Initial Problem

Start: n_evalSimpleSinglestart
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_evalSimpleSinglebb3in___5, n_evalSimpleSinglebb3in___8, n_evalSimpleSinglebbin___4, n_evalSimpleSinglebbin___7, n_evalSimpleSingleentryin___9, n_evalSimpleSinglereturnin___3, n_evalSimpleSinglereturnin___6, n_evalSimpleSinglestart, n_evalSimpleSinglestop___1, n_evalSimpleSinglestop___2
Transitions:
0:n_evalSimpleSinglebb3in___5(Arg_0,Arg_1) -> n_evalSimpleSinglebbin___4(Arg_0,Arg_1):|:1+Arg_0<=Arg_1
1:n_evalSimpleSinglebb3in___5(Arg_0,Arg_1) -> n_evalSimpleSinglereturnin___3(Arg_0,Arg_1):|:Arg_1<=Arg_0
2:n_evalSimpleSinglebb3in___8(Arg_0,Arg_1) -> n_evalSimpleSinglebbin___7(Arg_0,Arg_1):|:Arg_0<=0 && 0<=Arg_0 && 1+Arg_0<=Arg_1
3:n_evalSimpleSinglebb3in___8(Arg_0,Arg_1) -> n_evalSimpleSinglereturnin___6(Arg_0,Arg_1):|:Arg_0<=0 && 0<=Arg_0 && Arg_1<=Arg_0
4:n_evalSimpleSinglebbin___4(Arg_0,Arg_1) -> n_evalSimpleSinglebb3in___5(Arg_0+1,Arg_1):|:1+Arg_0<=Arg_1
5:n_evalSimpleSinglebbin___7(Arg_0,Arg_1) -> n_evalSimpleSinglebb3in___5(Arg_0+1,Arg_1):|:1<=Arg_1 && Arg_0<=0 && 0<=Arg_0
6:n_evalSimpleSingleentryin___9(Arg_0,Arg_1) -> n_evalSimpleSinglebb3in___8(0,Arg_1)
7:n_evalSimpleSinglereturnin___3(Arg_0,Arg_1) -> n_evalSimpleSinglestop___2(Arg_0,Arg_1):|:Arg_1<=Arg_0
8:n_evalSimpleSinglereturnin___6(Arg_0,Arg_1) -> n_evalSimpleSinglestop___1(Arg_0,Arg_1):|:Arg_1<=0 && Arg_0<=0 && 0<=Arg_0
9:n_evalSimpleSinglestart(Arg_0,Arg_1) -> n_evalSimpleSingleentryin___9(Arg_0,Arg_1)

Preprocessing

Found invariant 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_evalSimpleSinglebb3in___5

Found invariant Arg_0<=0 && 0<=Arg_0 for location n_evalSimpleSinglebb3in___8

Found invariant Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=0 && 0<=Arg_0 for location n_evalSimpleSinglestop___1

Found invariant Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_evalSimpleSinglereturnin___3

Found invariant 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location n_evalSimpleSinglebbin___4

Found invariant 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_evalSimpleSinglebbin___7

Found invariant Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_evalSimpleSinglestop___2

Found invariant Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=0 && 0<=Arg_0 for location n_evalSimpleSinglereturnin___6

Problem after Preprocessing

Start: n_evalSimpleSinglestart
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_evalSimpleSinglebb3in___5, n_evalSimpleSinglebb3in___8, n_evalSimpleSinglebbin___4, n_evalSimpleSinglebbin___7, n_evalSimpleSingleentryin___9, n_evalSimpleSinglereturnin___3, n_evalSimpleSinglereturnin___6, n_evalSimpleSinglestart, n_evalSimpleSinglestop___1, n_evalSimpleSinglestop___2
Transitions:
0:n_evalSimpleSinglebb3in___5(Arg_0,Arg_1) -> n_evalSimpleSinglebbin___4(Arg_0,Arg_1):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_1
1:n_evalSimpleSinglebb3in___5(Arg_0,Arg_1) -> n_evalSimpleSinglereturnin___3(Arg_0,Arg_1):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_1<=Arg_0
2:n_evalSimpleSinglebb3in___8(Arg_0,Arg_1) -> n_evalSimpleSinglebbin___7(Arg_0,Arg_1):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 1+Arg_0<=Arg_1
3:n_evalSimpleSinglebb3in___8(Arg_0,Arg_1) -> n_evalSimpleSinglereturnin___6(Arg_0,Arg_1):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=Arg_0
4:n_evalSimpleSinglebbin___4(Arg_0,Arg_1) -> n_evalSimpleSinglebb3in___5(Arg_0+1,Arg_1):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_1
5:n_evalSimpleSinglebbin___7(Arg_0,Arg_1) -> n_evalSimpleSinglebb3in___5(Arg_0+1,Arg_1):|:1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && 1<=Arg_1 && Arg_0<=0 && 0<=Arg_0
6:n_evalSimpleSingleentryin___9(Arg_0,Arg_1) -> n_evalSimpleSinglebb3in___8(0,Arg_1)
7:n_evalSimpleSinglereturnin___3(Arg_0,Arg_1) -> n_evalSimpleSinglestop___2(Arg_0,Arg_1):|:Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && Arg_1<=Arg_0
8:n_evalSimpleSinglereturnin___6(Arg_0,Arg_1) -> n_evalSimpleSinglestop___1(Arg_0,Arg_1):|:Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=0 && Arg_0<=0 && 0<=Arg_0
9:n_evalSimpleSinglestart(Arg_0,Arg_1) -> n_evalSimpleSingleentryin___9(Arg_0,Arg_1)

MPRF for transition 0:n_evalSimpleSinglebb3in___5(Arg_0,Arg_1) -> n_evalSimpleSinglebbin___4(Arg_0,Arg_1):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_1 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_evalSimpleSinglebbin___4 [Arg_1-Arg_0-1 ]
n_evalSimpleSinglebb3in___5 [Arg_1-Arg_0 ]

MPRF for transition 4:n_evalSimpleSinglebbin___4(Arg_0,Arg_1) -> n_evalSimpleSinglebb3in___5(Arg_0+1,Arg_1):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_1 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_evalSimpleSinglebbin___4 [Arg_1-Arg_0 ]
n_evalSimpleSinglebb3in___5 [Arg_1-Arg_0 ]

All Bounds

Timebounds

Overall timebound:2*Arg_1+10 {O(n)}
0: n_evalSimpleSinglebb3in___5->n_evalSimpleSinglebbin___4: Arg_1+1 {O(n)}
1: n_evalSimpleSinglebb3in___5->n_evalSimpleSinglereturnin___3: 1 {O(1)}
2: n_evalSimpleSinglebb3in___8->n_evalSimpleSinglebbin___7: 1 {O(1)}
3: n_evalSimpleSinglebb3in___8->n_evalSimpleSinglereturnin___6: 1 {O(1)}
4: n_evalSimpleSinglebbin___4->n_evalSimpleSinglebb3in___5: Arg_1+1 {O(n)}
5: n_evalSimpleSinglebbin___7->n_evalSimpleSinglebb3in___5: 1 {O(1)}
6: n_evalSimpleSingleentryin___9->n_evalSimpleSinglebb3in___8: 1 {O(1)}
7: n_evalSimpleSinglereturnin___3->n_evalSimpleSinglestop___2: 1 {O(1)}
8: n_evalSimpleSinglereturnin___6->n_evalSimpleSinglestop___1: 1 {O(1)}
9: n_evalSimpleSinglestart->n_evalSimpleSingleentryin___9: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_1+10 {O(n)}
0: n_evalSimpleSinglebb3in___5->n_evalSimpleSinglebbin___4: Arg_1+1 {O(n)}
1: n_evalSimpleSinglebb3in___5->n_evalSimpleSinglereturnin___3: 1 {O(1)}
2: n_evalSimpleSinglebb3in___8->n_evalSimpleSinglebbin___7: 1 {O(1)}
3: n_evalSimpleSinglebb3in___8->n_evalSimpleSinglereturnin___6: 1 {O(1)}
4: n_evalSimpleSinglebbin___4->n_evalSimpleSinglebb3in___5: Arg_1+1 {O(n)}
5: n_evalSimpleSinglebbin___7->n_evalSimpleSinglebb3in___5: 1 {O(1)}
6: n_evalSimpleSingleentryin___9->n_evalSimpleSinglebb3in___8: 1 {O(1)}
7: n_evalSimpleSinglereturnin___3->n_evalSimpleSinglestop___2: 1 {O(1)}
8: n_evalSimpleSinglereturnin___6->n_evalSimpleSinglestop___1: 1 {O(1)}
9: n_evalSimpleSinglestart->n_evalSimpleSingleentryin___9: 1 {O(1)}

Sizebounds

0: n_evalSimpleSinglebb3in___5->n_evalSimpleSinglebbin___4, Arg_0: Arg_1+2 {O(n)}
0: n_evalSimpleSinglebb3in___5->n_evalSimpleSinglebbin___4, Arg_1: Arg_1 {O(n)}
1: n_evalSimpleSinglebb3in___5->n_evalSimpleSinglereturnin___3, Arg_0: Arg_1+3 {O(n)}
1: n_evalSimpleSinglebb3in___5->n_evalSimpleSinglereturnin___3, Arg_1: 2*Arg_1 {O(n)}
2: n_evalSimpleSinglebb3in___8->n_evalSimpleSinglebbin___7, Arg_0: 0 {O(1)}
2: n_evalSimpleSinglebb3in___8->n_evalSimpleSinglebbin___7, Arg_1: Arg_1 {O(n)}
3: n_evalSimpleSinglebb3in___8->n_evalSimpleSinglereturnin___6, Arg_0: 0 {O(1)}
3: n_evalSimpleSinglebb3in___8->n_evalSimpleSinglereturnin___6, Arg_1: Arg_1 {O(n)}
4: n_evalSimpleSinglebbin___4->n_evalSimpleSinglebb3in___5, Arg_0: Arg_1+2 {O(n)}
4: n_evalSimpleSinglebbin___4->n_evalSimpleSinglebb3in___5, Arg_1: Arg_1 {O(n)}
5: n_evalSimpleSinglebbin___7->n_evalSimpleSinglebb3in___5, Arg_0: 1 {O(1)}
5: n_evalSimpleSinglebbin___7->n_evalSimpleSinglebb3in___5, Arg_1: Arg_1 {O(n)}
6: n_evalSimpleSingleentryin___9->n_evalSimpleSinglebb3in___8, Arg_0: 0 {O(1)}
6: n_evalSimpleSingleentryin___9->n_evalSimpleSinglebb3in___8, Arg_1: Arg_1 {O(n)}
7: n_evalSimpleSinglereturnin___3->n_evalSimpleSinglestop___2, Arg_0: Arg_1+3 {O(n)}
7: n_evalSimpleSinglereturnin___3->n_evalSimpleSinglestop___2, Arg_1: 2*Arg_1 {O(n)}
8: n_evalSimpleSinglereturnin___6->n_evalSimpleSinglestop___1, Arg_0: 0 {O(1)}
8: n_evalSimpleSinglereturnin___6->n_evalSimpleSinglestop___1, Arg_1: Arg_1 {O(n)}
9: n_evalSimpleSinglestart->n_evalSimpleSingleentryin___9, Arg_0: Arg_0 {O(n)}
9: n_evalSimpleSinglestart->n_evalSimpleSingleentryin___9, Arg_1: Arg_1 {O(n)}