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___8, n_eval_foo_bb1_in___4, n_eval_foo_bb1_in___5, n_eval_foo_bb1_in___7, n_eval_foo_bb2_in___1, n_eval_foo_bb2_in___6, n_eval_foo_bb3_in___3, n_eval_foo_start, n_eval_foo_stop___2
Transitions:
0:n_eval_foo_bb0_in___8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb1_in___7(1,Arg_4,Arg_2,Arg_3,Arg_4,Arg_5)
1:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:0<Arg_0 && 1<=Arg_0 && 0<Arg_0
2:n_eval_foo_bb1_in___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb3_in___3(0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 1+Arg_5<=Arg_1 && Arg_0<=0 && 0<=Arg_0
3:n_eval_foo_bb1_in___7(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:0<Arg_0 && Arg_1<=Arg_4 && Arg_4<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && 1<=Arg_0 && 0<Arg_0
4:n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb1_in___4(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5):|:1<=Arg_0 && Arg_1<Arg_5
5:n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb1_in___5(0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5):|:1<=Arg_0 && Arg_5<=Arg_1
6:n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb1_in___4(Arg_0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=1 && 1<=Arg_0 && Arg_1<=Arg_4 && Arg_4<=Arg_1 && Arg_1<Arg_5
7:n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb1_in___5(0,Arg_1+1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=1 && 1<=Arg_0 && Arg_1<=Arg_4 && Arg_4<=Arg_1 && Arg_5<=Arg_1
8:n_eval_foo_bb3_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):|:1+Arg_5<=Arg_1 && Arg_0<=0 && 0<=Arg_0
9:n_eval_foo_start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_eval_foo_bb0_in___8(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

Preprocessing

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

Found invariant Arg_4<=Arg_1 && Arg_1<=Arg_4 && Arg_0<=1 && 1<=Arg_0 for location n_eval_foo_bb1_in___7

Found invariant 1+Arg_4<=Arg_5 && Arg_1<=Arg_5 && 1+Arg_4<=Arg_1 && Arg_0<=1 && 1<=Arg_0 for location n_eval_foo_bb1_in___4

Found invariant 1+Arg_5<=Arg_1 && 1+Arg_4<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_stop___2

Found invariant 1+Arg_5<=Arg_1 && 1+Arg_4<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb1_in___5

Found invariant 1+Arg_5<=Arg_1 && 1+Arg_4<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_eval_foo_bb3_in___3

Found invariant 1+Arg_4<=Arg_5 && Arg_1<=Arg_5 && 1+Arg_4<=Arg_1 && Arg_0<=1 && 1<=Arg_0 for location n_eval_foo_bb2_in___1

Found invariant Arg_4<=Arg_1 && Arg_1<=Arg_4 && Arg_0<=1 && 1<=Arg_0 for location n_eval_foo_bb2_in___6

Problem after Preprocessing

Start: n_eval_foo_start
Program_Vars: Arg_0, Arg_1, Arg_4, Arg_5
Temp_Vars:
Locations: n_eval_foo_bb0_in___8, n_eval_foo_bb1_in___4, n_eval_foo_bb1_in___5, n_eval_foo_bb1_in___7, n_eval_foo_bb2_in___1, n_eval_foo_bb2_in___6, n_eval_foo_bb3_in___3, n_eval_foo_start, n_eval_foo_stop___2
Transitions:
20:n_eval_foo_bb0_in___8(Arg_0,Arg_1,Arg_4,Arg_5) -> n_eval_foo_bb1_in___7(1,Arg_4,Arg_4,Arg_5)
21:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_4,Arg_5) -> n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_4,Arg_5):|:1+Arg_4<=Arg_5 && Arg_1<=Arg_5 && 1+Arg_4<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && 0<Arg_0 && 1<=Arg_0 && 0<Arg_0
22:n_eval_foo_bb1_in___5(Arg_0,Arg_1,Arg_4,Arg_5) -> n_eval_foo_bb3_in___3(0,Arg_1,Arg_4,Arg_5):|:1+Arg_5<=Arg_1 && 1+Arg_4<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_5<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 1+Arg_5<=Arg_1 && Arg_0<=0 && 0<=Arg_0
23:n_eval_foo_bb1_in___7(Arg_0,Arg_1,Arg_4,Arg_5) -> n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_4,Arg_5):|:Arg_4<=Arg_1 && Arg_1<=Arg_4 && Arg_0<=1 && 1<=Arg_0 && 0<Arg_0 && Arg_1<=Arg_4 && Arg_4<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && 1<=Arg_0 && 0<Arg_0
24:n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_4,Arg_5) -> n_eval_foo_bb1_in___4(Arg_0,Arg_1+1,Arg_4,Arg_5):|:1+Arg_4<=Arg_5 && Arg_1<=Arg_5 && 1+Arg_4<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<Arg_5
25:n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_4,Arg_5) -> n_eval_foo_bb1_in___5(0,Arg_1+1,Arg_4,Arg_5):|:1+Arg_4<=Arg_5 && Arg_1<=Arg_5 && 1+Arg_4<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && 1<=Arg_0 && Arg_5<=Arg_1
26:n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_4,Arg_5) -> n_eval_foo_bb1_in___4(Arg_0,Arg_1+1,Arg_4,Arg_5):|:Arg_4<=Arg_1 && Arg_1<=Arg_4 && Arg_0<=1 && 1<=Arg_0 && Arg_0<=1 && 1<=Arg_0 && Arg_1<=Arg_4 && Arg_4<=Arg_1 && Arg_1<Arg_5
27:n_eval_foo_bb2_in___6(Arg_0,Arg_1,Arg_4,Arg_5) -> n_eval_foo_bb1_in___5(0,Arg_1+1,Arg_4,Arg_5):|:Arg_4<=Arg_1 && Arg_1<=Arg_4 && Arg_0<=1 && 1<=Arg_0 && Arg_0<=1 && 1<=Arg_0 && Arg_1<=Arg_4 && Arg_4<=Arg_1 && Arg_5<=Arg_1
28:n_eval_foo_bb3_in___3(Arg_0,Arg_1,Arg_4,Arg_5) -> n_eval_foo_stop___2(Arg_0,Arg_1,Arg_4,Arg_5):|:1+Arg_5<=Arg_1 && 1+Arg_4<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && 1+Arg_5<=Arg_1 && Arg_0<=0 && 0<=Arg_0
29:n_eval_foo_start(Arg_0,Arg_1,Arg_4,Arg_5) -> n_eval_foo_bb0_in___8(Arg_0,Arg_1,Arg_4,Arg_5)

MPRF for transition 21:n_eval_foo_bb1_in___4(Arg_0,Arg_1,Arg_4,Arg_5) -> n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_4,Arg_5):|:1+Arg_4<=Arg_5 && Arg_1<=Arg_5 && 1+Arg_4<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && 0<Arg_0 && 1<=Arg_0 && 0<Arg_0 of depth 1:

new bound:

Arg_4+Arg_5+2 {O(n)}

MPRF:

n_eval_foo_bb2_in___1 [Arg_5-Arg_1 ]
n_eval_foo_bb1_in___4 [Arg_5+1-Arg_1 ]

MPRF for transition 24:n_eval_foo_bb2_in___1(Arg_0,Arg_1,Arg_4,Arg_5) -> n_eval_foo_bb1_in___4(Arg_0,Arg_1+1,Arg_4,Arg_5):|:1+Arg_4<=Arg_5 && Arg_1<=Arg_5 && 1+Arg_4<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<Arg_5 of depth 1:

new bound:

Arg_4+Arg_5+1 {O(n)}

MPRF:

n_eval_foo_bb2_in___1 [Arg_5-Arg_1 ]
n_eval_foo_bb1_in___4 [Arg_5-Arg_1 ]

All Bounds

Timebounds

Overall timebound:2*Arg_4+2*Arg_5+11 {O(n)}
20: n_eval_foo_bb0_in___8->n_eval_foo_bb1_in___7: 1 {O(1)}
21: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___1: Arg_4+Arg_5+2 {O(n)}
22: n_eval_foo_bb1_in___5->n_eval_foo_bb3_in___3: 1 {O(1)}
23: n_eval_foo_bb1_in___7->n_eval_foo_bb2_in___6: 1 {O(1)}
24: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___4: Arg_4+Arg_5+1 {O(n)}
25: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___5: 1 {O(1)}
26: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4: 1 {O(1)}
27: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___5: 1 {O(1)}
28: n_eval_foo_bb3_in___3->n_eval_foo_stop___2: 1 {O(1)}
29: n_eval_foo_start->n_eval_foo_bb0_in___8: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_4+2*Arg_5+11 {O(n)}
20: n_eval_foo_bb0_in___8->n_eval_foo_bb1_in___7: 1 {O(1)}
21: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___1: Arg_4+Arg_5+2 {O(n)}
22: n_eval_foo_bb1_in___5->n_eval_foo_bb3_in___3: 1 {O(1)}
23: n_eval_foo_bb1_in___7->n_eval_foo_bb2_in___6: 1 {O(1)}
24: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___4: Arg_4+Arg_5+1 {O(n)}
25: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___5: 1 {O(1)}
26: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4: 1 {O(1)}
27: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___5: 1 {O(1)}
28: n_eval_foo_bb3_in___3->n_eval_foo_stop___2: 1 {O(1)}
29: n_eval_foo_start->n_eval_foo_bb0_in___8: 1 {O(1)}

Sizebounds

20: n_eval_foo_bb0_in___8->n_eval_foo_bb1_in___7, Arg_0: 1 {O(1)}
20: n_eval_foo_bb0_in___8->n_eval_foo_bb1_in___7, Arg_1: Arg_4 {O(n)}
20: n_eval_foo_bb0_in___8->n_eval_foo_bb1_in___7, Arg_4: Arg_4 {O(n)}
20: n_eval_foo_bb0_in___8->n_eval_foo_bb1_in___7, Arg_5: Arg_5 {O(n)}
21: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___1, Arg_0: 1 {O(1)}
21: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___1, Arg_1: 2*Arg_4+Arg_5+2 {O(n)}
21: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___1, Arg_4: Arg_4 {O(n)}
21: n_eval_foo_bb1_in___4->n_eval_foo_bb2_in___1, Arg_5: Arg_5 {O(n)}
22: n_eval_foo_bb1_in___5->n_eval_foo_bb3_in___3, Arg_0: 0 {O(1)}
22: n_eval_foo_bb1_in___5->n_eval_foo_bb3_in___3, Arg_1: 3*Arg_4+Arg_5+4 {O(n)}
22: n_eval_foo_bb1_in___5->n_eval_foo_bb3_in___3, Arg_4: 2*Arg_4 {O(n)}
22: n_eval_foo_bb1_in___5->n_eval_foo_bb3_in___3, Arg_5: 2*Arg_5 {O(n)}
23: n_eval_foo_bb1_in___7->n_eval_foo_bb2_in___6, Arg_0: 1 {O(1)}
23: n_eval_foo_bb1_in___7->n_eval_foo_bb2_in___6, Arg_1: Arg_4 {O(n)}
23: n_eval_foo_bb1_in___7->n_eval_foo_bb2_in___6, Arg_4: Arg_4 {O(n)}
23: n_eval_foo_bb1_in___7->n_eval_foo_bb2_in___6, Arg_5: Arg_5 {O(n)}
24: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___4, Arg_0: 1 {O(1)}
24: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___4, Arg_1: 2*Arg_4+Arg_5+2 {O(n)}
24: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___4, Arg_4: Arg_4 {O(n)}
24: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___4, Arg_5: Arg_5 {O(n)}
25: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___5, Arg_0: 0 {O(1)}
25: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___5, Arg_1: 2*Arg_4+Arg_5+3 {O(n)}
25: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___5, Arg_4: Arg_4 {O(n)}
25: n_eval_foo_bb2_in___1->n_eval_foo_bb1_in___5, Arg_5: Arg_5 {O(n)}
26: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4, Arg_0: 1 {O(1)}
26: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4, Arg_1: Arg_4+1 {O(n)}
26: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4, Arg_4: Arg_4 {O(n)}
26: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___4, Arg_5: Arg_5 {O(n)}
27: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___5, Arg_0: 0 {O(1)}
27: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___5, Arg_1: Arg_4+1 {O(n)}
27: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___5, Arg_4: Arg_4 {O(n)}
27: n_eval_foo_bb2_in___6->n_eval_foo_bb1_in___5, Arg_5: Arg_5 {O(n)}
28: n_eval_foo_bb3_in___3->n_eval_foo_stop___2, Arg_0: 0 {O(1)}
28: n_eval_foo_bb3_in___3->n_eval_foo_stop___2, Arg_1: 3*Arg_4+Arg_5+4 {O(n)}
28: n_eval_foo_bb3_in___3->n_eval_foo_stop___2, Arg_4: 2*Arg_4 {O(n)}
28: n_eval_foo_bb3_in___3->n_eval_foo_stop___2, Arg_5: 2*Arg_5 {O(n)}
29: n_eval_foo_start->n_eval_foo_bb0_in___8, Arg_0: Arg_0 {O(n)}
29: n_eval_foo_start->n_eval_foo_bb0_in___8, Arg_1: Arg_1 {O(n)}
29: n_eval_foo_start->n_eval_foo_bb0_in___8, Arg_4: Arg_4 {O(n)}
29: n_eval_foo_start->n_eval_foo_bb0_in___8, Arg_5: Arg_5 {O(n)}