Initial Problem

Start: n_f3
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: A_P, B_P, NoDet0
Locations: n_f2___4, n_f2___5, n_f2___6, n_f2___7, n_f3, n_f300___1, n_f300___2, n_f300___3
Transitions:
0:n_f2___4(Arg_0,Arg_1,Arg_2) -> n_f2___4(Arg_0,0,Arg_2):|:0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && 0<=Arg_0
1:n_f2___4(Arg_0,Arg_1,Arg_2) -> n_f2___5(A_P,B_P,Arg_2):|:0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && 1+B_P<=0 && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
2:n_f2___4(Arg_0,Arg_1,Arg_2) -> n_f2___6(A_P,B_P,Arg_2):|:0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && 1<=B_P && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
3:n_f2___5(Arg_0,Arg_1,Arg_2) -> n_f2___4(Arg_0,0,Arg_2):|:0<=1+Arg_0 && 1+Arg_1<=0 && 0<=Arg_0
4:n_f2___5(Arg_0,Arg_1,Arg_2) -> n_f2___5(A_P,B_P,Arg_2):|:0<=1+Arg_0 && 1+Arg_1<=0 && 1+B_P<=0 && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
5:n_f2___5(Arg_0,Arg_1,Arg_2) -> n_f2___6(A_P,B_P,Arg_2):|:0<=1+Arg_0 && 1+Arg_1<=0 && 1<=B_P && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
6:n_f2___5(Arg_0,Arg_1,Arg_2) -> n_f300___1(Arg_0,Arg_1,NoDet0):|:0<=1+Arg_0 && 1+Arg_1<=0 && 1+Arg_0<=0
7:n_f2___6(Arg_0,Arg_1,Arg_2) -> n_f2___4(Arg_0,0,Arg_2):|:0<=1+Arg_0 && 1<=Arg_1 && 0<=Arg_0
8:n_f2___6(Arg_0,Arg_1,Arg_2) -> n_f2___5(A_P,B_P,Arg_2):|:0<=1+Arg_0 && 1<=Arg_1 && 1+B_P<=0 && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
9:n_f2___6(Arg_0,Arg_1,Arg_2) -> n_f2___6(A_P,B_P,Arg_2):|:0<=1+Arg_0 && 1<=Arg_1 && 1<=B_P && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
10:n_f2___6(Arg_0,Arg_1,Arg_2) -> n_f300___2(Arg_0,Arg_1,NoDet0):|:0<=1+Arg_0 && 1<=Arg_1 && 1+Arg_0<=0
11:n_f2___7(Arg_0,Arg_1,Arg_2) -> n_f2___4(Arg_0,0,Arg_2):|:0<=Arg_0
12:n_f2___7(Arg_0,Arg_1,Arg_2) -> n_f2___5(A_P,B_P,Arg_2):|:1+B_P<=0 && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
13:n_f2___7(Arg_0,Arg_1,Arg_2) -> n_f2___6(A_P,B_P,Arg_2):|:1<=B_P && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
14:n_f2___7(Arg_0,Arg_1,Arg_2) -> n_f300___3(Arg_0,Arg_1,NoDet0):|:1+Arg_0<=0
15:n_f3(Arg_0,Arg_1,Arg_2) -> n_f2___7(Arg_0,Arg_1,Arg_2)

Preprocessing

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

Found invariant 1+Arg_1<=0 && Arg_1<=Arg_0 && 2+Arg_0+Arg_1<=0 && 1+Arg_0<=0 && 0<=1+Arg_0 for location n_f300___1

Found invariant 1<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=1+Arg_0 for location n_f2___6

Found invariant 1<=Arg_1 && 0<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && 1+Arg_0<=0 && 0<=1+Arg_0 for location n_f300___2

Found invariant 1+Arg_1<=0 && Arg_1<=Arg_0 && 0<=1+Arg_0 for location n_f2___5

Found invariant 1+Arg_0<=0 for location n_f300___3

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

Problem after Preprocessing

Start: n_f3
Program_Vars: Arg_0, Arg_1
Temp_Vars: A_P, B_P
Locations: n_f2___4, n_f2___5, n_f2___6, n_f2___7, n_f3, n_f300___1, n_f300___2, n_f300___3
Transitions:
32:n_f2___4(Arg_0,Arg_1) -> n_f2___4(Arg_0,0):|:Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && 0<=Arg_0
33:n_f2___4(Arg_0,Arg_1) -> n_f2___5(A_P,B_P):|:Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && 1+B_P<=0 && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
34:n_f2___4(Arg_0,Arg_1) -> n_f2___6(A_P,B_P):|:Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && 1<=B_P && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
35:n_f2___5(Arg_0,Arg_1) -> n_f2___4(Arg_0,0):|:1+Arg_1<=0 && Arg_1<=Arg_0 && 0<=1+Arg_0 && 0<=1+Arg_0 && 1+Arg_1<=0 && 0<=Arg_0
36:n_f2___5(Arg_0,Arg_1) -> n_f2___5(A_P,B_P):|:1+Arg_1<=0 && Arg_1<=Arg_0 && 0<=1+Arg_0 && 0<=1+Arg_0 && 1+Arg_1<=0 && 1+B_P<=0 && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
37:n_f2___5(Arg_0,Arg_1) -> n_f2___6(A_P,B_P):|:1+Arg_1<=0 && Arg_1<=Arg_0 && 0<=1+Arg_0 && 0<=1+Arg_0 && 1+Arg_1<=0 && 1<=B_P && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
38:n_f2___5(Arg_0,Arg_1) -> n_f300___1(Arg_0,Arg_1):|:1+Arg_1<=0 && Arg_1<=Arg_0 && 0<=1+Arg_0 && 0<=1+Arg_0 && 1+Arg_1<=0 && 1+Arg_0<=0
39:n_f2___6(Arg_0,Arg_1) -> n_f2___4(Arg_0,0):|:1<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=1+Arg_0 && 0<=1+Arg_0 && 1<=Arg_1 && 0<=Arg_0
40:n_f2___6(Arg_0,Arg_1) -> n_f2___5(A_P,B_P):|:1<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=1+Arg_0 && 0<=1+Arg_0 && 1<=Arg_1 && 1+B_P<=0 && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
41:n_f2___6(Arg_0,Arg_1) -> n_f2___6(A_P,B_P):|:1<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=1+Arg_0 && 0<=1+Arg_0 && 1<=Arg_1 && 1<=B_P && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
42:n_f2___6(Arg_0,Arg_1) -> n_f300___2(Arg_0,Arg_1):|:1<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=1+Arg_0 && 0<=1+Arg_0 && 1<=Arg_1 && 1+Arg_0<=0
43:n_f2___7(Arg_0,Arg_1) -> n_f2___4(Arg_0,0):|:0<=Arg_0
44:n_f2___7(Arg_0,Arg_1) -> n_f2___5(A_P,B_P):|:1+B_P<=0 && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
45:n_f2___7(Arg_0,Arg_1) -> n_f2___6(A_P,B_P):|:1<=B_P && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0
46:n_f2___7(Arg_0,Arg_1) -> n_f300___3(Arg_0,Arg_1):|:1+Arg_0<=0
47:n_f3(Arg_0,Arg_1) -> n_f2___7(Arg_0,Arg_1)

MPRF for transition 33:n_f2___4(Arg_0,Arg_1) -> n_f2___5(A_P,B_P):|:Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && 1+B_P<=0 && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0 of depth 1:

new bound:

3*Arg_0+5 {O(n)}

MPRF:

n_f2___4 [Arg_0+1 ]
n_f2___5 [Arg_0+1 ]
n_f2___6 [Arg_0+1 ]

MPRF for transition 34:n_f2___4(Arg_0,Arg_1) -> n_f2___6(A_P,B_P):|:Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 && 0<=Arg_0 && 1<=B_P && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0 of depth 1:

new bound:

3*Arg_0+5 {O(n)}

MPRF:

n_f2___4 [Arg_0+1 ]
n_f2___5 [Arg_0+1 ]
n_f2___6 [Arg_0+1 ]

MPRF for transition 35:n_f2___5(Arg_0,Arg_1) -> n_f2___4(Arg_0,0):|:1+Arg_1<=0 && Arg_1<=Arg_0 && 0<=1+Arg_0 && 0<=1+Arg_0 && 1+Arg_1<=0 && 0<=Arg_0 of depth 1:

new bound:

3*Arg_0+3 {O(n)}

MPRF:

n_f2___4 [Arg_0 ]
n_f2___5 [Arg_0+1 ]
n_f2___6 [Arg_0 ]

MPRF for transition 36:n_f2___5(Arg_0,Arg_1) -> n_f2___5(A_P,B_P):|:1+Arg_1<=0 && Arg_1<=Arg_0 && 0<=1+Arg_0 && 0<=1+Arg_0 && 1+Arg_1<=0 && 1+B_P<=0 && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0 of depth 1:

new bound:

3*Arg_0+6 {O(n)}

MPRF:

n_f2___4 [Arg_0+1 ]
n_f2___5 [Arg_0+2 ]
n_f2___6 [Arg_0+1 ]

MPRF for transition 37:n_f2___5(Arg_0,Arg_1) -> n_f2___6(A_P,B_P):|:1+Arg_1<=0 && Arg_1<=Arg_0 && 0<=1+Arg_0 && 0<=1+Arg_0 && 1+Arg_1<=0 && 1<=B_P && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0 of depth 1:

new bound:

3*Arg_0+6 {O(n)}

MPRF:

n_f2___4 [Arg_0+1 ]
n_f2___5 [Arg_0+2 ]
n_f2___6 [Arg_0+1 ]

MPRF for transition 39:n_f2___6(Arg_0,Arg_1) -> n_f2___4(Arg_0,0):|:1<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=1+Arg_0 && 0<=1+Arg_0 && 1<=Arg_1 && 0<=Arg_0 of depth 1:

new bound:

3*Arg_0+3 {O(n)}

MPRF:

n_f2___4 [Arg_0 ]
n_f2___5 [Arg_0 ]
n_f2___6 [Arg_0+1 ]

MPRF for transition 40:n_f2___6(Arg_0,Arg_1) -> n_f2___5(A_P,B_P):|:1<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=1+Arg_0 && 0<=1+Arg_0 && 1<=Arg_1 && 1+B_P<=0 && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0 of depth 1:

new bound:

3*Arg_0+6 {O(n)}

MPRF:

n_f2___4 [Arg_0+1 ]
n_f2___5 [Arg_0+1 ]
n_f2___6 [Arg_0+2 ]

MPRF for transition 41:n_f2___6(Arg_0,Arg_1) -> n_f2___6(A_P,B_P):|:1<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=1+Arg_0 && 0<=1+Arg_0 && 1<=Arg_1 && 1<=B_P && 0<=1+A_P && Arg_0<=A_P+1 && 1+A_P<=Arg_0 of depth 1:

new bound:

3*Arg_0+6 {O(n)}

MPRF:

n_f2___4 [Arg_0+1 ]
n_f2___5 [Arg_0+1 ]
n_f2___6 [Arg_0+2 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
32: n_f2___4->n_f2___4: inf {Infinity}
33: n_f2___4->n_f2___5: 3*Arg_0+5 {O(n)}
34: n_f2___4->n_f2___6: 3*Arg_0+5 {O(n)}
35: n_f2___5->n_f2___4: 3*Arg_0+3 {O(n)}
36: n_f2___5->n_f2___5: 3*Arg_0+6 {O(n)}
37: n_f2___5->n_f2___6: 3*Arg_0+6 {O(n)}
38: n_f2___5->n_f300___1: 1 {O(1)}
39: n_f2___6->n_f2___4: 3*Arg_0+3 {O(n)}
40: n_f2___6->n_f2___5: 3*Arg_0+6 {O(n)}
41: n_f2___6->n_f2___6: 3*Arg_0+6 {O(n)}
42: n_f2___6->n_f300___2: 1 {O(1)}
43: n_f2___7->n_f2___4: 1 {O(1)}
44: n_f2___7->n_f2___5: 1 {O(1)}
45: n_f2___7->n_f2___6: 1 {O(1)}
46: n_f2___7->n_f300___3: 1 {O(1)}
47: n_f3->n_f2___7: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
32: n_f2___4->n_f2___4: inf {Infinity}
33: n_f2___4->n_f2___5: 3*Arg_0+5 {O(n)}
34: n_f2___4->n_f2___6: 3*Arg_0+5 {O(n)}
35: n_f2___5->n_f2___4: 3*Arg_0+3 {O(n)}
36: n_f2___5->n_f2___5: 3*Arg_0+6 {O(n)}
37: n_f2___5->n_f2___6: 3*Arg_0+6 {O(n)}
38: n_f2___5->n_f300___1: 1 {O(1)}
39: n_f2___6->n_f2___4: 3*Arg_0+3 {O(n)}
40: n_f2___6->n_f2___5: 3*Arg_0+6 {O(n)}
41: n_f2___6->n_f2___6: 3*Arg_0+6 {O(n)}
42: n_f2___6->n_f300___2: 1 {O(1)}
43: n_f2___7->n_f2___4: 1 {O(1)}
44: n_f2___7->n_f2___5: 1 {O(1)}
45: n_f2___7->n_f2___6: 1 {O(1)}
46: n_f2___7->n_f300___3: 1 {O(1)}
47: n_f3->n_f2___7: 1 {O(1)}

Sizebounds

32: n_f2___4->n_f2___4, Arg_0: 9*Arg_0+7 {O(n)}
32: n_f2___4->n_f2___4, Arg_1: 0 {O(1)}
33: n_f2___4->n_f2___5, Arg_0: 9*Arg_0+7 {O(n)}
34: n_f2___4->n_f2___6, Arg_0: 9*Arg_0+7 {O(n)}
35: n_f2___5->n_f2___4, Arg_0: 9*Arg_0+7 {O(n)}
35: n_f2___5->n_f2___4, Arg_1: 0 {O(1)}
36: n_f2___5->n_f2___5, Arg_0: 9*Arg_0+7 {O(n)}
37: n_f2___5->n_f2___6, Arg_0: 9*Arg_0+7 {O(n)}
38: n_f2___5->n_f300___1, Arg_0: 1 {O(1)}
39: n_f2___6->n_f2___4, Arg_0: 9*Arg_0+7 {O(n)}
39: n_f2___6->n_f2___4, Arg_1: 0 {O(1)}
40: n_f2___6->n_f2___5, Arg_0: 9*Arg_0+7 {O(n)}
41: n_f2___6->n_f2___6, Arg_0: 9*Arg_0+7 {O(n)}
42: n_f2___6->n_f300___2, Arg_0: 1 {O(1)}
43: n_f2___7->n_f2___4, Arg_0: Arg_0 {O(n)}
43: n_f2___7->n_f2___4, Arg_1: 0 {O(1)}
44: n_f2___7->n_f2___5, Arg_0: Arg_0+1 {O(n)}
45: n_f2___7->n_f2___6, Arg_0: Arg_0+1 {O(n)}
46: n_f2___7->n_f300___3, Arg_0: Arg_0 {O(n)}
46: n_f2___7->n_f300___3, Arg_1: Arg_1 {O(n)}
47: n_f3->n_f2___7, Arg_0: Arg_0 {O(n)}
47: n_f3->n_f2___7, Arg_1: Arg_1 {O(n)}