Initial Problem

Start: n_f1
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
Temp_Vars: E_P, NoDet0, NoDet1
Locations: n_f0___4, n_f0___5, n_f0___6, n_f0___7, n_f1, n_f2___1, n_f2___2, n_f2___3
Transitions:
0:n_f0___4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f0___4(Arg_0-1,Arg_1,NoDet0,NoDet1,E_P,Arg_5):|:0<=Arg_0 && 1<=Arg_4 && 1<=E_P && 1<=Arg_0
1:n_f0___4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f0___5(Arg_0-1,Arg_1,NoDet0,NoDet1,E_P,Arg_5):|:0<=Arg_0 && 1<=Arg_4 && 1+E_P<=0 && 1<=Arg_0
2:n_f0___4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f0___6(Arg_0,Arg_1,Arg_2-1,NoDet0,0,NoDet1):|:0<=Arg_0 && 1<=Arg_4 && 3<=Arg_2 && 1<=Arg_0
3:n_f0___4(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f2___1(Arg_0,NoDet0,Arg_2,Arg_3,Arg_4,Arg_5):|:0<=Arg_0 && 1<=Arg_4 && Arg_0<=0
4:n_f0___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f0___4(Arg_0-1,Arg_1,NoDet0,NoDet1,E_P,Arg_5):|:0<=Arg_0 && 1+Arg_4<=0 && 1<=E_P && 1<=Arg_0
5:n_f0___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f0___5(Arg_0-1,Arg_1,NoDet0,NoDet1,E_P,Arg_5):|:0<=Arg_0 && 1+Arg_4<=0 && 1+E_P<=0 && 1<=Arg_0
6:n_f0___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f0___6(Arg_0,Arg_1,Arg_2-1,NoDet0,0,NoDet1):|:0<=Arg_0 && 1+Arg_4<=0 && 3<=Arg_2 && 1<=Arg_0
7:n_f0___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f2___2(Arg_0,NoDet0,Arg_2,Arg_3,Arg_4,Arg_5):|:0<=Arg_0 && 1+Arg_4<=0 && Arg_0<=0
8:n_f0___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f0___4(Arg_0-1,Arg_1,NoDet0,NoDet1,E_P,Arg_5):|:1<=Arg_0 && Arg_4<=0 && 0<=Arg_4 && 1<=Arg_0 && 2<=Arg_2 && 1<=Arg_0 && 1<=Arg_0 && 1<=E_P && 1<=Arg_0
9:n_f0___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f0___5(Arg_0-1,Arg_1,NoDet0,NoDet1,E_P,Arg_5):|:1<=Arg_0 && Arg_4<=0 && 0<=Arg_4 && 1<=Arg_0 && 2<=Arg_2 && 1<=Arg_0 && 1<=Arg_0 && 1+E_P<=0 && 1<=Arg_0
10:n_f0___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f0___6(Arg_0,Arg_1,Arg_2-1,NoDet0,0,NoDet1):|:1<=Arg_0 && Arg_4<=0 && 0<=Arg_4 && 1<=Arg_0 && 2<=Arg_2 && 1<=Arg_0 && 1<=Arg_0 && 3<=Arg_2 && 1<=Arg_0
11:n_f0___7(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f0___4(Arg_0-1,Arg_1,NoDet0,NoDet1,E_P,Arg_5):|:1<=E_P && 1<=Arg_0
12:n_f0___7(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f0___5(Arg_0-1,Arg_1,NoDet0,NoDet1,E_P,Arg_5):|:1+E_P<=0 && 1<=Arg_0
13:n_f0___7(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f0___6(Arg_0,Arg_1,Arg_2-1,NoDet0,0,NoDet1):|:3<=Arg_2 && 1<=Arg_0
14:n_f0___7(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f2___3(Arg_0,NoDet0,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_0<=0
15:n_f1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f0___7(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

Preprocessing

Eliminate variables {NoDet1,Arg_1,Arg_3,Arg_5} that do not contribute to the problem

Found invariant 1<=Arg_4 && 1<=Arg_0+Arg_4 && 1+Arg_0<=Arg_4 && Arg_0<=0 && 0<=Arg_0 for location n_f2___1

Found invariant Arg_4<=0 && 2+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=Arg_4 && 2<=Arg_2+Arg_4 && 1<=Arg_0+Arg_4 && 2<=Arg_2 && 3<=Arg_0+Arg_2 && 1<=Arg_0 for location n_f0___6

Found invariant 1<=Arg_4 && 1<=Arg_0+Arg_4 && 0<=Arg_0 for location n_f0___4

Found invariant 1+Arg_4<=0 && 1+Arg_4<=Arg_0 && 0<=Arg_0 for location n_f0___5

Found invariant 1+Arg_4<=0 && 1+Arg_4<=Arg_0 && 1+Arg_0+Arg_4<=0 && Arg_0<=0 && 0<=Arg_0 for location n_f2___2

Found invariant Arg_0<=0 for location n_f2___3

Problem after Preprocessing

Start: n_f1
Program_Vars: Arg_0, Arg_2, Arg_4
Temp_Vars: E_P, NoDet0
Locations: n_f0___4, n_f0___5, n_f0___6, n_f0___7, n_f1, n_f2___1, n_f2___2, n_f2___3
Transitions:
32:n_f0___4(Arg_0,Arg_2,Arg_4) -> n_f0___4(Arg_0-1,NoDet0,E_P):|:1<=Arg_4 && 1<=Arg_0+Arg_4 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_4 && 1<=E_P && 1<=Arg_0
33:n_f0___4(Arg_0,Arg_2,Arg_4) -> n_f0___5(Arg_0-1,NoDet0,E_P):|:1<=Arg_4 && 1<=Arg_0+Arg_4 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_4 && 1+E_P<=0 && 1<=Arg_0
34:n_f0___4(Arg_0,Arg_2,Arg_4) -> n_f0___6(Arg_0,Arg_2-1,0):|:1<=Arg_4 && 1<=Arg_0+Arg_4 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_4 && 3<=Arg_2 && 1<=Arg_0
35:n_f0___4(Arg_0,Arg_2,Arg_4) -> n_f2___1(Arg_0,Arg_2,Arg_4):|:1<=Arg_4 && 1<=Arg_0+Arg_4 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_4 && Arg_0<=0
36:n_f0___5(Arg_0,Arg_2,Arg_4) -> n_f0___4(Arg_0-1,NoDet0,E_P):|:1+Arg_4<=0 && 1+Arg_4<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 1+Arg_4<=0 && 1<=E_P && 1<=Arg_0
37:n_f0___5(Arg_0,Arg_2,Arg_4) -> n_f0___5(Arg_0-1,NoDet0,E_P):|:1+Arg_4<=0 && 1+Arg_4<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 1+Arg_4<=0 && 1+E_P<=0 && 1<=Arg_0
38:n_f0___5(Arg_0,Arg_2,Arg_4) -> n_f0___6(Arg_0,Arg_2-1,0):|:1+Arg_4<=0 && 1+Arg_4<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 1+Arg_4<=0 && 3<=Arg_2 && 1<=Arg_0
39:n_f0___5(Arg_0,Arg_2,Arg_4) -> n_f2___2(Arg_0,Arg_2,Arg_4):|:1+Arg_4<=0 && 1+Arg_4<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 1+Arg_4<=0 && Arg_0<=0
40:n_f0___6(Arg_0,Arg_2,Arg_4) -> n_f0___4(Arg_0-1,NoDet0,E_P):|:Arg_4<=0 && 2+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=Arg_4 && 2<=Arg_2+Arg_4 && 1<=Arg_0+Arg_4 && 2<=Arg_2 && 3<=Arg_0+Arg_2 && 1<=Arg_0 && 1<=Arg_0 && Arg_4<=0 && 0<=Arg_4 && 1<=Arg_0 && 2<=Arg_2 && 1<=Arg_0 && 1<=Arg_0 && 1<=E_P && 1<=Arg_0
41:n_f0___6(Arg_0,Arg_2,Arg_4) -> n_f0___5(Arg_0-1,NoDet0,E_P):|:Arg_4<=0 && 2+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=Arg_4 && 2<=Arg_2+Arg_4 && 1<=Arg_0+Arg_4 && 2<=Arg_2 && 3<=Arg_0+Arg_2 && 1<=Arg_0 && 1<=Arg_0 && Arg_4<=0 && 0<=Arg_4 && 1<=Arg_0 && 2<=Arg_2 && 1<=Arg_0 && 1<=Arg_0 && 1+E_P<=0 && 1<=Arg_0
42:n_f0___6(Arg_0,Arg_2,Arg_4) -> n_f0___6(Arg_0,Arg_2-1,0):|:Arg_4<=0 && 2+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=Arg_4 && 2<=Arg_2+Arg_4 && 1<=Arg_0+Arg_4 && 2<=Arg_2 && 3<=Arg_0+Arg_2 && 1<=Arg_0 && 1<=Arg_0 && Arg_4<=0 && 0<=Arg_4 && 1<=Arg_0 && 2<=Arg_2 && 1<=Arg_0 && 1<=Arg_0 && 3<=Arg_2 && 1<=Arg_0
43:n_f0___7(Arg_0,Arg_2,Arg_4) -> n_f0___4(Arg_0-1,NoDet0,E_P):|:1<=E_P && 1<=Arg_0
44:n_f0___7(Arg_0,Arg_2,Arg_4) -> n_f0___5(Arg_0-1,NoDet0,E_P):|:1+E_P<=0 && 1<=Arg_0
45:n_f0___7(Arg_0,Arg_2,Arg_4) -> n_f0___6(Arg_0,Arg_2-1,0):|:3<=Arg_2 && 1<=Arg_0
46:n_f0___7(Arg_0,Arg_2,Arg_4) -> n_f2___3(Arg_0,Arg_2,Arg_4):|:Arg_0<=0
47:n_f1(Arg_0,Arg_2,Arg_4) -> n_f0___7(Arg_0,Arg_2,Arg_4)

MPRF for transition 32:n_f0___4(Arg_0,Arg_2,Arg_4) -> n_f0___4(Arg_0-1,NoDet0,E_P):|:1<=Arg_4 && 1<=Arg_0+Arg_4 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_4 && 1<=E_P && 1<=Arg_0 of depth 1:

new bound:

3*Arg_0+1 {O(n)}

MPRF:

n_f0___4 [Arg_0+1 ]
n_f0___5 [Arg_0 ]
n_f0___6 [Arg_0 ]

MPRF for transition 33:n_f0___4(Arg_0,Arg_2,Arg_4) -> n_f0___5(Arg_0-1,NoDet0,E_P):|:1<=Arg_4 && 1<=Arg_0+Arg_4 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_4 && 1+E_P<=0 && 1<=Arg_0 of depth 1:

new bound:

3*Arg_0+1 {O(n)}

MPRF:

n_f0___4 [Arg_0+1 ]
n_f0___5 [Arg_0 ]
n_f0___6 [Arg_0 ]

MPRF for transition 34:n_f0___4(Arg_0,Arg_2,Arg_4) -> n_f0___6(Arg_0,Arg_2-1,0):|:1<=Arg_4 && 1<=Arg_0+Arg_4 && 0<=Arg_0 && 0<=Arg_0 && 1<=Arg_4 && 3<=Arg_2 && 1<=Arg_0 of depth 1:

new bound:

3*Arg_0+2 {O(n)}

MPRF:

n_f0___4 [Arg_0+1 ]
n_f0___5 [Arg_0+1 ]
n_f0___6 [Arg_0 ]

MPRF for transition 36:n_f0___5(Arg_0,Arg_2,Arg_4) -> n_f0___4(Arg_0-1,NoDet0,E_P):|:1+Arg_4<=0 && 1+Arg_4<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 1+Arg_4<=0 && 1<=E_P && 1<=Arg_0 of depth 1:

new bound:

3*Arg_0+1 {O(n)}

MPRF:

n_f0___4 [Arg_0 ]
n_f0___5 [Arg_0+1 ]
n_f0___6 [Arg_0 ]

MPRF for transition 37:n_f0___5(Arg_0,Arg_2,Arg_4) -> n_f0___5(Arg_0-1,NoDet0,E_P):|:1+Arg_4<=0 && 1+Arg_4<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 1+Arg_4<=0 && 1+E_P<=0 && 1<=Arg_0 of depth 1:

new bound:

3*Arg_0+1 {O(n)}

MPRF:

n_f0___4 [Arg_0 ]
n_f0___5 [Arg_0+1 ]
n_f0___6 [Arg_0 ]

MPRF for transition 38:n_f0___5(Arg_0,Arg_2,Arg_4) -> n_f0___6(Arg_0,Arg_2-1,0):|:1+Arg_4<=0 && 1+Arg_4<=Arg_0 && 0<=Arg_0 && 0<=Arg_0 && 1+Arg_4<=0 && 3<=Arg_2 && 1<=Arg_0 of depth 1:

new bound:

3*Arg_0+1 {O(n)}

MPRF:

n_f0___4 [Arg_0 ]
n_f0___5 [Arg_0+1 ]
n_f0___6 [Arg_0 ]

MPRF for transition 40:n_f0___6(Arg_0,Arg_2,Arg_4) -> n_f0___4(Arg_0-1,NoDet0,E_P):|:Arg_4<=0 && 2+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=Arg_4 && 2<=Arg_2+Arg_4 && 1<=Arg_0+Arg_4 && 2<=Arg_2 && 3<=Arg_0+Arg_2 && 1<=Arg_0 && 1<=Arg_0 && Arg_4<=0 && 0<=Arg_4 && 1<=Arg_0 && 2<=Arg_2 && 1<=Arg_0 && 1<=Arg_0 && 1<=E_P && 1<=Arg_0 of depth 1:

new bound:

3*Arg_0 {O(n)}

MPRF:

n_f0___4 [Arg_0 ]
n_f0___5 [Arg_0 ]
n_f0___6 [Arg_0 ]

MPRF for transition 41:n_f0___6(Arg_0,Arg_2,Arg_4) -> n_f0___5(Arg_0-1,NoDet0,E_P):|:Arg_4<=0 && 2+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=Arg_4 && 2<=Arg_2+Arg_4 && 1<=Arg_0+Arg_4 && 2<=Arg_2 && 3<=Arg_0+Arg_2 && 1<=Arg_0 && 1<=Arg_0 && Arg_4<=0 && 0<=Arg_4 && 1<=Arg_0 && 2<=Arg_2 && 1<=Arg_0 && 1<=Arg_0 && 1+E_P<=0 && 1<=Arg_0 of depth 1:

new bound:

3*Arg_0 {O(n)}

MPRF:

n_f0___4 [Arg_0 ]
n_f0___5 [Arg_0 ]
n_f0___6 [Arg_0 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
32: n_f0___4->n_f0___4: 3*Arg_0+1 {O(n)}
33: n_f0___4->n_f0___5: 3*Arg_0+1 {O(n)}
34: n_f0___4->n_f0___6: 3*Arg_0+2 {O(n)}
35: n_f0___4->n_f2___1: 1 {O(1)}
36: n_f0___5->n_f0___4: 3*Arg_0+1 {O(n)}
37: n_f0___5->n_f0___5: 3*Arg_0+1 {O(n)}
38: n_f0___5->n_f0___6: 3*Arg_0+1 {O(n)}
39: n_f0___5->n_f2___2: 1 {O(1)}
40: n_f0___6->n_f0___4: 3*Arg_0 {O(n)}
41: n_f0___6->n_f0___5: 3*Arg_0 {O(n)}
42: n_f0___6->n_f0___6: inf {Infinity}
43: n_f0___7->n_f0___4: 1 {O(1)}
44: n_f0___7->n_f0___5: 1 {O(1)}
45: n_f0___7->n_f0___6: 1 {O(1)}
46: n_f0___7->n_f2___3: 1 {O(1)}
47: n_f1->n_f0___7: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
32: n_f0___4->n_f0___4: 3*Arg_0+1 {O(n)}
33: n_f0___4->n_f0___5: 3*Arg_0+1 {O(n)}
34: n_f0___4->n_f0___6: 3*Arg_0+2 {O(n)}
35: n_f0___4->n_f2___1: 1 {O(1)}
36: n_f0___5->n_f0___4: 3*Arg_0+1 {O(n)}
37: n_f0___5->n_f0___5: 3*Arg_0+1 {O(n)}
38: n_f0___5->n_f0___6: 3*Arg_0+1 {O(n)}
39: n_f0___5->n_f2___2: 1 {O(1)}
40: n_f0___6->n_f0___4: 3*Arg_0 {O(n)}
41: n_f0___6->n_f0___5: 3*Arg_0 {O(n)}
42: n_f0___6->n_f0___6: inf {Infinity}
43: n_f0___7->n_f0___4: 1 {O(1)}
44: n_f0___7->n_f0___5: 1 {O(1)}
45: n_f0___7->n_f0___6: 1 {O(1)}
46: n_f0___7->n_f2___3: 1 {O(1)}
47: n_f1->n_f0___7: 1 {O(1)}

Sizebounds

32: n_f0___4->n_f0___4, Arg_0: 9*Arg_0 {O(n)}
33: n_f0___4->n_f0___5, Arg_0: 9*Arg_0 {O(n)}
34: n_f0___4->n_f0___6, Arg_0: 9*Arg_0 {O(n)}
34: n_f0___4->n_f0___6, Arg_4: 0 {O(1)}
35: n_f0___4->n_f2___1, Arg_0: 0 {O(1)}
36: n_f0___5->n_f0___4, Arg_0: 9*Arg_0 {O(n)}
37: n_f0___5->n_f0___5, Arg_0: 9*Arg_0 {O(n)}
38: n_f0___5->n_f0___6, Arg_0: 9*Arg_0 {O(n)}
38: n_f0___5->n_f0___6, Arg_4: 0 {O(1)}
39: n_f0___5->n_f2___2, Arg_0: 0 {O(1)}
40: n_f0___6->n_f0___4, Arg_0: 9*Arg_0 {O(n)}
41: n_f0___6->n_f0___5, Arg_0: 9*Arg_0 {O(n)}
42: n_f0___6->n_f0___6, Arg_0: 9*Arg_0 {O(n)}
42: n_f0___6->n_f0___6, Arg_4: 0 {O(1)}
43: n_f0___7->n_f0___4, Arg_0: Arg_0 {O(n)}
44: n_f0___7->n_f0___5, Arg_0: Arg_0 {O(n)}
45: n_f0___7->n_f0___6, Arg_0: Arg_0 {O(n)}
45: n_f0___7->n_f0___6, Arg_2: Arg_2 {O(n)}
45: n_f0___7->n_f0___6, Arg_4: 0 {O(1)}
46: n_f0___7->n_f2___3, Arg_0: Arg_0 {O(n)}
46: n_f0___7->n_f2___3, Arg_2: Arg_2 {O(n)}
46: n_f0___7->n_f2___3, Arg_4: Arg_4 {O(n)}
47: n_f1->n_f0___7, Arg_0: Arg_0 {O(n)}
47: n_f1->n_f0___7, Arg_2: Arg_2 {O(n)}
47: n_f1->n_f0___7, Arg_4: Arg_4 {O(n)}