Initial Problem

Start: n_f300
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: B_P, NoDet0
Locations: n_f1___1, n_f1___2, n_f1___6, n_f1___7, n_f1___8, n_f2___3, n_f2___4, n_f2___5, n_f2___9, n_f300
Transitions:
0:n_f2___3(Arg_0,Arg_1,Arg_2) -> n_f1___1(Arg_0-1,B_P,NoDet0):|:1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0 && Arg_0<=1 && 1+B_P<=0
1:n_f2___3(Arg_0,Arg_1,Arg_2) -> n_f1___2(Arg_0-1,B_P,NoDet0):|:1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0 && Arg_0<=1 && 1<=B_P
2:n_f2___3(Arg_0,Arg_1,Arg_2) -> n_f2___3(Arg_0,0,Arg_2):|:1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_0
3:n_f2___3(Arg_0,Arg_1,Arg_2) -> n_f2___4(Arg_0-1,B_P,Arg_2):|:1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0 && 1+B_P<=0 && 2<=Arg_0
4:n_f2___3(Arg_0,Arg_1,Arg_2) -> n_f2___5(Arg_0-1,B_P,Arg_2):|:1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0 && 1<=B_P && 2<=Arg_0
5:n_f2___4(Arg_0,Arg_1,Arg_2) -> n_f1___1(Arg_0-1,B_P,NoDet0):|:1<=Arg_0 && 1<=Arg_0 && 1+Arg_1<=0 && 1<=Arg_0 && Arg_0<=1 && 1+B_P<=0
6:n_f2___4(Arg_0,Arg_1,Arg_2) -> n_f1___2(Arg_0-1,B_P,NoDet0):|:1<=Arg_0 && 1<=Arg_0 && 1+Arg_1<=0 && 1<=Arg_0 && Arg_0<=1 && 1<=B_P
7:n_f2___4(Arg_0,Arg_1,Arg_2) -> n_f2___3(Arg_0,0,Arg_2):|:1<=Arg_0 && 1<=Arg_0 && 1+Arg_1<=0 && 1<=Arg_0 && 1<=Arg_0
8:n_f2___4(Arg_0,Arg_1,Arg_2) -> n_f2___4(Arg_0-1,B_P,Arg_2):|:1<=Arg_0 && 1<=Arg_0 && 1+Arg_1<=0 && 1<=Arg_0 && 1+B_P<=0 && 2<=Arg_0
9:n_f2___4(Arg_0,Arg_1,Arg_2) -> n_f2___5(Arg_0-1,B_P,Arg_2):|:1<=Arg_0 && 1<=Arg_0 && 1+Arg_1<=0 && 1<=Arg_0 && 1<=B_P && 2<=Arg_0
10:n_f2___5(Arg_0,Arg_1,Arg_2) -> n_f1___1(Arg_0-1,B_P,NoDet0):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && Arg_0<=1 && 1+B_P<=0
11:n_f2___5(Arg_0,Arg_1,Arg_2) -> n_f1___2(Arg_0-1,B_P,NoDet0):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && Arg_0<=1 && 1<=B_P
12:n_f2___5(Arg_0,Arg_1,Arg_2) -> n_f2___3(Arg_0,0,Arg_2):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1<=Arg_0
13:n_f2___5(Arg_0,Arg_1,Arg_2) -> n_f2___4(Arg_0-1,B_P,Arg_2):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1+B_P<=0 && 2<=Arg_0
14:n_f2___5(Arg_0,Arg_1,Arg_2) -> n_f2___5(Arg_0-1,B_P,Arg_2):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1<=B_P && 2<=Arg_0
15:n_f2___9(Arg_0,Arg_1,Arg_2) -> n_f1___6(Arg_0,0,NoDet0):|:Arg_0<=0
16:n_f2___9(Arg_0,Arg_1,Arg_2) -> n_f1___7(Arg_0-1,B_P,NoDet0):|:Arg_0<=1 && 1+B_P<=0
17:n_f2___9(Arg_0,Arg_1,Arg_2) -> n_f1___8(Arg_0-1,B_P,NoDet0):|:Arg_0<=1 && 1<=B_P
18:n_f2___9(Arg_0,Arg_1,Arg_2) -> n_f2___3(Arg_0,0,Arg_2):|:1<=Arg_0
19:n_f2___9(Arg_0,Arg_1,Arg_2) -> n_f2___4(Arg_0-1,B_P,Arg_2):|:1+B_P<=0 && 2<=Arg_0
20:n_f2___9(Arg_0,Arg_1,Arg_2) -> n_f2___5(Arg_0-1,B_P,Arg_2):|:1<=B_P && 2<=Arg_0
21:n_f300(Arg_0,Arg_1,Arg_2) -> n_f2___9(Arg_0,Arg_1,Arg_2)

Preprocessing

Eliminate variables {NoDet0,Arg_2} that do not contribute to the problem

Found invariant 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_f1___2

Found invariant 1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 for location n_f2___5

Found invariant 1+Arg_1<=0 && 1+Arg_0+Arg_1<=0 && Arg_0<=0 for location n_f1___7

Found invariant 1+Arg_1<=0 && 1+Arg_1<=Arg_0 && 1+Arg_0+Arg_1<=0 && Arg_0<=0 && 0<=Arg_0 for location n_f1___1

Found invariant Arg_1<=0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 for location n_f1___6

Found invariant 1+Arg_1<=0 && 2+Arg_1<=Arg_0 && 1<=Arg_0 for location n_f2___4

Found invariant 1<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 for location n_f1___8

Found invariant Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_f2___3

Problem after Preprocessing

Start: n_f300
Program_Vars: Arg_0, Arg_1
Temp_Vars: B_P
Locations: n_f1___1, n_f1___2, n_f1___6, n_f1___7, n_f1___8, n_f2___3, n_f2___4, n_f2___5, n_f2___9, n_f300
Transitions:
44:n_f2___3(Arg_0,Arg_1) -> n_f1___1(Arg_0-1,B_P):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0 && Arg_0<=1 && 1+B_P<=0
45:n_f2___3(Arg_0,Arg_1) -> n_f1___2(Arg_0-1,B_P):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0 && Arg_0<=1 && 1<=B_P
46:n_f2___3(Arg_0,Arg_1) -> n_f2___3(Arg_0,0):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_0
47:n_f2___3(Arg_0,Arg_1) -> n_f2___4(Arg_0-1,B_P):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0 && 1+B_P<=0 && 2<=Arg_0
48:n_f2___3(Arg_0,Arg_1) -> n_f2___5(Arg_0-1,B_P):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0 && 1<=B_P && 2<=Arg_0
49:n_f2___4(Arg_0,Arg_1) -> n_f1___1(Arg_0-1,B_P):|:1+Arg_1<=0 && 2+Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1+Arg_1<=0 && 1<=Arg_0 && Arg_0<=1 && 1+B_P<=0
50:n_f2___4(Arg_0,Arg_1) -> n_f1___2(Arg_0-1,B_P):|:1+Arg_1<=0 && 2+Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1+Arg_1<=0 && 1<=Arg_0 && Arg_0<=1 && 1<=B_P
51:n_f2___4(Arg_0,Arg_1) -> n_f2___3(Arg_0,0):|:1+Arg_1<=0 && 2+Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1+Arg_1<=0 && 1<=Arg_0 && 1<=Arg_0
52:n_f2___4(Arg_0,Arg_1) -> n_f2___4(Arg_0-1,B_P):|:1+Arg_1<=0 && 2+Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1+Arg_1<=0 && 1<=Arg_0 && 1+B_P<=0 && 2<=Arg_0
53:n_f2___4(Arg_0,Arg_1) -> n_f2___5(Arg_0-1,B_P):|:1+Arg_1<=0 && 2+Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1+Arg_1<=0 && 1<=Arg_0 && 1<=B_P && 2<=Arg_0
54:n_f2___5(Arg_0,Arg_1) -> n_f1___1(Arg_0-1,B_P):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && Arg_0<=1 && 1+B_P<=0
55:n_f2___5(Arg_0,Arg_1) -> n_f1___2(Arg_0-1,B_P):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && Arg_0<=1 && 1<=B_P
56:n_f2___5(Arg_0,Arg_1) -> n_f2___3(Arg_0,0):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1<=Arg_0
57:n_f2___5(Arg_0,Arg_1) -> n_f2___4(Arg_0-1,B_P):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1+B_P<=0 && 2<=Arg_0
58:n_f2___5(Arg_0,Arg_1) -> n_f2___5(Arg_0-1,B_P):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1<=B_P && 2<=Arg_0
59:n_f2___9(Arg_0,Arg_1) -> n_f1___6(Arg_0,0):|:Arg_0<=0
60:n_f2___9(Arg_0,Arg_1) -> n_f1___7(Arg_0-1,B_P):|:Arg_0<=1 && 1+B_P<=0
61:n_f2___9(Arg_0,Arg_1) -> n_f1___8(Arg_0-1,B_P):|:Arg_0<=1 && 1<=B_P
62:n_f2___9(Arg_0,Arg_1) -> n_f2___3(Arg_0,0):|:1<=Arg_0
63:n_f2___9(Arg_0,Arg_1) -> n_f2___4(Arg_0-1,B_P):|:1+B_P<=0 && 2<=Arg_0
64:n_f2___9(Arg_0,Arg_1) -> n_f2___5(Arg_0-1,B_P):|:1<=B_P && 2<=Arg_0
65:n_f300(Arg_0,Arg_1) -> n_f2___9(Arg_0,Arg_1)

MPRF for transition 47:n_f2___3(Arg_0,Arg_1) -> n_f2___4(Arg_0-1,B_P):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0 && 1+B_P<=0 && 2<=Arg_0 of depth 1:

new bound:

3*Arg_0 {O(n)}

MPRF:

n_f2___3 [Arg_0 ]
n_f2___4 [Arg_0 ]
n_f2___5 [Arg_0 ]

MPRF for transition 48:n_f2___3(Arg_0,Arg_1) -> n_f2___5(Arg_0-1,B_P):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 1<=Arg_0 && 1<=B_P && 2<=Arg_0 of depth 1:

new bound:

3*Arg_0+1 {O(n)}

MPRF:

n_f2___3 [Arg_0 ]
n_f2___4 [Arg_0+1 ]
n_f2___5 [Arg_0 ]

MPRF for transition 51:n_f2___4(Arg_0,Arg_1) -> n_f2___3(Arg_0,0):|:1+Arg_1<=0 && 2+Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1+Arg_1<=0 && 1<=Arg_0 && 1<=Arg_0 of depth 1:

new bound:

3*Arg_0+1 {O(n)}

MPRF:

n_f2___3 [Arg_0-1 ]
n_f2___4 [Arg_0 ]
n_f2___5 [Arg_0 ]

MPRF for transition 52:n_f2___4(Arg_0,Arg_1) -> n_f2___4(Arg_0-1,B_P):|:1+Arg_1<=0 && 2+Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1+Arg_1<=0 && 1<=Arg_0 && 1+B_P<=0 && 2<=Arg_0 of depth 1:

new bound:

3*Arg_0 {O(n)}

MPRF:

n_f2___3 [Arg_0 ]
n_f2___4 [Arg_0 ]
n_f2___5 [Arg_0 ]

MPRF for transition 53:n_f2___4(Arg_0,Arg_1) -> n_f2___5(Arg_0-1,B_P):|:1+Arg_1<=0 && 2+Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1+Arg_1<=0 && 1<=Arg_0 && 1<=B_P && 2<=Arg_0 of depth 1:

new bound:

3*Arg_0+2 {O(n)}

MPRF:

n_f2___3 [Arg_0-1 ]
n_f2___4 [Arg_0 ]
n_f2___5 [Arg_0-1 ]

MPRF for transition 56:n_f2___5(Arg_0,Arg_1) -> n_f2___3(Arg_0,0):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1<=Arg_0 of depth 1:

new bound:

3*Arg_0+1 {O(n)}

MPRF:

n_f2___3 [Arg_0-1 ]
n_f2___4 [Arg_0 ]
n_f2___5 [Arg_0 ]

MPRF for transition 57:n_f2___5(Arg_0,Arg_1) -> n_f2___4(Arg_0-1,B_P):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1+B_P<=0 && 2<=Arg_0 of depth 1:

new bound:

3*Arg_0+2 {O(n)}

MPRF:

n_f2___3 [Arg_0-1 ]
n_f2___4 [Arg_0-1 ]
n_f2___5 [Arg_0 ]

MPRF for transition 58:n_f2___5(Arg_0,Arg_1) -> n_f2___5(Arg_0-1,B_P):|:1<=Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_1 && 1<=Arg_0 && 1<=B_P && 2<=Arg_0 of depth 1:

new bound:

3*Arg_0 {O(n)}

MPRF:

n_f2___3 [Arg_0 ]
n_f2___4 [Arg_0 ]
n_f2___5 [Arg_0 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
44: n_f2___3->n_f1___1: 1 {O(1)}
45: n_f2___3->n_f1___2: 1 {O(1)}
46: n_f2___3->n_f2___3: inf {Infinity}
47: n_f2___3->n_f2___4: 3*Arg_0 {O(n)}
48: n_f2___3->n_f2___5: 3*Arg_0+1 {O(n)}
49: n_f2___4->n_f1___1: 1 {O(1)}
50: n_f2___4->n_f1___2: 1 {O(1)}
51: n_f2___4->n_f2___3: 3*Arg_0+1 {O(n)}
52: n_f2___4->n_f2___4: 3*Arg_0 {O(n)}
53: n_f2___4->n_f2___5: 3*Arg_0+2 {O(n)}
54: n_f2___5->n_f1___1: 1 {O(1)}
55: n_f2___5->n_f1___2: 1 {O(1)}
56: n_f2___5->n_f2___3: 3*Arg_0+1 {O(n)}
57: n_f2___5->n_f2___4: 3*Arg_0+2 {O(n)}
58: n_f2___5->n_f2___5: 3*Arg_0 {O(n)}
59: n_f2___9->n_f1___6: 1 {O(1)}
60: n_f2___9->n_f1___7: 1 {O(1)}
61: n_f2___9->n_f1___8: 1 {O(1)}
62: n_f2___9->n_f2___3: 1 {O(1)}
63: n_f2___9->n_f2___4: 1 {O(1)}
64: n_f2___9->n_f2___5: 1 {O(1)}
65: n_f300->n_f2___9: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
44: n_f2___3->n_f1___1: 1 {O(1)}
45: n_f2___3->n_f1___2: 1 {O(1)}
46: n_f2___3->n_f2___3: inf {Infinity}
47: n_f2___3->n_f2___4: 3*Arg_0 {O(n)}
48: n_f2___3->n_f2___5: 3*Arg_0+1 {O(n)}
49: n_f2___4->n_f1___1: 1 {O(1)}
50: n_f2___4->n_f1___2: 1 {O(1)}
51: n_f2___4->n_f2___3: 3*Arg_0+1 {O(n)}
52: n_f2___4->n_f2___4: 3*Arg_0 {O(n)}
53: n_f2___4->n_f2___5: 3*Arg_0+2 {O(n)}
54: n_f2___5->n_f1___1: 1 {O(1)}
55: n_f2___5->n_f1___2: 1 {O(1)}
56: n_f2___5->n_f2___3: 3*Arg_0+1 {O(n)}
57: n_f2___5->n_f2___4: 3*Arg_0+2 {O(n)}
58: n_f2___5->n_f2___5: 3*Arg_0 {O(n)}
59: n_f2___9->n_f1___6: 1 {O(1)}
60: n_f2___9->n_f1___7: 1 {O(1)}
61: n_f2___9->n_f1___8: 1 {O(1)}
62: n_f2___9->n_f2___3: 1 {O(1)}
63: n_f2___9->n_f2___4: 1 {O(1)}
64: n_f2___9->n_f2___5: 1 {O(1)}
65: n_f300->n_f2___9: 1 {O(1)}

Sizebounds

44: n_f2___3->n_f1___1, Arg_0: 0 {O(1)}
45: n_f2___3->n_f1___2, Arg_0: 0 {O(1)}
46: n_f2___3->n_f2___3, Arg_0: 9*Arg_0 {O(n)}
46: n_f2___3->n_f2___3, Arg_1: 0 {O(1)}
47: n_f2___3->n_f2___4, Arg_0: 9*Arg_0 {O(n)}
48: n_f2___3->n_f2___5, Arg_0: 9*Arg_0 {O(n)}
49: n_f2___4->n_f1___1, Arg_0: 0 {O(1)}
50: n_f2___4->n_f1___2, Arg_0: 0 {O(1)}
51: n_f2___4->n_f2___3, Arg_0: 9*Arg_0 {O(n)}
51: n_f2___4->n_f2___3, Arg_1: 0 {O(1)}
52: n_f2___4->n_f2___4, Arg_0: 9*Arg_0 {O(n)}
53: n_f2___4->n_f2___5, Arg_0: 9*Arg_0 {O(n)}
54: n_f2___5->n_f1___1, Arg_0: 0 {O(1)}
55: n_f2___5->n_f1___2, Arg_0: 0 {O(1)}
56: n_f2___5->n_f2___3, Arg_0: 9*Arg_0 {O(n)}
56: n_f2___5->n_f2___3, Arg_1: 0 {O(1)}
57: n_f2___5->n_f2___4, Arg_0: 9*Arg_0 {O(n)}
58: n_f2___5->n_f2___5, Arg_0: 9*Arg_0 {O(n)}
59: n_f2___9->n_f1___6, Arg_0: Arg_0 {O(n)}
59: n_f2___9->n_f1___6, Arg_1: 0 {O(1)}
60: n_f2___9->n_f1___7, Arg_0: Arg_0+1 {O(n)}
61: n_f2___9->n_f1___8, Arg_0: Arg_0+1 {O(n)}
62: n_f2___9->n_f2___3, Arg_0: Arg_0 {O(n)}
62: n_f2___9->n_f2___3, Arg_1: 0 {O(1)}
63: n_f2___9->n_f2___4, Arg_0: Arg_0 {O(n)}
64: n_f2___9->n_f2___5, Arg_0: Arg_0 {O(n)}
65: n_f300->n_f2___9, Arg_0: Arg_0 {O(n)}
65: n_f300->n_f2___9, Arg_1: Arg_1 {O(n)}