Initial Problem

Start: n_eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
Temp_Vars:
Locations: n_eval_foo_bb0_in___11, n_eval_foo_bb1_in___10, n_eval_foo_bb1_in___4, n_eval_foo_bb2_in___6, n_eval_foo_bb2_in___9, n_eval_foo_bb3_in___7, n_eval_foo_bb4_in___5, n_eval_foo_bb5_in___3, n_eval_foo_bb5_in___8, n_eval_foo_start, n_eval_foo_stop___1, n_eval_foo_stop___2
Transitions:
0:n_eval_foo_bb0_in___11(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb1_in___10(Arg_4,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)
1:n_eval_foo_bb1_in___10(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb2_in___9(Arg_0,Arg_0,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=Arg_4 && Arg_4<=Arg_0 && 1<Arg_0
2:n_eval_foo_bb1_in___10(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb5_in___8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=Arg_4 && Arg_4<=Arg_0 && Arg_0<=1
3:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb5_in___3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=1
4:n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb3_in___7(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:1<Arg_1
5:n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb4_in___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<=1
6:n_eval_foo_bb2_in___9(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb3_in___7(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:1<Arg_1 && 1<Arg_1
7:n_eval_foo_bb3_in___7(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb2_in___6(Arg_0,Arg_1-2,Arg_2,Arg_3,Arg_4,Arg_5):|:1<Arg_1
8:n_eval_foo_bb4_in___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb1_in___4(Arg_1,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1<=1
9:n_eval_foo_bb5_in___3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_stop___2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=1 && Arg_0<=Arg_1 && Arg_1<=Arg_0
10:n_eval_foo_bb5_in___8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_stop___1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=1 && Arg_0<=Arg_4 && Arg_4<=Arg_0
11:n_eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb0_in___11(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

Preprocessing

Eliminate variables {Arg_2,Arg_3,Arg_5} that do not contribute to the problem

Found invariant Arg_4<=1 && Arg_4<=Arg_0 && Arg_0+Arg_4<=2 && Arg_0<=Arg_4 && Arg_0<=1 for location n_eval_foo_bb5_in___8

Found invariant 2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 2+Arg_0<=Arg_4 && Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 0<=Arg_0 for location n_eval_foo_bb1_in___4

Found invariant 2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 2+Arg_0<=Arg_4 && Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 0<=Arg_0 for location n_eval_foo_stop___2

Found invariant Arg_4<=Arg_0 && Arg_0<=Arg_4 for location n_eval_foo_bb1_in___10

Found invariant 2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 2+Arg_0<=Arg_4 && Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 0<=Arg_0 for location n_eval_foo_bb5_in___3

Found invariant Arg_4<=1 && Arg_4<=Arg_0 && Arg_0+Arg_4<=2 && Arg_0<=Arg_4 && Arg_0<=1 for location n_eval_foo_stop___1

Found invariant Arg_4<=Arg_0 && 2<=Arg_4 && 4<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_foo_bb3_in___7

Found invariant Arg_4<=Arg_0 && 2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_foo_bb2_in___6

Found invariant Arg_4<=Arg_1 && Arg_4<=Arg_0 && 2<=Arg_4 && 4<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 2<=Arg_0 for location n_eval_foo_bb2_in___9

Found invariant Arg_4<=Arg_0 && 2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=1 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 for location n_eval_foo_bb4_in___5

Problem after Preprocessing

Start: n_eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_4
Temp_Vars:
Locations: n_eval_foo_bb0_in___11, n_eval_foo_bb1_in___10, n_eval_foo_bb1_in___4, n_eval_foo_bb2_in___6, n_eval_foo_bb2_in___9, n_eval_foo_bb3_in___7, n_eval_foo_bb4_in___5, n_eval_foo_bb5_in___3, n_eval_foo_bb5_in___8, n_eval_foo_start, n_eval_foo_stop___1, n_eval_foo_stop___2
Transitions:
24:n_eval_foo_bb0_in___11(Arg_0,Arg_1,Arg_4) -> n_eval_foo_bb1_in___10(Arg_4,Arg_1,Arg_4)
25:n_eval_foo_bb1_in___10(Arg_0,Arg_1,Arg_4) -> n_eval_foo_bb2_in___9(Arg_0,Arg_0,Arg_4):|:Arg_4<=Arg_0 && Arg_0<=Arg_4 && Arg_0<=Arg_4 && Arg_4<=Arg_0 && 1<Arg_0
26:n_eval_foo_bb1_in___10(Arg_0,Arg_1,Arg_4) -> n_eval_foo_bb5_in___8(Arg_0,Arg_1,Arg_4):|:Arg_4<=Arg_0 && Arg_0<=Arg_4 && Arg_0<=Arg_4 && Arg_4<=Arg_0 && Arg_0<=1
27:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_4) -> n_eval_foo_bb5_in___3(Arg_0,Arg_1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 2+Arg_0<=Arg_4 && Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 0<=Arg_0 && Arg_0<=1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=1
28:n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_4) -> n_eval_foo_bb3_in___7(Arg_0,Arg_1,Arg_4):|:Arg_4<=Arg_0 && 2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && 1<Arg_1
29:n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_4) -> n_eval_foo_bb4_in___5(Arg_0,Arg_1,Arg_4):|:Arg_4<=Arg_0 && 2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<=1
30:n_eval_foo_bb2_in___9(Arg_0,Arg_1,Arg_4) -> n_eval_foo_bb3_in___7(Arg_0,Arg_1,Arg_4):|:Arg_4<=Arg_1 && Arg_4<=Arg_0 && 2<=Arg_4 && 4<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 2<=Arg_0 && 1<Arg_1 && 1<Arg_1
31:n_eval_foo_bb3_in___7(Arg_0,Arg_1,Arg_4) -> n_eval_foo_bb2_in___6(Arg_0,Arg_1-2,Arg_4):|:Arg_4<=Arg_0 && 2<=Arg_4 && 4<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && 1<Arg_1
32:n_eval_foo_bb4_in___5(Arg_0,Arg_1,Arg_4) -> n_eval_foo_bb1_in___4(Arg_1,Arg_1,Arg_4):|:Arg_4<=Arg_0 && 2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=1 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1<=1
33:n_eval_foo_bb5_in___3(Arg_0,Arg_1,Arg_4) -> n_eval_foo_stop___2(Arg_0,Arg_1,Arg_4):|:2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 2<=Arg_0+Arg_4 && 2+Arg_0<=Arg_4 && Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 0<=Arg_0 && Arg_0<=1 && Arg_0<=Arg_1 && Arg_1<=Arg_0
34:n_eval_foo_bb5_in___8(Arg_0,Arg_1,Arg_4) -> n_eval_foo_stop___1(Arg_0,Arg_1,Arg_4):|:Arg_4<=1 && Arg_4<=Arg_0 && Arg_0+Arg_4<=2 && Arg_0<=Arg_4 && Arg_0<=1 && Arg_0<=1 && Arg_0<=Arg_4 && Arg_4<=Arg_0
35:n_eval_foo_start(Arg_0,Arg_1,Arg_4) -> n_eval_foo_bb0_in___11(Arg_0,Arg_1,Arg_4)

MPRF for transition 28:n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_4) -> n_eval_foo_bb3_in___7(Arg_0,Arg_1,Arg_4):|:Arg_4<=Arg_0 && 2<=Arg_4 && 2<=Arg_1+Arg_4 && 2+Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && 1<Arg_1 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

n_eval_foo_bb3_in___7 [Arg_1-1 ]
n_eval_foo_bb2_in___6 [Arg_1+1 ]

MPRF for transition 31:n_eval_foo_bb3_in___7(Arg_0,Arg_1,Arg_4) -> n_eval_foo_bb2_in___6(Arg_0,Arg_1-2,Arg_4):|:Arg_4<=Arg_0 && 2<=Arg_4 && 4<=Arg_1+Arg_4 && Arg_1<=Arg_4 && 4<=Arg_0+Arg_4 && Arg_0<=Arg_4 && Arg_1<=Arg_0 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && 1<Arg_1 of depth 1:

new bound:

Arg_4+1 {O(n)}

MPRF:

n_eval_foo_bb3_in___7 [Arg_1-1 ]
n_eval_foo_bb2_in___6 [Arg_1-1 ]

All Bounds

Timebounds

Overall timebound:2*Arg_4+12 {O(n)}
24: n_eval_foo_bb0_in___11->n_eval_foo_bb1_in___10: 1 {O(1)}
25: n_eval_foo_bb1_in___10->n_eval_foo_bb2_in___9: 1 {O(1)}
26: n_eval_foo_bb1_in___10->n_eval_foo_bb5_in___8: 1 {O(1)}
27: n_eval_foo_bb1_in___4->n_eval_foo_bb5_in___3: 1 {O(1)}
28: n_eval_foo_bb2_in___6->n_eval_foo_bb3_in___7: Arg_4+1 {O(n)}
29: n_eval_foo_bb2_in___6->n_eval_foo_bb4_in___5: 1 {O(1)}
30: n_eval_foo_bb2_in___9->n_eval_foo_bb3_in___7: 1 {O(1)}
31: n_eval_foo_bb3_in___7->n_eval_foo_bb2_in___6: Arg_4+1 {O(n)}
32: n_eval_foo_bb4_in___5->n_eval_foo_bb1_in___4: 1 {O(1)}
33: n_eval_foo_bb5_in___3->n_eval_foo_stop___2: 1 {O(1)}
34: n_eval_foo_bb5_in___8->n_eval_foo_stop___1: 1 {O(1)}
35: n_eval_foo_start->n_eval_foo_bb0_in___11: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_4+12 {O(n)}
24: n_eval_foo_bb0_in___11->n_eval_foo_bb1_in___10: 1 {O(1)}
25: n_eval_foo_bb1_in___10->n_eval_foo_bb2_in___9: 1 {O(1)}
26: n_eval_foo_bb1_in___10->n_eval_foo_bb5_in___8: 1 {O(1)}
27: n_eval_foo_bb1_in___4->n_eval_foo_bb5_in___3: 1 {O(1)}
28: n_eval_foo_bb2_in___6->n_eval_foo_bb3_in___7: Arg_4+1 {O(n)}
29: n_eval_foo_bb2_in___6->n_eval_foo_bb4_in___5: 1 {O(1)}
30: n_eval_foo_bb2_in___9->n_eval_foo_bb3_in___7: 1 {O(1)}
31: n_eval_foo_bb3_in___7->n_eval_foo_bb2_in___6: Arg_4+1 {O(n)}
32: n_eval_foo_bb4_in___5->n_eval_foo_bb1_in___4: 1 {O(1)}
33: n_eval_foo_bb5_in___3->n_eval_foo_stop___2: 1 {O(1)}
34: n_eval_foo_bb5_in___8->n_eval_foo_stop___1: 1 {O(1)}
35: n_eval_foo_start->n_eval_foo_bb0_in___11: 1 {O(1)}

Sizebounds

24: n_eval_foo_bb0_in___11->n_eval_foo_bb1_in___10, Arg_0: Arg_4 {O(n)}
24: n_eval_foo_bb0_in___11->n_eval_foo_bb1_in___10, Arg_1: Arg_1 {O(n)}
24: n_eval_foo_bb0_in___11->n_eval_foo_bb1_in___10, Arg_4: Arg_4 {O(n)}
25: n_eval_foo_bb1_in___10->n_eval_foo_bb2_in___9, Arg_0: Arg_4 {O(n)}
25: n_eval_foo_bb1_in___10->n_eval_foo_bb2_in___9, Arg_1: Arg_4 {O(n)}
25: n_eval_foo_bb1_in___10->n_eval_foo_bb2_in___9, Arg_4: Arg_4 {O(n)}
26: n_eval_foo_bb1_in___10->n_eval_foo_bb5_in___8, Arg_0: Arg_4 {O(n)}
26: n_eval_foo_bb1_in___10->n_eval_foo_bb5_in___8, Arg_1: Arg_1 {O(n)}
26: n_eval_foo_bb1_in___10->n_eval_foo_bb5_in___8, Arg_4: Arg_4 {O(n)}
27: n_eval_foo_bb1_in___4->n_eval_foo_bb5_in___3, Arg_0: 1 {O(1)}
27: n_eval_foo_bb1_in___4->n_eval_foo_bb5_in___3, Arg_1: 1 {O(1)}
27: n_eval_foo_bb1_in___4->n_eval_foo_bb5_in___3, Arg_4: Arg_4 {O(n)}
28: n_eval_foo_bb2_in___6->n_eval_foo_bb3_in___7, Arg_0: Arg_4 {O(n)}
28: n_eval_foo_bb2_in___6->n_eval_foo_bb3_in___7, Arg_1: Arg_4 {O(n)}
28: n_eval_foo_bb2_in___6->n_eval_foo_bb3_in___7, Arg_4: Arg_4 {O(n)}
29: n_eval_foo_bb2_in___6->n_eval_foo_bb4_in___5, Arg_0: Arg_4 {O(n)}
29: n_eval_foo_bb2_in___6->n_eval_foo_bb4_in___5, Arg_1: 1 {O(1)}
29: n_eval_foo_bb2_in___6->n_eval_foo_bb4_in___5, Arg_4: Arg_4 {O(n)}
30: n_eval_foo_bb2_in___9->n_eval_foo_bb3_in___7, Arg_0: Arg_4 {O(n)}
30: n_eval_foo_bb2_in___9->n_eval_foo_bb3_in___7, Arg_1: Arg_4 {O(n)}
30: n_eval_foo_bb2_in___9->n_eval_foo_bb3_in___7, Arg_4: Arg_4 {O(n)}
31: n_eval_foo_bb3_in___7->n_eval_foo_bb2_in___6, Arg_0: Arg_4 {O(n)}
31: n_eval_foo_bb3_in___7->n_eval_foo_bb2_in___6, Arg_1: Arg_4 {O(n)}
31: n_eval_foo_bb3_in___7->n_eval_foo_bb2_in___6, Arg_4: Arg_4 {O(n)}
32: n_eval_foo_bb4_in___5->n_eval_foo_bb1_in___4, Arg_0: 1 {O(1)}
32: n_eval_foo_bb4_in___5->n_eval_foo_bb1_in___4, Arg_1: 1 {O(1)}
32: n_eval_foo_bb4_in___5->n_eval_foo_bb1_in___4, Arg_4: Arg_4 {O(n)}
33: n_eval_foo_bb5_in___3->n_eval_foo_stop___2, Arg_0: 1 {O(1)}
33: n_eval_foo_bb5_in___3->n_eval_foo_stop___2, Arg_1: 1 {O(1)}
33: n_eval_foo_bb5_in___3->n_eval_foo_stop___2, Arg_4: Arg_4 {O(n)}
34: n_eval_foo_bb5_in___8->n_eval_foo_stop___1, Arg_0: Arg_4 {O(n)}
34: n_eval_foo_bb5_in___8->n_eval_foo_stop___1, Arg_1: Arg_1 {O(n)}
34: n_eval_foo_bb5_in___8->n_eval_foo_stop___1, Arg_4: Arg_4 {O(n)}
35: n_eval_foo_start->n_eval_foo_bb0_in___11, Arg_0: Arg_0 {O(n)}
35: n_eval_foo_start->n_eval_foo_bb0_in___11, Arg_1: Arg_1 {O(n)}
35: n_eval_foo_start->n_eval_foo_bb0_in___11, Arg_4: Arg_4 {O(n)}