Initial Problem

Start: n_evalaaron2start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_evalaaron2bb3in___6, n_evalaaron2bb4in___4, n_evalaaron2bb5in___3, n_evalaaron2bb6in___8, n_evalaaron2entryin___9, n_evalaaron2returnin___5, n_evalaaron2returnin___7, n_evalaaron2start, n_evalaaron2stop___1, n_evalaaron2stop___2
Transitions:
0:n_evalaaron2bb3in___6(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb4in___4(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0
1:n_evalaaron2bb3in___6(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb4in___4(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0
2:n_evalaaron2bb3in___6(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb5in___3(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0
3:n_evalaaron2bb4in___4(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb6in___8(Arg_0,Arg_1,Arg_2-Arg_0-1):|:Arg_1<=Arg_2 && 0<=Arg_0
4:n_evalaaron2bb5in___3(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb6in___8(Arg_0,Arg_0+Arg_1+1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0
5:n_evalaaron2bb6in___8(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb3in___6(Arg_0,Arg_1,Arg_2):|:0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && Arg_1<=Arg_2
6:n_evalaaron2bb6in___8(Arg_0,Arg_1,Arg_2) -> n_evalaaron2returnin___5(Arg_0,Arg_1,Arg_2):|:0<=Arg_0 && 0<=Arg_0 && 1+Arg_2<=Arg_1
7:n_evalaaron2entryin___9(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb6in___8(Arg_0,Arg_2,Arg_1):|:0<=Arg_0
8:n_evalaaron2entryin___9(Arg_0,Arg_1,Arg_2) -> n_evalaaron2returnin___7(Arg_0,Arg_1,Arg_2):|:1+Arg_0<=0
9:n_evalaaron2returnin___5(Arg_0,Arg_1,Arg_2) -> n_evalaaron2stop___2(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 0<=Arg_0
10:n_evalaaron2returnin___7(Arg_0,Arg_1,Arg_2) -> n_evalaaron2stop___1(Arg_0,Arg_1,Arg_2):|:1+Arg_0<=0
11:n_evalaaron2start(Arg_0,Arg_1,Arg_2) -> n_evalaaron2entryin___9(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant 1+Arg_0<=0 for location n_evalaaron2returnin___7

Found invariant 1+Arg_2<=Arg_1 && 0<=Arg_0 for location n_evalaaron2returnin___5

Found invariant 1+Arg_0<=0 for location n_evalaaron2stop___1

Found invariant 1+Arg_2<=Arg_1 && 0<=Arg_0 for location n_evalaaron2stop___2

Found invariant Arg_1<=Arg_2 && 0<=Arg_0 for location n_evalaaron2bb3in___6

Found invariant Arg_1<=Arg_2 && 0<=Arg_0 for location n_evalaaron2bb4in___4

Found invariant 0<=Arg_0 for location n_evalaaron2bb6in___8

Found invariant Arg_1<=Arg_2 && 0<=Arg_0 for location n_evalaaron2bb5in___3

Problem after Preprocessing

Start: n_evalaaron2start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_evalaaron2bb3in___6, n_evalaaron2bb4in___4, n_evalaaron2bb5in___3, n_evalaaron2bb6in___8, n_evalaaron2entryin___9, n_evalaaron2returnin___5, n_evalaaron2returnin___7, n_evalaaron2start, n_evalaaron2stop___1, n_evalaaron2stop___2
Transitions:
0:n_evalaaron2bb3in___6(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb4in___4(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0 && Arg_1<=Arg_2 && 0<=Arg_0
1:n_evalaaron2bb3in___6(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb4in___4(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0 && Arg_1<=Arg_2 && 0<=Arg_0
2:n_evalaaron2bb3in___6(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb5in___3(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0 && Arg_1<=Arg_2 && 0<=Arg_0
3:n_evalaaron2bb4in___4(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb6in___8(Arg_0,Arg_1,Arg_2-Arg_0-1):|:Arg_1<=Arg_2 && 0<=Arg_0 && Arg_1<=Arg_2 && 0<=Arg_0
4:n_evalaaron2bb5in___3(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb6in___8(Arg_0,Arg_0+Arg_1+1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0 && Arg_1<=Arg_2 && 0<=Arg_0
5:n_evalaaron2bb6in___8(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb3in___6(Arg_0,Arg_1,Arg_2):|:0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && Arg_1<=Arg_2
6:n_evalaaron2bb6in___8(Arg_0,Arg_1,Arg_2) -> n_evalaaron2returnin___5(Arg_0,Arg_1,Arg_2):|:0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 1+Arg_2<=Arg_1
7:n_evalaaron2entryin___9(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb6in___8(Arg_0,Arg_2,Arg_1):|:0<=Arg_0
8:n_evalaaron2entryin___9(Arg_0,Arg_1,Arg_2) -> n_evalaaron2returnin___7(Arg_0,Arg_1,Arg_2):|:1+Arg_0<=0
9:n_evalaaron2returnin___5(Arg_0,Arg_1,Arg_2) -> n_evalaaron2stop___2(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 0<=Arg_0 && 1+Arg_2<=Arg_1 && 0<=Arg_0
10:n_evalaaron2returnin___7(Arg_0,Arg_1,Arg_2) -> n_evalaaron2stop___1(Arg_0,Arg_1,Arg_2):|:1+Arg_0<=0 && 1+Arg_0<=0
11:n_evalaaron2start(Arg_0,Arg_1,Arg_2) -> n_evalaaron2entryin___9(Arg_0,Arg_1,Arg_2)

MPRF for transition 0:n_evalaaron2bb3in___6(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb4in___4(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0 && Arg_1<=Arg_2 && 0<=Arg_0 of depth 1:

new bound:

Arg_1+Arg_2+1 {O(n)}

MPRF:

n_evalaaron2bb4in___4 [Arg_2-Arg_1 ]
n_evalaaron2bb5in___3 [Arg_2-Arg_1 ]
n_evalaaron2bb6in___8 [Arg_2+1-Arg_1 ]
n_evalaaron2bb3in___6 [Arg_2+1-Arg_1 ]

MPRF for transition 1:n_evalaaron2bb3in___6(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb4in___4(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0 && Arg_1<=Arg_2 && 0<=Arg_0 of depth 1:

new bound:

Arg_1+Arg_2+1 {O(n)}

MPRF:

n_evalaaron2bb4in___4 [Arg_2-Arg_1 ]
n_evalaaron2bb5in___3 [Arg_2-Arg_1 ]
n_evalaaron2bb6in___8 [Arg_2+1-Arg_1 ]
n_evalaaron2bb3in___6 [Arg_2+1-Arg_1 ]

MPRF for transition 2:n_evalaaron2bb3in___6(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb5in___3(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0 && Arg_1<=Arg_2 && 0<=Arg_0 of depth 1:

new bound:

Arg_1+Arg_2+1 {O(n)}

MPRF:

n_evalaaron2bb4in___4 [Arg_2-Arg_1 ]
n_evalaaron2bb5in___3 [Arg_2-Arg_1 ]
n_evalaaron2bb6in___8 [Arg_2+1-Arg_1 ]
n_evalaaron2bb3in___6 [Arg_2+1-Arg_1 ]

MPRF for transition 3:n_evalaaron2bb4in___4(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb6in___8(Arg_0,Arg_1,Arg_2-Arg_0-1):|:Arg_1<=Arg_2 && 0<=Arg_0 && Arg_1<=Arg_2 && 0<=Arg_0 of depth 1:

new bound:

Arg_1+Arg_2+1 {O(n)}

MPRF:

n_evalaaron2bb4in___4 [Arg_2+1-Arg_1 ]
n_evalaaron2bb5in___3 [Arg_2-Arg_1 ]
n_evalaaron2bb6in___8 [Arg_2+1-Arg_1 ]
n_evalaaron2bb3in___6 [Arg_2+1-Arg_1 ]

MPRF for transition 4:n_evalaaron2bb5in___3(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb6in___8(Arg_0,Arg_0+Arg_1+1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0 && Arg_1<=Arg_2 && 0<=Arg_0 of depth 1:

new bound:

Arg_1+Arg_2+1 {O(n)}

MPRF:

n_evalaaron2bb4in___4 [Arg_2-Arg_1 ]
n_evalaaron2bb5in___3 [Arg_2+1-Arg_1 ]
n_evalaaron2bb6in___8 [Arg_2+1-Arg_1 ]
n_evalaaron2bb3in___6 [Arg_2+1-Arg_1 ]

MPRF for transition 5:n_evalaaron2bb6in___8(Arg_0,Arg_1,Arg_2) -> n_evalaaron2bb3in___6(Arg_0,Arg_1,Arg_2):|:0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && Arg_1<=Arg_2 of depth 1:

new bound:

Arg_1+Arg_2+1 {O(n)}

MPRF:

n_evalaaron2bb4in___4 [Arg_2-Arg_1 ]
n_evalaaron2bb5in___3 [Arg_2-Arg_1 ]
n_evalaaron2bb6in___8 [Arg_2+1-Arg_1 ]
n_evalaaron2bb3in___6 [Arg_2-Arg_1 ]

All Bounds

Timebounds

Overall timebound:6*Arg_1+6*Arg_2+12 {O(n)}
0: n_evalaaron2bb3in___6->n_evalaaron2bb4in___4: Arg_1+Arg_2+1 {O(n)}
1: n_evalaaron2bb3in___6->n_evalaaron2bb4in___4: Arg_1+Arg_2+1 {O(n)}
2: n_evalaaron2bb3in___6->n_evalaaron2bb5in___3: Arg_1+Arg_2+1 {O(n)}
3: n_evalaaron2bb4in___4->n_evalaaron2bb6in___8: Arg_1+Arg_2+1 {O(n)}
4: n_evalaaron2bb5in___3->n_evalaaron2bb6in___8: Arg_1+Arg_2+1 {O(n)}
5: n_evalaaron2bb6in___8->n_evalaaron2bb3in___6: Arg_1+Arg_2+1 {O(n)}
6: n_evalaaron2bb6in___8->n_evalaaron2returnin___5: 1 {O(1)}
7: n_evalaaron2entryin___9->n_evalaaron2bb6in___8: 1 {O(1)}
8: n_evalaaron2entryin___9->n_evalaaron2returnin___7: 1 {O(1)}
9: n_evalaaron2returnin___5->n_evalaaron2stop___2: 1 {O(1)}
10: n_evalaaron2returnin___7->n_evalaaron2stop___1: 1 {O(1)}
11: n_evalaaron2start->n_evalaaron2entryin___9: 1 {O(1)}

Costbounds

Overall costbound: 6*Arg_1+6*Arg_2+12 {O(n)}
0: n_evalaaron2bb3in___6->n_evalaaron2bb4in___4: Arg_1+Arg_2+1 {O(n)}
1: n_evalaaron2bb3in___6->n_evalaaron2bb4in___4: Arg_1+Arg_2+1 {O(n)}
2: n_evalaaron2bb3in___6->n_evalaaron2bb5in___3: Arg_1+Arg_2+1 {O(n)}
3: n_evalaaron2bb4in___4->n_evalaaron2bb6in___8: Arg_1+Arg_2+1 {O(n)}
4: n_evalaaron2bb5in___3->n_evalaaron2bb6in___8: Arg_1+Arg_2+1 {O(n)}
5: n_evalaaron2bb6in___8->n_evalaaron2bb3in___6: Arg_1+Arg_2+1 {O(n)}
6: n_evalaaron2bb6in___8->n_evalaaron2returnin___5: 1 {O(1)}
7: n_evalaaron2entryin___9->n_evalaaron2bb6in___8: 1 {O(1)}
8: n_evalaaron2entryin___9->n_evalaaron2returnin___7: 1 {O(1)}
9: n_evalaaron2returnin___5->n_evalaaron2stop___2: 1 {O(1)}
10: n_evalaaron2returnin___7->n_evalaaron2stop___1: 1 {O(1)}
11: n_evalaaron2start->n_evalaaron2entryin___9: 1 {O(1)}

Sizebounds

0: n_evalaaron2bb3in___6->n_evalaaron2bb4in___4, Arg_0: Arg_0 {O(n)}
0: n_evalaaron2bb3in___6->n_evalaaron2bb4in___4, Arg_1: Arg_0*Arg_1+Arg_0*Arg_2+2*Arg_0+2*Arg_2+Arg_1+1 {O(n^2)}
0: n_evalaaron2bb3in___6->n_evalaaron2bb4in___4, Arg_2: 2*Arg_0*Arg_1+2*Arg_0*Arg_2+2*Arg_1+4*Arg_0+Arg_2+1 {O(n^2)}
1: n_evalaaron2bb3in___6->n_evalaaron2bb4in___4, Arg_0: Arg_0 {O(n)}
1: n_evalaaron2bb3in___6->n_evalaaron2bb4in___4, Arg_1: Arg_0*Arg_1+Arg_0*Arg_2+2*Arg_0+2*Arg_2+Arg_1+1 {O(n^2)}
1: n_evalaaron2bb3in___6->n_evalaaron2bb4in___4, Arg_2: 2*Arg_0*Arg_1+2*Arg_0*Arg_2+2*Arg_1+4*Arg_0+Arg_2+1 {O(n^2)}
2: n_evalaaron2bb3in___6->n_evalaaron2bb5in___3, Arg_0: Arg_0 {O(n)}
2: n_evalaaron2bb3in___6->n_evalaaron2bb5in___3, Arg_1: Arg_0*Arg_1+Arg_0*Arg_2+2*Arg_0+2*Arg_2+Arg_1+1 {O(n^2)}
2: n_evalaaron2bb3in___6->n_evalaaron2bb5in___3, Arg_2: 2*Arg_0*Arg_1+2*Arg_0*Arg_2+2*Arg_1+4*Arg_0+Arg_2+1 {O(n^2)}
3: n_evalaaron2bb4in___4->n_evalaaron2bb6in___8, Arg_0: Arg_0 {O(n)}
3: n_evalaaron2bb4in___4->n_evalaaron2bb6in___8, Arg_1: Arg_0*Arg_1+Arg_0*Arg_2+2*Arg_0+2*Arg_2+Arg_1+1 {O(n^2)}
3: n_evalaaron2bb4in___4->n_evalaaron2bb6in___8, Arg_2: 2*Arg_0*Arg_1+2*Arg_0*Arg_2+2*Arg_1+4*Arg_0+Arg_2+1 {O(n^2)}
4: n_evalaaron2bb5in___3->n_evalaaron2bb6in___8, Arg_0: Arg_0 {O(n)}
4: n_evalaaron2bb5in___3->n_evalaaron2bb6in___8, Arg_1: Arg_0*Arg_1+Arg_0*Arg_2+2*Arg_0+2*Arg_2+Arg_1+1 {O(n^2)}
4: n_evalaaron2bb5in___3->n_evalaaron2bb6in___8, Arg_2: 2*Arg_0*Arg_1+2*Arg_0*Arg_2+2*Arg_1+4*Arg_0+Arg_2+1 {O(n^2)}
5: n_evalaaron2bb6in___8->n_evalaaron2bb3in___6, Arg_0: Arg_0 {O(n)}
5: n_evalaaron2bb6in___8->n_evalaaron2bb3in___6, Arg_1: Arg_0*Arg_1+Arg_0*Arg_2+2*Arg_0+2*Arg_2+Arg_1+1 {O(n^2)}
5: n_evalaaron2bb6in___8->n_evalaaron2bb3in___6, Arg_2: 2*Arg_0*Arg_1+2*Arg_0*Arg_2+2*Arg_1+4*Arg_0+Arg_2+1 {O(n^2)}
6: n_evalaaron2bb6in___8->n_evalaaron2returnin___5, Arg_0: 3*Arg_0 {O(n)}
6: n_evalaaron2bb6in___8->n_evalaaron2returnin___5, Arg_1: 2*Arg_0*Arg_1+2*Arg_0*Arg_2+2*Arg_1+4*Arg_0+5*Arg_2+2 {O(n^2)}
6: n_evalaaron2bb6in___8->n_evalaaron2returnin___5, Arg_2: 4*Arg_0*Arg_1+4*Arg_0*Arg_2+2*Arg_2+5*Arg_1+8*Arg_0+2 {O(n^2)}
7: n_evalaaron2entryin___9->n_evalaaron2bb6in___8, Arg_0: Arg_0 {O(n)}
7: n_evalaaron2entryin___9->n_evalaaron2bb6in___8, Arg_1: Arg_2 {O(n)}
7: n_evalaaron2entryin___9->n_evalaaron2bb6in___8, Arg_2: Arg_1 {O(n)}
8: n_evalaaron2entryin___9->n_evalaaron2returnin___7, Arg_0: Arg_0 {O(n)}
8: n_evalaaron2entryin___9->n_evalaaron2returnin___7, Arg_1: Arg_1 {O(n)}
8: n_evalaaron2entryin___9->n_evalaaron2returnin___7, Arg_2: Arg_2 {O(n)}
9: n_evalaaron2returnin___5->n_evalaaron2stop___2, Arg_0: 3*Arg_0 {O(n)}
9: n_evalaaron2returnin___5->n_evalaaron2stop___2, Arg_1: 2*Arg_0*Arg_1+2*Arg_0*Arg_2+2*Arg_1+4*Arg_0+5*Arg_2+2 {O(n^2)}
9: n_evalaaron2returnin___5->n_evalaaron2stop___2, Arg_2: 4*Arg_0*Arg_1+4*Arg_0*Arg_2+2*Arg_2+5*Arg_1+8*Arg_0+2 {O(n^2)}
10: n_evalaaron2returnin___7->n_evalaaron2stop___1, Arg_0: Arg_0 {O(n)}
10: n_evalaaron2returnin___7->n_evalaaron2stop___1, Arg_1: Arg_1 {O(n)}
10: n_evalaaron2returnin___7->n_evalaaron2stop___1, Arg_2: Arg_2 {O(n)}
11: n_evalaaron2start->n_evalaaron2entryin___9, Arg_0: Arg_0 {O(n)}
11: n_evalaaron2start->n_evalaaron2entryin___9, Arg_1: Arg_1 {O(n)}
11: n_evalaaron2start->n_evalaaron2entryin___9, Arg_2: Arg_2 {O(n)}