Initial Problem

Start: n_start
Program_Vars: Arg_0
Temp_Vars: A_P
Locations: n_a___1, n_a___2, n_a___3, n_a___4, n_start
Transitions:
0:n_a___1(Arg_0) -> n_a___1(A_P):|:1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P+1 && 1+2*A_P<=Arg_0
1:n_a___1(Arg_0) -> n_a___4(A_P):|:1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P && 2*A_P<=Arg_0
2:n_a___2(Arg_0) -> n_a___3(A_P):|:2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 4<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P && 2*A_P<=Arg_0
3:n_a___2(Arg_0) -> n_a___4(A_P):|:2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 4<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P+1 && 1+2*A_P<=Arg_0
4:n_a___3(Arg_0) -> n_a___1(A_P):|:2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P+1 && 1+2*A_P<=Arg_0
5:n_a___3(Arg_0) -> n_a___4(A_P):|:2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P && 2*A_P<=Arg_0
6:n_a___4(Arg_0) -> n_a___1(A_P):|:1<=Arg_0 && 1<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P+1 && 1+2*A_P<=Arg_0
7:n_a___4(Arg_0) -> n_a___4(A_P):|:1<=Arg_0 && 1<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P && 2*A_P<=Arg_0
8:n_start(Arg_0) -> n_a___2(Arg_0):|:4<=Arg_0
9:n_start(Arg_0) -> n_a___3(Arg_0):|:2<=Arg_0
10:n_start(Arg_0) -> n_a___4(Arg_0):|:1<=Arg_0

Preprocessing

Found invariant 1<=Arg_0 for location n_a___1

Found invariant 1<=Arg_0 for location n_a___4

Found invariant 4<=Arg_0 for location n_a___2

Found invariant 2<=Arg_0 for location n_a___3

Problem after Preprocessing

Start: n_start
Program_Vars: Arg_0
Temp_Vars: A_P
Locations: n_a___1, n_a___2, n_a___3, n_a___4, n_start
Transitions:
0:n_a___1(Arg_0) -> n_a___1(A_P):|:1<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P+1 && 1+2*A_P<=Arg_0
1:n_a___1(Arg_0) -> n_a___4(A_P):|:1<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P && 2*A_P<=Arg_0
2:n_a___2(Arg_0) -> n_a___3(A_P):|:4<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 4<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P && 2*A_P<=Arg_0
3:n_a___2(Arg_0) -> n_a___4(A_P):|:4<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 4<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P+1 && 1+2*A_P<=Arg_0
4:n_a___3(Arg_0) -> n_a___1(A_P):|:2<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P+1 && 1+2*A_P<=Arg_0
5:n_a___3(Arg_0) -> n_a___4(A_P):|:2<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 2<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P && 2*A_P<=Arg_0
6:n_a___4(Arg_0) -> n_a___1(A_P):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P+1 && 1+2*A_P<=Arg_0
7:n_a___4(Arg_0) -> n_a___4(A_P):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P && 2*A_P<=Arg_0
8:n_start(Arg_0) -> n_a___2(Arg_0):|:4<=Arg_0
9:n_start(Arg_0) -> n_a___3(Arg_0):|:2<=Arg_0
10:n_start(Arg_0) -> n_a___4(Arg_0):|:1<=Arg_0

MPRF for transition 0:n_a___1(Arg_0) -> n_a___1(A_P):|:1<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P+1 && 1+2*A_P<=Arg_0 of depth 1:

new bound:

20*Arg_0 {O(n)}

MPRF:

n_a___1 [2*Arg_0 ]
n_a___4 [4*Arg_0 ]

MPRF for transition 1:n_a___1(Arg_0) -> n_a___4(A_P):|:1<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P && 2*A_P<=Arg_0 of depth 1:

new bound:

40*Arg_0+19 {O(n)}

MPRF:

n_a___1 [4*Arg_0-1 ]
n_a___4 [8*Arg_0-6 ]

MPRF for transition 6:n_a___4(Arg_0) -> n_a___1(A_P):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P+1 && 1+2*A_P<=Arg_0 of depth 1:

new bound:

20*Arg_0+4 {O(n)}

MPRF:

n_a___1 [2*Arg_0-1 ]
n_a___4 [4*Arg_0-1 ]

MPRF for transition 7:n_a___4(Arg_0) -> n_a___4(A_P):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=2*Arg_0 && 2<=Arg_0 && Arg_0<=2*A_P && 2*A_P<=Arg_0 of depth 1:

new bound:

24*Arg_0 {O(n)}

MPRF:

n_a___1 [4*Arg_0 ]
n_a___4 [4*Arg_0 ]

All Bounds

Timebounds

Overall timebound:104*Arg_0+30 {O(n)}
0: n_a___1->n_a___1: 20*Arg_0 {O(n)}
1: n_a___1->n_a___4: 40*Arg_0+19 {O(n)}
2: n_a___2->n_a___3: 1 {O(1)}
3: n_a___2->n_a___4: 1 {O(1)}
4: n_a___3->n_a___1: 1 {O(1)}
5: n_a___3->n_a___4: 1 {O(1)}
6: n_a___4->n_a___1: 20*Arg_0+4 {O(n)}
7: n_a___4->n_a___4: 24*Arg_0 {O(n)}
8: n_start->n_a___2: 1 {O(1)}
9: n_start->n_a___3: 1 {O(1)}
10: n_start->n_a___4: 1 {O(1)}

Costbounds

Overall costbound: 104*Arg_0+30 {O(n)}
0: n_a___1->n_a___1: 20*Arg_0 {O(n)}
1: n_a___1->n_a___4: 40*Arg_0+19 {O(n)}
2: n_a___2->n_a___3: 1 {O(1)}
3: n_a___2->n_a___4: 1 {O(1)}
4: n_a___3->n_a___1: 1 {O(1)}
5: n_a___3->n_a___4: 1 {O(1)}
6: n_a___4->n_a___1: 20*Arg_0+4 {O(n)}
7: n_a___4->n_a___4: 24*Arg_0 {O(n)}
8: n_start->n_a___2: 1 {O(1)}
9: n_start->n_a___3: 1 {O(1)}
10: n_start->n_a___4: 1 {O(1)}

Sizebounds

0: n_a___1->n_a___1, Arg_0: 12*Arg_0 {O(n)}
1: n_a___1->n_a___4, Arg_0: 12*Arg_0 {O(n)}
2: n_a___2->n_a___3, Arg_0: Arg_0 {O(n)}
3: n_a___2->n_a___4, Arg_0: Arg_0 {O(n)}
4: n_a___3->n_a___1, Arg_0: 2*Arg_0 {O(n)}
5: n_a___3->n_a___4, Arg_0: 2*Arg_0 {O(n)}
6: n_a___4->n_a___1, Arg_0: 12*Arg_0 {O(n)}
7: n_a___4->n_a___4, Arg_0: 12*Arg_0 {O(n)}
8: n_start->n_a___2, Arg_0: Arg_0 {O(n)}
9: n_start->n_a___3, Arg_0: Arg_0 {O(n)}
10: n_start->n_a___4, Arg_0: Arg_0 {O(n)}