1 && Arg_0<=102 && 52<=Arg_0 for location n_eval_foo_bb2_in___3

Found invariant Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb2_in___9

Found invariant Arg_1<=51 && Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=51 && 2<=Arg_0 for location n_eval_foo_bb1_in___6

Problem after Preprocessing

Start: n_eval_foo_start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_eval_foo_bb0_in___11, n_eval_foo_bb1_in___10, n_eval_foo_bb1_in___4, n_eval_foo_bb1_in___6, n_eval_foo_bb1_in___8, 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:
26:n_eval_foo_bb0_in___11(Arg_0,Arg_1) -> n_eval_foo_bb1_in___10(0,0)
27:n_eval_foo_bb1_in___10(Arg_0,Arg_1) -> n_eval_foo_bb2_in___9(Arg_0,Arg_1):|:Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=50 && 0<=Arg_1 && Arg_1<=0 && 0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && Arg_0<=51 && 0<=Arg_1
28:n_eval_foo_bb1_in___4(Arg_0,Arg_1) -> n_eval_foo_bb2_in___3(Arg_0,Arg_1):|:Arg_1<=50 && 2+Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 0<=1+Arg_1 && 102<=Arg_0+Arg_1 && Arg_0<=104+Arg_1 && Arg_0<=103 && 52<=Arg_0 && 50<Arg_0 && 0<=Arg_1
29:n_eval_foo_bb1_in___4(Arg_0,Arg_1) -> n_eval_foo_bb3_in___2(Arg_0,Arg_1):|:Arg_1<=50 && 2+Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 0<=1+Arg_1 && 102<=Arg_0+Arg_1 && Arg_0<=104+Arg_1 && Arg_0<=103 && 52<=Arg_0 && 50<Arg_0 && Arg_1<0
30:n_eval_foo_bb1_in___6(Arg_0,Arg_1) -> n_eval_foo_bb2_in___5(Arg_0,Arg_1):|:Arg_1<=51 && Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=51 && 2<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && Arg_0<=51 && 0<=Arg_1
31:n_eval_foo_bb1_in___8(Arg_0,Arg_1) -> n_eval_foo_bb2_in___7(Arg_0,Arg_1):|:Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && Arg_0<=50 && 0<=Arg_1 && 0<=Arg_1 && Arg_0<=51 && 0<=Arg_1
32:n_eval_foo_bb2_in___3(Arg_0,Arg_1) -> n_eval_foo_bb1_in___4(Arg_0+1,Arg_1-1):|:Arg_1<=50 && 2+Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 0<=Arg_1 && 102<=Arg_0+Arg_1 && Arg_0<=102+Arg_1 && Arg_0<=102 && 52<=Arg_0 && 0<=Arg_1 && 50<Arg_0 && 50<Arg_0
33:n_eval_foo_bb2_in___5(Arg_0,Arg_1) -> n_eval_foo_bb1_in___4(Arg_0+1,Arg_1-1):|:Arg_1<=51 && Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=51 && 2<=Arg_0 && Arg_0<=51 && 0<=Arg_1 && 50<Arg_0
34:n_eval_foo_bb2_in___5(Arg_0,Arg_1) -> n_eval_foo_bb1_in___6(Arg_0+1,Arg_1+1):|:Arg_1<=51 && Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=51 && 2<=Arg_0 && Arg_0<=51 && 0<=Arg_1 && Arg_0<=50
35:n_eval_foo_bb2_in___7(Arg_0,Arg_1) -> n_eval_foo_bb1_in___6(Arg_0+1,Arg_1+1):|:Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && Arg_0<=50 && 0<=Arg_1 && Arg_0<=50
36:n_eval_foo_bb2_in___9(Arg_0,Arg_1) -> n_eval_foo_bb1_in___8(Arg_0+1,Arg_1+1):|:Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && Arg_0<=50
37:n_eval_foo_bb3_in___2(Arg_0,Arg_1) -> n_eval_foo_stop___1(Arg_0,Arg_1):|:1+Arg_1<=0 && 104+Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 0<=1+Arg_1 && 102<=Arg_0+Arg_1 && Arg_0<=104+Arg_1 && Arg_0<=103 && 103<=Arg_0 && Arg_1<0 && 50<Arg_0
38:n_eval_foo_start(Arg_0,Arg_1) -> n_eval_foo_bb0_in___11(Arg_0,Arg_1)

MPRF for transition 30:n_eval_foo_bb1_in___6(Arg_0,Arg_1) -> n_eval_foo_bb2_in___5(Arg_0,Arg_1):|:Arg_1<=51 && Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=51 && 2<=Arg_0 && 0<=Arg_1 && 0<=Arg_1 && Arg_0<=51 && 0<=Arg_1 of depth 1:

new bound:

54 {O(1)}

MPRF:

n_eval_foo_bb2_in___5 [51-Arg_0 ]
n_eval_foo_bb1_in___6 [52-Arg_0 ]

MPRF for transition 34:n_eval_foo_bb2_in___5(Arg_0,Arg_1) -> n_eval_foo_bb1_in___6(Arg_0+1,Arg_1+1):|:Arg_1<=51 && Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=51 && 2<=Arg_0 && Arg_0<=51 && 0<=Arg_1 && Arg_0<=50 of depth 1:

new bound:

54 {O(1)}

MPRF:

n_eval_foo_bb2_in___5 [52-Arg_0 ]
n_eval_foo_bb1_in___6 [52-Arg_0 ]

MPRF for transition 28:n_eval_foo_bb1_in___4(Arg_0,Arg_1) -> n_eval_foo_bb2_in___3(Arg_0,Arg_1):|:Arg_1<=50 && 2+Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 0<=1+Arg_1 && 102<=Arg_0+Arg_1 && Arg_0<=104+Arg_1 && Arg_0<=103 && 52<=Arg_0 && 50<Arg_0 && 0<=Arg_1 of depth 1:

new bound:

156 {O(1)}

MPRF:

n_eval_foo_bb2_in___3 [103-Arg_0 ]
n_eval_foo_bb1_in___4 [104-Arg_0 ]

MPRF for transition 32:n_eval_foo_bb2_in___3(Arg_0,Arg_1) -> n_eval_foo_bb1_in___4(Arg_0+1,Arg_1-1):|:Arg_1<=50 && 2+Arg_1<=Arg_0 && Arg_0+Arg_1<=102 && 0<=Arg_1 && 102<=Arg_0+Arg_1 && Arg_0<=102+Arg_1 && Arg_0<=102 && 52<=Arg_0 && 0<=Arg_1 && 50<Arg_0 && 50<Arg_0 of depth 1:

new bound:

51 {O(1)}

MPRF:

n_eval_foo_bb2_in___3 [Arg_1+1 ]
n_eval_foo_bb1_in___4 [Arg_1+1 ]

All Bounds

Timebounds

Overall timebound:324 {O(1)}
26: n_eval_foo_bb0_in___11->n_eval_foo_bb1_in___10: 1 {O(1)}
27: n_eval_foo_bb1_in___10->n_eval_foo_bb2_in___9: 1 {O(1)}
28: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___3: 156 {O(1)}
29: n_eval_foo_bb1_in___4->n_eval_foo_bb3_in___2: 1 {O(1)}
30: n_eval_foo_bb1_in___6->n_eval_foo_bb2_in___5: 54 {O(1)}
31: n_eval_foo_bb1_in___8->n_eval_foo_bb2_in___7: 1 {O(1)}
32: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___4: 51 {O(1)}
33: n_eval_foo_bb2_in___5->n_eval_foo_bb1_in___4: 1 {O(1)}
34: n_eval_foo_bb2_in___5->n_eval_foo_bb1_in___6: 54 {O(1)}
35: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___6: 1 {O(1)}
36: n_eval_foo_bb2_in___9->n_eval_foo_bb1_in___8: 1 {O(1)}
37: n_eval_foo_bb3_in___2->n_eval_foo_stop___1: 1 {O(1)}
38: n_eval_foo_start->n_eval_foo_bb0_in___11: 1 {O(1)}

Costbounds

Overall costbound: 324 {O(1)}
26: n_eval_foo_bb0_in___11->n_eval_foo_bb1_in___10: 1 {O(1)}
27: n_eval_foo_bb1_in___10->n_eval_foo_bb2_in___9: 1 {O(1)}
28: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___3: 156 {O(1)}
29: n_eval_foo_bb1_in___4->n_eval_foo_bb3_in___2: 1 {O(1)}
30: n_eval_foo_bb1_in___6->n_eval_foo_bb2_in___5: 54 {O(1)}
31: n_eval_foo_bb1_in___8->n_eval_foo_bb2_in___7: 1 {O(1)}
32: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___4: 51 {O(1)}
33: n_eval_foo_bb2_in___5->n_eval_foo_bb1_in___4: 1 {O(1)}
34: n_eval_foo_bb2_in___5->n_eval_foo_bb1_in___6: 54 {O(1)}
35: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___6: 1 {O(1)}
36: n_eval_foo_bb2_in___9->n_eval_foo_bb1_in___8: 1 {O(1)}
37: n_eval_foo_bb3_in___2->n_eval_foo_stop___1: 1 {O(1)}
38: n_eval_foo_start->n_eval_foo_bb0_in___11: 1 {O(1)}

Sizebounds

26: n_eval_foo_bb0_in___11->n_eval_foo_bb1_in___10, Arg_0: 0 {O(1)}
26: n_eval_foo_bb0_in___11->n_eval_foo_bb1_in___10, Arg_1: 0 {O(1)}
27: n_eval_foo_bb1_in___10->n_eval_foo_bb2_in___9, Arg_0: 0 {O(1)}
27: n_eval_foo_bb1_in___10->n_eval_foo_bb2_in___9, Arg_1: 0 {O(1)}
28: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___3, Arg_0: 102 {O(1)}
28: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___3, Arg_1: 50 {O(1)}
29: n_eval_foo_bb1_in___4->n_eval_foo_bb3_in___2, Arg_0: 103 {O(1)}
29: n_eval_foo_bb1_in___4->n_eval_foo_bb3_in___2, Arg_1: 1 {O(1)}
30: n_eval_foo_bb1_in___6->n_eval_foo_bb2_in___5, Arg_0: 51 {O(1)}
30: n_eval_foo_bb1_in___6->n_eval_foo_bb2_in___5, Arg_1: 51 {O(1)}
31: n_eval_foo_bb1_in___8->n_eval_foo_bb2_in___7, Arg_0: 1 {O(1)}
31: n_eval_foo_bb1_in___8->n_eval_foo_bb2_in___7, Arg_1: 1 {O(1)}
32: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___4, Arg_0: 103 {O(1)}
32: n_eval_foo_bb2_in___3->n_eval_foo_bb1_in___4, Arg_1: 49 {O(1)}
33: n_eval_foo_bb2_in___5->n_eval_foo_bb1_in___4, Arg_0: 52 {O(1)}
33: n_eval_foo_bb2_in___5->n_eval_foo_bb1_in___4, Arg_1: 50 {O(1)}
34: n_eval_foo_bb2_in___5->n_eval_foo_bb1_in___6, Arg_0: 51 {O(1)}
34: n_eval_foo_bb2_in___5->n_eval_foo_bb1_in___6, Arg_1: 51 {O(1)}
35: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___6, Arg_0: 2 {O(1)}
35: n_eval_foo_bb2_in___7->n_eval_foo_bb1_in___6, Arg_1: 2 {O(1)}
36: n_eval_foo_bb2_in___9->n_eval_foo_bb1_in___8, Arg_0: 1 {O(1)}
36: n_eval_foo_bb2_in___9->n_eval_foo_bb1_in___8, Arg_1: 1 {O(1)}
37: n_eval_foo_bb3_in___2->n_eval_foo_stop___1, Arg_0: 103 {O(1)}
37: n_eval_foo_bb3_in___2->n_eval_foo_stop___1, Arg_1: 1 {O(1)}
38: n_eval_foo_start->n_eval_foo_bb0_in___11, Arg_0: Arg_0 {O(n)}
38: n_eval_foo_start->n_eval_foo_bb0_in___11, Arg_1: Arg_1 {O(n)}