Initial Problem

Start: n_evalfstart
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_evalfbb1in___4, n_evalfbb2in___3, n_evalfbb2in___6, n_evalfbb3in___2, n_evalfbb4in___7, n_evalfentryin___8, n_evalfreturnin___5, n_evalfstart, n_evalfstop___1
Transitions:
0:n_evalfbb1in___4(Arg_0,Arg_1,Arg_2) -> n_evalfbb2in___3(Arg_0,Arg_1,Arg_2-1):|:1<=Arg_1 && Arg_0<=Arg_2 && Arg_2<=Arg_0
1:n_evalfbb2in___3(Arg_0,Arg_1,Arg_2) -> n_evalfbb3in___2(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0
2:n_evalfbb2in___6(Arg_0,Arg_1,Arg_2) -> n_evalfbb1in___4(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_2 && Arg_0<=Arg_2
3:n_evalfbb3in___2(Arg_0,Arg_1,Arg_2) -> n_evalfbb4in___7(Arg_0,Arg_1-1,Arg_2):|:1+Arg_2<=Arg_0
4:n_evalfbb4in___7(Arg_0,Arg_1,Arg_2) -> n_evalfbb2in___6(Arg_0,Arg_1,Arg_0):|:1<=Arg_1
5:n_evalfbb4in___7(Arg_0,Arg_1,Arg_2) -> n_evalfreturnin___5(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
6:n_evalfentryin___8(Arg_0,Arg_1,Arg_2) -> n_evalfbb4in___7(Arg_1,Arg_0,Arg_2)
7:n_evalfreturnin___5(Arg_0,Arg_1,Arg_2) -> n_evalfstop___1(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
8:n_evalfstart(Arg_0,Arg_1,Arg_2) -> n_evalfentryin___8(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant Arg_2<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_1 for location n_evalfbb2in___6

Found invariant Arg_1<=0 for location n_evalfreturnin___5

Found invariant 1+Arg_2<=Arg_0 && Arg_0<=1+Arg_2 && 1<=Arg_1 for location n_evalfbb3in___2

Found invariant 1+Arg_2<=Arg_0 && Arg_0<=1+Arg_2 && 1<=Arg_1 for location n_evalfbb2in___3

Found invariant Arg_2<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_1 for location n_evalfbb1in___4

Found invariant Arg_1<=0 for location n_evalfstop___1

Problem after Preprocessing

Start: n_evalfstart
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_evalfbb1in___4, n_evalfbb2in___3, n_evalfbb2in___6, n_evalfbb3in___2, n_evalfbb4in___7, n_evalfentryin___8, n_evalfreturnin___5, n_evalfstart, n_evalfstop___1
Transitions:
0:n_evalfbb1in___4(Arg_0,Arg_1,Arg_2) -> n_evalfbb2in___3(Arg_0,Arg_1,Arg_2-1):|:Arg_2<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_1 && Arg_0<=Arg_2 && Arg_2<=Arg_0
1:n_evalfbb2in___3(Arg_0,Arg_1,Arg_2) -> n_evalfbb3in___2(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0
2:n_evalfbb2in___6(Arg_0,Arg_1,Arg_2) -> n_evalfbb1in___4(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_1 && Arg_0<=Arg_2 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_2 && Arg_0<=Arg_2
3:n_evalfbb3in___2(Arg_0,Arg_1,Arg_2) -> n_evalfbb4in___7(Arg_0,Arg_1-1,Arg_2):|:1+Arg_2<=Arg_0 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 1+Arg_2<=Arg_0
4:n_evalfbb4in___7(Arg_0,Arg_1,Arg_2) -> n_evalfbb2in___6(Arg_0,Arg_1,Arg_0):|:1<=Arg_1
5:n_evalfbb4in___7(Arg_0,Arg_1,Arg_2) -> n_evalfreturnin___5(Arg_0,Arg_1,Arg_2):|:Arg_1<=0
6:n_evalfentryin___8(Arg_0,Arg_1,Arg_2) -> n_evalfbb4in___7(Arg_1,Arg_0,Arg_2)
7:n_evalfreturnin___5(Arg_0,Arg_1,Arg_2) -> n_evalfstop___1(Arg_0,Arg_1,Arg_2):|:Arg_1<=0 && Arg_1<=0
8:n_evalfstart(Arg_0,Arg_1,Arg_2) -> n_evalfentryin___8(Arg_0,Arg_1,Arg_2)

MPRF for transition 0:n_evalfbb1in___4(Arg_0,Arg_1,Arg_2) -> n_evalfbb2in___3(Arg_0,Arg_1,Arg_2-1):|:Arg_2<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_1 && Arg_0<=Arg_2 && Arg_2<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_evalfbb2in___3 [Arg_1-1 ]
n_evalfbb1in___4 [Arg_1 ]
n_evalfbb3in___2 [Arg_1-1 ]
n_evalfbb4in___7 [Arg_1 ]
n_evalfbb2in___6 [Arg_1 ]

MPRF for transition 1:n_evalfbb2in___3(Arg_0,Arg_1,Arg_2) -> n_evalfbb3in___2(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_evalfbb2in___3 [Arg_1 ]
n_evalfbb1in___4 [Arg_1 ]
n_evalfbb3in___2 [Arg_1-1 ]
n_evalfbb4in___7 [Arg_1 ]
n_evalfbb2in___6 [Arg_1 ]

MPRF for transition 2:n_evalfbb2in___6(Arg_0,Arg_1,Arg_2) -> n_evalfbb1in___4(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && Arg_0<=Arg_2 && 1<=Arg_1 && Arg_0<=Arg_2 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_2 && Arg_0<=Arg_2 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_evalfbb2in___3 [Arg_1-1 ]
n_evalfbb1in___4 [Arg_1-1 ]
n_evalfbb3in___2 [Arg_1-1 ]
n_evalfbb4in___7 [Arg_1 ]
n_evalfbb2in___6 [Arg_1 ]

MPRF for transition 3:n_evalfbb3in___2(Arg_0,Arg_1,Arg_2) -> n_evalfbb4in___7(Arg_0,Arg_1-1,Arg_2):|:1+Arg_2<=Arg_0 && Arg_0<=1+Arg_2 && 1<=Arg_1 && 1+Arg_2<=Arg_0 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

n_evalfbb2in___3 [Arg_1+1 ]
n_evalfbb1in___4 [Arg_1+1 ]
n_evalfbb3in___2 [Arg_1+1 ]
n_evalfbb4in___7 [Arg_1+1 ]
n_evalfbb2in___6 [Arg_1+1 ]

MPRF for transition 4:n_evalfbb4in___7(Arg_0,Arg_1,Arg_2) -> n_evalfbb2in___6(Arg_0,Arg_1,Arg_0):|:1<=Arg_1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

n_evalfbb2in___3 [Arg_1 ]
n_evalfbb1in___4 [Arg_1 ]
n_evalfbb3in___2 [Arg_1 ]
n_evalfbb4in___7 [Arg_1+1 ]
n_evalfbb2in___6 [Arg_1 ]

All Bounds

Timebounds

Overall timebound:5*Arg_0+6 {O(n)}
0: n_evalfbb1in___4->n_evalfbb2in___3: Arg_0 {O(n)}
1: n_evalfbb2in___3->n_evalfbb3in___2: Arg_0 {O(n)}
2: n_evalfbb2in___6->n_evalfbb1in___4: Arg_0 {O(n)}
3: n_evalfbb3in___2->n_evalfbb4in___7: Arg_0+1 {O(n)}
4: n_evalfbb4in___7->n_evalfbb2in___6: Arg_0+1 {O(n)}
5: n_evalfbb4in___7->n_evalfreturnin___5: 1 {O(1)}
6: n_evalfentryin___8->n_evalfbb4in___7: 1 {O(1)}
7: n_evalfreturnin___5->n_evalfstop___1: 1 {O(1)}
8: n_evalfstart->n_evalfentryin___8: 1 {O(1)}

Costbounds

Overall costbound: 5*Arg_0+6 {O(n)}
0: n_evalfbb1in___4->n_evalfbb2in___3: Arg_0 {O(n)}
1: n_evalfbb2in___3->n_evalfbb3in___2: Arg_0 {O(n)}
2: n_evalfbb2in___6->n_evalfbb1in___4: Arg_0 {O(n)}
3: n_evalfbb3in___2->n_evalfbb4in___7: Arg_0+1 {O(n)}
4: n_evalfbb4in___7->n_evalfbb2in___6: Arg_0+1 {O(n)}
5: n_evalfbb4in___7->n_evalfreturnin___5: 1 {O(1)}
6: n_evalfentryin___8->n_evalfbb4in___7: 1 {O(1)}
7: n_evalfreturnin___5->n_evalfstop___1: 1 {O(1)}
8: n_evalfstart->n_evalfentryin___8: 1 {O(1)}

Sizebounds

0: n_evalfbb1in___4->n_evalfbb2in___3, Arg_0: Arg_1 {O(n)}
0: n_evalfbb1in___4->n_evalfbb2in___3, Arg_1: Arg_0 {O(n)}
0: n_evalfbb1in___4->n_evalfbb2in___3, Arg_2: 2*Arg_1+1 {O(n)}
1: n_evalfbb2in___3->n_evalfbb3in___2, Arg_0: Arg_1 {O(n)}
1: n_evalfbb2in___3->n_evalfbb3in___2, Arg_1: Arg_0 {O(n)}
1: n_evalfbb2in___3->n_evalfbb3in___2, Arg_2: 2*Arg_1+1 {O(n)}
2: n_evalfbb2in___6->n_evalfbb1in___4, Arg_0: Arg_1 {O(n)}
2: n_evalfbb2in___6->n_evalfbb1in___4, Arg_1: Arg_0 {O(n)}
2: n_evalfbb2in___6->n_evalfbb1in___4, Arg_2: 2*Arg_1 {O(n)}
3: n_evalfbb3in___2->n_evalfbb4in___7, Arg_0: Arg_1 {O(n)}
3: n_evalfbb3in___2->n_evalfbb4in___7, Arg_1: Arg_0 {O(n)}
3: n_evalfbb3in___2->n_evalfbb4in___7, Arg_2: 2*Arg_1+1 {O(n)}
4: n_evalfbb4in___7->n_evalfbb2in___6, Arg_0: Arg_1 {O(n)}
4: n_evalfbb4in___7->n_evalfbb2in___6, Arg_1: Arg_0 {O(n)}
4: n_evalfbb4in___7->n_evalfbb2in___6, Arg_2: 2*Arg_1 {O(n)}
5: n_evalfbb4in___7->n_evalfreturnin___5, Arg_0: 2*Arg_1 {O(n)}
5: n_evalfbb4in___7->n_evalfreturnin___5, Arg_1: 2*Arg_0 {O(n)}
5: n_evalfbb4in___7->n_evalfreturnin___5, Arg_2: 2*Arg_1+Arg_2+1 {O(n)}
6: n_evalfentryin___8->n_evalfbb4in___7, Arg_0: Arg_1 {O(n)}
6: n_evalfentryin___8->n_evalfbb4in___7, Arg_1: Arg_0 {O(n)}
6: n_evalfentryin___8->n_evalfbb4in___7, Arg_2: Arg_2 {O(n)}
7: n_evalfreturnin___5->n_evalfstop___1, Arg_0: 2*Arg_1 {O(n)}
7: n_evalfreturnin___5->n_evalfstop___1, Arg_1: 2*Arg_0 {O(n)}
7: n_evalfreturnin___5->n_evalfstop___1, Arg_2: 2*Arg_1+Arg_2+1 {O(n)}
8: n_evalfstart->n_evalfentryin___8, Arg_0: Arg_0 {O(n)}
8: n_evalfstart->n_evalfentryin___8, Arg_1: Arg_1 {O(n)}
8: n_evalfstart->n_evalfentryin___8, Arg_2: Arg_2 {O(n)}