Initial Problem

Start: n_evalgcdstart
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_evalgcdbb4in___7, n_evalgcdbb4in___8, n_evalgcdbb5in___5, n_evalgcdbb6in___4, n_evalgcdbb7in___11, n_evalgcdentryin___12, n_evalgcdreturnin___10, n_evalgcdreturnin___6, n_evalgcdreturnin___9, n_evalgcdstart, n_evalgcdstop___1, n_evalgcdstop___2, n_evalgcdstop___3
Transitions:
0:n_evalgcdbb4in___7(Arg_0,Arg_1) -> n_evalgcdbb6in___4(Arg_0,Arg_1):|:1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1
1:n_evalgcdbb4in___8(Arg_0,Arg_1) -> n_evalgcdbb5in___5(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 1+Arg_1<=Arg_0
2:n_evalgcdbb5in___5(Arg_0,Arg_1) -> n_evalgcdbb7in___11(Arg_0-Arg_1,Arg_1):|:1+Arg_1<=Arg_0 && 1<=Arg_1
3:n_evalgcdbb6in___4(Arg_0,Arg_1) -> n_evalgcdbb7in___11(Arg_0,Arg_1-Arg_0):|:1+Arg_0<=Arg_1 && 1<=Arg_0
4:n_evalgcdbb7in___11(Arg_0,Arg_1) -> n_evalgcdbb4in___7(Arg_0,Arg_1):|:1<=Arg_0 && 1<=Arg_1 && 1+Arg_0<=Arg_1
5:n_evalgcdbb7in___11(Arg_0,Arg_1) -> n_evalgcdbb4in___8(Arg_0,Arg_1):|:1<=Arg_0 && 1<=Arg_1 && 1+Arg_1<=Arg_0
6:n_evalgcdbb7in___11(Arg_0,Arg_1) -> n_evalgcdreturnin___6(Arg_0,Arg_0):|:1<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0
7:n_evalgcdentryin___12(Arg_0,Arg_1) -> n_evalgcdbb7in___11(Arg_1,Arg_0):|:1<=Arg_0 && 1<=Arg_1
8:n_evalgcdentryin___12(Arg_0,Arg_1) -> n_evalgcdreturnin___10(Arg_0,Arg_1):|:Arg_0<=0
9:n_evalgcdentryin___12(Arg_0,Arg_1) -> n_evalgcdreturnin___9(Arg_0,Arg_1):|:Arg_1<=0
10:n_evalgcdreturnin___10(Arg_0,Arg_1) -> n_evalgcdstop___2(Arg_0,Arg_1):|:Arg_0<=0
11:n_evalgcdreturnin___6(Arg_0,Arg_1) -> n_evalgcdstop___3(Arg_0,Arg_1):|:1<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0
12:n_evalgcdreturnin___9(Arg_0,Arg_1) -> n_evalgcdstop___1(Arg_0,Arg_1):|:Arg_1<=0
13:n_evalgcdstart(Arg_0,Arg_1) -> n_evalgcdentryin___12(Arg_0,Arg_1)

Preprocessing

Found invariant Arg_1<=0 for location n_evalgcdstop___1

Found invariant 2<=Arg_0+Arg_1 for location n_evalgcdbb7in___11

Found invariant Arg_0<=0 for location n_evalgcdreturnin___10

Found invariant Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_evalgcdreturnin___6

Found invariant 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location n_evalgcdbb4in___7

Found invariant Arg_0<=0 for location n_evalgcdstop___2

Found invariant 2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 for location n_evalgcdbb6in___4

Found invariant 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_evalgcdbb4in___8

Found invariant Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_evalgcdstop___3

Found invariant 1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 for location n_evalgcdbb5in___5

Found invariant Arg_1<=0 for location n_evalgcdreturnin___9

Problem after Preprocessing

Start: n_evalgcdstart
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_evalgcdbb4in___7, n_evalgcdbb4in___8, n_evalgcdbb5in___5, n_evalgcdbb6in___4, n_evalgcdbb7in___11, n_evalgcdentryin___12, n_evalgcdreturnin___10, n_evalgcdreturnin___6, n_evalgcdreturnin___9, n_evalgcdstart, n_evalgcdstop___1, n_evalgcdstop___2, n_evalgcdstop___3
Transitions:
0:n_evalgcdbb4in___7(Arg_0,Arg_1) -> n_evalgcdbb6in___4(Arg_0,Arg_1):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1
1:n_evalgcdbb4in___8(Arg_0,Arg_1) -> n_evalgcdbb5in___5(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 1+Arg_1<=Arg_0
2:n_evalgcdbb5in___5(Arg_0,Arg_1) -> n_evalgcdbb7in___11(Arg_0-Arg_1,Arg_1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1+Arg_1<=Arg_0 && 1<=Arg_1
3:n_evalgcdbb6in___4(Arg_0,Arg_1) -> n_evalgcdbb7in___11(Arg_0,Arg_1-Arg_0):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_1 && 1<=Arg_0
4:n_evalgcdbb7in___11(Arg_0,Arg_1) -> n_evalgcdbb4in___7(Arg_0,Arg_1):|:2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_1 && 1+Arg_0<=Arg_1
5:n_evalgcdbb7in___11(Arg_0,Arg_1) -> n_evalgcdbb4in___8(Arg_0,Arg_1):|:2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_1 && 1+Arg_1<=Arg_0
6:n_evalgcdbb7in___11(Arg_0,Arg_1) -> n_evalgcdreturnin___6(Arg_0,Arg_0):|:2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0
7:n_evalgcdentryin___12(Arg_0,Arg_1) -> n_evalgcdbb7in___11(Arg_1,Arg_0):|:1<=Arg_0 && 1<=Arg_1
8:n_evalgcdentryin___12(Arg_0,Arg_1) -> n_evalgcdreturnin___10(Arg_0,Arg_1):|:Arg_0<=0
9:n_evalgcdentryin___12(Arg_0,Arg_1) -> n_evalgcdreturnin___9(Arg_0,Arg_1):|:Arg_1<=0
10:n_evalgcdreturnin___10(Arg_0,Arg_1) -> n_evalgcdstop___2(Arg_0,Arg_1):|:Arg_0<=0 && Arg_0<=0
11:n_evalgcdreturnin___6(Arg_0,Arg_1) -> n_evalgcdstop___3(Arg_0,Arg_1):|:Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0
12:n_evalgcdreturnin___9(Arg_0,Arg_1) -> n_evalgcdstop___1(Arg_0,Arg_1):|:Arg_1<=0 && Arg_1<=0
13:n_evalgcdstart(Arg_0,Arg_1) -> n_evalgcdentryin___12(Arg_0,Arg_1)

MPRF for transition 0:n_evalgcdbb4in___7(Arg_0,Arg_1) -> n_evalgcdbb6in___4(Arg_0,Arg_1):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_evalgcdbb5in___5 [Arg_1 ]
n_evalgcdbb6in___4 [Arg_1-Arg_0 ]
n_evalgcdbb4in___7 [Arg_1+1-Arg_0 ]
n_evalgcdbb7in___11 [Arg_1 ]
n_evalgcdbb4in___8 [Arg_1 ]

MPRF for transition 1:n_evalgcdbb4in___8(Arg_0,Arg_1) -> n_evalgcdbb5in___5(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1+Arg_1<=Arg_0 && 1<=Arg_1 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

n_evalgcdbb5in___5 [Arg_0-Arg_1 ]
n_evalgcdbb6in___4 [Arg_0 ]
n_evalgcdbb4in___7 [Arg_0 ]
n_evalgcdbb7in___11 [Arg_0 ]
n_evalgcdbb4in___8 [Arg_0 ]

MPRF for transition 2:n_evalgcdbb5in___5(Arg_0,Arg_1) -> n_evalgcdbb7in___11(Arg_0-Arg_1,Arg_1):|:1+Arg_1<=Arg_0 && 1<=Arg_1 && 3<=Arg_0+Arg_1 && 2<=Arg_0 && 1+Arg_1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

Arg_0+Arg_1+2 {O(n)}

MPRF:

n_evalgcdbb5in___5 [Arg_0-1 ]
n_evalgcdbb6in___4 [Arg_1-1 ]
n_evalgcdbb4in___7 [Arg_0+Arg_1-2 ]
n_evalgcdbb7in___11 [Arg_0+Arg_1-2 ]
n_evalgcdbb4in___8 [Arg_0-1 ]

MPRF for transition 3:n_evalgcdbb6in___4(Arg_0,Arg_1) -> n_evalgcdbb7in___11(Arg_0,Arg_1-Arg_0):|:2<=Arg_1 && 3<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_0 && 1+Arg_0<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_0+Arg_1+2 {O(n)}

MPRF:

n_evalgcdbb5in___5 [Arg_0-1 ]
n_evalgcdbb6in___4 [Arg_1-1 ]
n_evalgcdbb4in___7 [Arg_0+Arg_1-2 ]
n_evalgcdbb7in___11 [Arg_0+Arg_1-2 ]
n_evalgcdbb4in___8 [Arg_0-1 ]

MPRF for transition 4:n_evalgcdbb7in___11(Arg_0,Arg_1) -> n_evalgcdbb4in___7(Arg_0,Arg_1):|:2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_1 && 1+Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_evalgcdbb5in___5 [Arg_1 ]
n_evalgcdbb6in___4 [Arg_1-1 ]
n_evalgcdbb4in___7 [Arg_1-1 ]
n_evalgcdbb7in___11 [Arg_1 ]
n_evalgcdbb4in___8 [Arg_1 ]

MPRF for transition 5:n_evalgcdbb7in___11(Arg_0,Arg_1) -> n_evalgcdbb4in___8(Arg_0,Arg_1):|:2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_1 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

n_evalgcdbb5in___5 [Arg_0-1 ]
n_evalgcdbb6in___4 [Arg_0 ]
n_evalgcdbb4in___7 [Arg_0 ]
n_evalgcdbb7in___11 [Arg_0 ]
n_evalgcdbb4in___8 [Arg_0-1 ]

All Bounds

Timebounds

Overall timebound:4*Arg_0+4*Arg_1+12 {O(n)}
0: n_evalgcdbb4in___7->n_evalgcdbb6in___4: Arg_0 {O(n)}
1: n_evalgcdbb4in___8->n_evalgcdbb5in___5: Arg_1 {O(n)}
2: n_evalgcdbb5in___5->n_evalgcdbb7in___11: Arg_0+Arg_1+2 {O(n)}
3: n_evalgcdbb6in___4->n_evalgcdbb7in___11: Arg_0+Arg_1+2 {O(n)}
4: n_evalgcdbb7in___11->n_evalgcdbb4in___7: Arg_0 {O(n)}
5: n_evalgcdbb7in___11->n_evalgcdbb4in___8: Arg_1 {O(n)}
6: n_evalgcdbb7in___11->n_evalgcdreturnin___6: 1 {O(1)}
7: n_evalgcdentryin___12->n_evalgcdbb7in___11: 1 {O(1)}
8: n_evalgcdentryin___12->n_evalgcdreturnin___10: 1 {O(1)}
9: n_evalgcdentryin___12->n_evalgcdreturnin___9: 1 {O(1)}
10: n_evalgcdreturnin___10->n_evalgcdstop___2: 1 {O(1)}
11: n_evalgcdreturnin___6->n_evalgcdstop___3: 1 {O(1)}
12: n_evalgcdreturnin___9->n_evalgcdstop___1: 1 {O(1)}
13: n_evalgcdstart->n_evalgcdentryin___12: 1 {O(1)}

Costbounds

Overall costbound: 4*Arg_0+4*Arg_1+12 {O(n)}
0: n_evalgcdbb4in___7->n_evalgcdbb6in___4: Arg_0 {O(n)}
1: n_evalgcdbb4in___8->n_evalgcdbb5in___5: Arg_1 {O(n)}
2: n_evalgcdbb5in___5->n_evalgcdbb7in___11: Arg_0+Arg_1+2 {O(n)}
3: n_evalgcdbb6in___4->n_evalgcdbb7in___11: Arg_0+Arg_1+2 {O(n)}
4: n_evalgcdbb7in___11->n_evalgcdbb4in___7: Arg_0 {O(n)}
5: n_evalgcdbb7in___11->n_evalgcdbb4in___8: Arg_1 {O(n)}
6: n_evalgcdbb7in___11->n_evalgcdreturnin___6: 1 {O(1)}
7: n_evalgcdentryin___12->n_evalgcdbb7in___11: 1 {O(1)}
8: n_evalgcdentryin___12->n_evalgcdreturnin___10: 1 {O(1)}
9: n_evalgcdentryin___12->n_evalgcdreturnin___9: 1 {O(1)}
10: n_evalgcdreturnin___10->n_evalgcdstop___2: 1 {O(1)}
11: n_evalgcdreturnin___6->n_evalgcdstop___3: 1 {O(1)}
12: n_evalgcdreturnin___9->n_evalgcdstop___1: 1 {O(1)}
13: n_evalgcdstart->n_evalgcdentryin___12: 1 {O(1)}

Sizebounds

0: n_evalgcdbb4in___7->n_evalgcdbb6in___4, Arg_0: 2*Arg_1 {O(n)}
0: n_evalgcdbb4in___7->n_evalgcdbb6in___4, Arg_1: 2*Arg_0 {O(n)}
1: n_evalgcdbb4in___8->n_evalgcdbb5in___5, Arg_0: 2*Arg_1 {O(n)}
1: n_evalgcdbb4in___8->n_evalgcdbb5in___5, Arg_1: 2*Arg_0 {O(n)}
2: n_evalgcdbb5in___5->n_evalgcdbb7in___11, Arg_0: 2*Arg_1 {O(n)}
2: n_evalgcdbb5in___5->n_evalgcdbb7in___11, Arg_1: 2*Arg_0 {O(n)}
3: n_evalgcdbb6in___4->n_evalgcdbb7in___11, Arg_0: 2*Arg_1 {O(n)}
3: n_evalgcdbb6in___4->n_evalgcdbb7in___11, Arg_1: 2*Arg_0 {O(n)}
4: n_evalgcdbb7in___11->n_evalgcdbb4in___7, Arg_0: 2*Arg_1 {O(n)}
4: n_evalgcdbb7in___11->n_evalgcdbb4in___7, Arg_1: 2*Arg_0 {O(n)}
5: n_evalgcdbb7in___11->n_evalgcdbb4in___8, Arg_0: 2*Arg_1 {O(n)}
5: n_evalgcdbb7in___11->n_evalgcdbb4in___8, Arg_1: 2*Arg_0 {O(n)}
6: n_evalgcdbb7in___11->n_evalgcdreturnin___6, Arg_0: 5*Arg_1 {O(n)}
6: n_evalgcdbb7in___11->n_evalgcdreturnin___6, Arg_1: 5*Arg_1 {O(n)}
7: n_evalgcdentryin___12->n_evalgcdbb7in___11, Arg_0: Arg_1 {O(n)}
7: n_evalgcdentryin___12->n_evalgcdbb7in___11, Arg_1: Arg_0 {O(n)}
8: n_evalgcdentryin___12->n_evalgcdreturnin___10, Arg_0: Arg_0 {O(n)}
8: n_evalgcdentryin___12->n_evalgcdreturnin___10, Arg_1: Arg_1 {O(n)}
9: n_evalgcdentryin___12->n_evalgcdreturnin___9, Arg_0: Arg_0 {O(n)}
9: n_evalgcdentryin___12->n_evalgcdreturnin___9, Arg_1: Arg_1 {O(n)}
10: n_evalgcdreturnin___10->n_evalgcdstop___2, Arg_0: Arg_0 {O(n)}
10: n_evalgcdreturnin___10->n_evalgcdstop___2, Arg_1: Arg_1 {O(n)}
11: n_evalgcdreturnin___6->n_evalgcdstop___3, Arg_0: 5*Arg_1 {O(n)}
11: n_evalgcdreturnin___6->n_evalgcdstop___3, Arg_1: 5*Arg_1 {O(n)}
12: n_evalgcdreturnin___9->n_evalgcdstop___1, Arg_0: Arg_0 {O(n)}
12: n_evalgcdreturnin___9->n_evalgcdstop___1, Arg_1: Arg_1 {O(n)}
13: n_evalgcdstart->n_evalgcdentryin___12, Arg_0: Arg_0 {O(n)}
13: n_evalgcdstart->n_evalgcdentryin___12, Arg_1: Arg_1 {O(n)}