Initial Problem

Start: n_f2
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars: B_P, C_P, NoDet0
Locations: n_f1___1, n_f1___2, n_f1___6, n_f2, n_f300___3, n_f300___4, n_f300___5, n_f300___7
Transitions:
0:n_f2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___7(Arg_0,Arg_1,Arg_2,Arg_3)
1:n_f300___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___3(Arg_0,Arg_1,0,Arg_3):|:1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1
2:n_f300___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___4(Arg_0+1,Arg_1,C_P,Arg_3):|:1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+C_P<=0
3:n_f300___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___5(Arg_0+1,B_P,C_P,Arg_3):|:1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && 1+Arg_0<=Arg_1 && 1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
4:n_f300___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f1___1(Arg_0,B_P,Arg_2,NoDet0):|:Arg_0<=Arg_1 && 1+Arg_2<=0 && B_P<=Arg_0 && Arg_1<=B_P && B_P<=Arg_1
5:n_f300___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___3(Arg_0,Arg_1,0,Arg_3):|:Arg_0<=Arg_1 && 1+Arg_2<=0 && 1+Arg_0<=Arg_1
6:n_f300___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___4(Arg_0+1,Arg_1,C_P,Arg_3):|:Arg_0<=Arg_1 && 1+Arg_2<=0 && 1+Arg_0<=Arg_1 && 1+C_P<=0
7:n_f300___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___5(Arg_0+1,B_P,C_P,Arg_3):|:Arg_0<=Arg_1 && 1+Arg_2<=0 && 1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
8:n_f300___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f1___2(Arg_0,B_P,Arg_2,NoDet0):|:Arg_0<=Arg_1 && 1<=Arg_2 && B_P<=Arg_0 && Arg_1<=B_P && B_P<=Arg_1
9:n_f300___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___3(Arg_0,Arg_1,0,Arg_3):|:Arg_0<=Arg_1 && 1<=Arg_2 && 1+Arg_0<=Arg_1
10:n_f300___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___4(Arg_0+1,Arg_1,C_P,Arg_3):|:Arg_0<=Arg_1 && 1<=Arg_2 && 1+Arg_0<=Arg_1 && 1+C_P<=0
11:n_f300___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___5(Arg_0+1,B_P,C_P,Arg_3):|:Arg_0<=Arg_1 && 1<=Arg_2 && 1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
12:n_f300___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f1___6(Arg_0,B_P,Arg_2,NoDet0):|:B_P<=Arg_0 && Arg_1<=B_P && B_P<=Arg_1
13:n_f300___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___3(Arg_0,Arg_1,0,Arg_3):|:1+Arg_0<=Arg_1
14:n_f300___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___4(Arg_0+1,Arg_1,C_P,Arg_3):|:1+Arg_0<=Arg_1 && 1+C_P<=0
15:n_f300___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___5(Arg_0+1,B_P,C_P,Arg_3):|:1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1

Preprocessing

Eliminate variables {NoDet0,Arg_3} that do not contribute to the problem

Found invariant 1<=Arg_2 && Arg_1<=Arg_0 && Arg_0<=Arg_1 for location n_f1___2

Found invariant Arg_2<=0 && 0<=Arg_2 && 1+Arg_0<=Arg_1 for location n_f300___3

Found invariant 1<=Arg_2 && Arg_0<=Arg_1 for location n_f300___5

Found invariant 1+Arg_2<=0 && Arg_1<=Arg_0 && Arg_0<=Arg_1 for location n_f1___1

Found invariant Arg_1<=Arg_0 for location n_f1___6

Found invariant 1+Arg_2<=0 && Arg_0<=Arg_1 for location n_f300___4

Problem after Preprocessing

Start: n_f2
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: B_P, C_P
Locations: n_f1___1, n_f1___2, n_f1___6, n_f2, n_f300___3, n_f300___4, n_f300___5, n_f300___7
Transitions:
32:n_f2(Arg_0,Arg_1,Arg_2) -> n_f300___7(Arg_0,Arg_1,Arg_2)
33:n_f300___3(Arg_0,Arg_1,Arg_2) -> n_f300___3(Arg_0,Arg_1,0):|:Arg_2<=0 && 0<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1
34:n_f300___3(Arg_0,Arg_1,Arg_2) -> n_f300___4(Arg_0+1,Arg_1,C_P):|:Arg_2<=0 && 0<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+C_P<=0
35:n_f300___3(Arg_0,Arg_1,Arg_2) -> n_f300___5(Arg_0+1,B_P,C_P):|:Arg_2<=0 && 0<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && 1+Arg_0<=Arg_1 && 1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
36:n_f300___4(Arg_0,Arg_1,Arg_2) -> n_f1___1(Arg_0,B_P,Arg_2):|:1+Arg_2<=0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1+Arg_2<=0 && B_P<=Arg_0 && Arg_1<=B_P && B_P<=Arg_1
37:n_f300___4(Arg_0,Arg_1,Arg_2) -> n_f300___3(Arg_0,Arg_1,0):|:1+Arg_2<=0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1+Arg_2<=0 && 1+Arg_0<=Arg_1
38:n_f300___4(Arg_0,Arg_1,Arg_2) -> n_f300___4(Arg_0+1,Arg_1,C_P):|:1+Arg_2<=0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1+Arg_2<=0 && 1+Arg_0<=Arg_1 && 1+C_P<=0
39:n_f300___4(Arg_0,Arg_1,Arg_2) -> n_f300___5(Arg_0+1,B_P,C_P):|:1+Arg_2<=0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1+Arg_2<=0 && 1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
40:n_f300___5(Arg_0,Arg_1,Arg_2) -> n_f1___2(Arg_0,B_P,Arg_2):|:1<=Arg_2 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1<=Arg_2 && B_P<=Arg_0 && Arg_1<=B_P && B_P<=Arg_1
41:n_f300___5(Arg_0,Arg_1,Arg_2) -> n_f300___3(Arg_0,Arg_1,0):|:1<=Arg_2 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1<=Arg_2 && 1+Arg_0<=Arg_1
42:n_f300___5(Arg_0,Arg_1,Arg_2) -> n_f300___4(Arg_0+1,Arg_1,C_P):|:1<=Arg_2 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1<=Arg_2 && 1+Arg_0<=Arg_1 && 1+C_P<=0
43:n_f300___5(Arg_0,Arg_1,Arg_2) -> n_f300___5(Arg_0+1,B_P,C_P):|:1<=Arg_2 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1<=Arg_2 && 1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
44:n_f300___7(Arg_0,Arg_1,Arg_2) -> n_f1___6(Arg_0,B_P,Arg_2):|:B_P<=Arg_0 && Arg_1<=B_P && B_P<=Arg_1
45:n_f300___7(Arg_0,Arg_1,Arg_2) -> n_f300___3(Arg_0,Arg_1,0):|:1+Arg_0<=Arg_1
46:n_f300___7(Arg_0,Arg_1,Arg_2) -> n_f300___4(Arg_0+1,Arg_1,C_P):|:1+Arg_0<=Arg_1 && 1+C_P<=0
47:n_f300___7(Arg_0,Arg_1,Arg_2) -> n_f300___5(Arg_0+1,B_P,C_P):|:1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1

MPRF for transition 34:n_f300___3(Arg_0,Arg_1,Arg_2) -> n_f300___4(Arg_0+1,Arg_1,C_P):|:Arg_2<=0 && 0<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+C_P<=0 of depth 1:

new bound:

3*Arg_0+3*Arg_1+2 {O(n)}

MPRF:

n_f300___3 [Arg_1-Arg_0 ]
n_f300___4 [Arg_1-Arg_0 ]
n_f300___5 [Arg_1-Arg_0 ]

MPRF for transition 35:n_f300___3(Arg_0,Arg_1,Arg_2) -> n_f300___5(Arg_0+1,B_P,C_P):|:Arg_2<=0 && 0<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && 1+Arg_0<=Arg_1 && 1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1 of depth 1:

new bound:

3*Arg_0+3*Arg_1+3 {O(n)}

MPRF:

n_f300___3 [Arg_1-Arg_0 ]
n_f300___4 [Arg_1+1-Arg_0 ]
n_f300___5 [Arg_1-Arg_0 ]

MPRF for transition 37:n_f300___4(Arg_0,Arg_1,Arg_2) -> n_f300___3(Arg_0,Arg_1,0):|:1+Arg_2<=0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1+Arg_2<=0 && 1+Arg_0<=Arg_1 of depth 1:

new bound:

3*Arg_0+3*Arg_1+3 {O(n)}

MPRF:

n_f300___3 [Arg_1-Arg_0 ]
n_f300___4 [Arg_1+1-Arg_0 ]
n_f300___5 [Arg_1-Arg_0 ]

MPRF for transition 38:n_f300___4(Arg_0,Arg_1,Arg_2) -> n_f300___4(Arg_0+1,Arg_1,C_P):|:1+Arg_2<=0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1+Arg_2<=0 && 1+Arg_0<=Arg_1 && 1+C_P<=0 of depth 1:

new bound:

3*Arg_0+3*Arg_1+3 {O(n)}

MPRF:

n_f300___3 [Arg_1-Arg_0 ]
n_f300___4 [Arg_1+1-Arg_0 ]
n_f300___5 [Arg_1-Arg_0 ]

MPRF for transition 39:n_f300___4(Arg_0,Arg_1,Arg_2) -> n_f300___5(Arg_0+1,B_P,C_P):|:1+Arg_2<=0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1+Arg_2<=0 && 1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1 of depth 1:

new bound:

3*Arg_0+3*Arg_1+3 {O(n)}

MPRF:

n_f300___3 [Arg_1-Arg_0 ]
n_f300___4 [Arg_1+1-Arg_0 ]
n_f300___5 [Arg_1-Arg_0 ]

MPRF for transition 41:n_f300___5(Arg_0,Arg_1,Arg_2) -> n_f300___3(Arg_0,Arg_1,0):|:1<=Arg_2 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1<=Arg_2 && 1+Arg_0<=Arg_1 of depth 1:

new bound:

3*Arg_0+3*Arg_1+3 {O(n)}

MPRF:

n_f300___3 [Arg_1-Arg_0 ]
n_f300___4 [Arg_1-Arg_0 ]
n_f300___5 [Arg_1+1-Arg_0 ]

MPRF for transition 42:n_f300___5(Arg_0,Arg_1,Arg_2) -> n_f300___4(Arg_0+1,Arg_1,C_P):|:1<=Arg_2 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1<=Arg_2 && 1+Arg_0<=Arg_1 && 1+C_P<=0 of depth 1:

new bound:

3*Arg_0+3*Arg_1+3 {O(n)}

MPRF:

n_f300___3 [Arg_1-Arg_0 ]
n_f300___4 [Arg_1-Arg_0 ]
n_f300___5 [Arg_1+1-Arg_0 ]

MPRF for transition 43:n_f300___5(Arg_0,Arg_1,Arg_2) -> n_f300___5(Arg_0+1,B_P,C_P):|:1<=Arg_2 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1<=Arg_2 && 1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1 of depth 1:

new bound:

3*Arg_0+3*Arg_1+3 {O(n)}

MPRF:

n_f300___3 [Arg_1-Arg_0 ]
n_f300___4 [Arg_1-Arg_0 ]
n_f300___5 [Arg_1+1-Arg_0 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
32: n_f2->n_f300___7: 1 {O(1)}
33: n_f300___3->n_f300___3: inf {Infinity}
34: n_f300___3->n_f300___4: 3*Arg_0+3*Arg_1+2 {O(n)}
35: n_f300___3->n_f300___5: 3*Arg_0+3*Arg_1+3 {O(n)}
36: n_f300___4->n_f1___1: 1 {O(1)}
37: n_f300___4->n_f300___3: 3*Arg_0+3*Arg_1+3 {O(n)}
38: n_f300___4->n_f300___4: 3*Arg_0+3*Arg_1+3 {O(n)}
39: n_f300___4->n_f300___5: 3*Arg_0+3*Arg_1+3 {O(n)}
40: n_f300___5->n_f1___2: 1 {O(1)}
41: n_f300___5->n_f300___3: 3*Arg_0+3*Arg_1+3 {O(n)}
42: n_f300___5->n_f300___4: 3*Arg_0+3*Arg_1+3 {O(n)}
43: n_f300___5->n_f300___5: 3*Arg_0+3*Arg_1+3 {O(n)}
44: n_f300___7->n_f1___6: 1 {O(1)}
45: n_f300___7->n_f300___3: 1 {O(1)}
46: n_f300___7->n_f300___4: 1 {O(1)}
47: n_f300___7->n_f300___5: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
32: n_f2->n_f300___7: 1 {O(1)}
33: n_f300___3->n_f300___3: inf {Infinity}
34: n_f300___3->n_f300___4: 3*Arg_0+3*Arg_1+2 {O(n)}
35: n_f300___3->n_f300___5: 3*Arg_0+3*Arg_1+3 {O(n)}
36: n_f300___4->n_f1___1: 1 {O(1)}
37: n_f300___4->n_f300___3: 3*Arg_0+3*Arg_1+3 {O(n)}
38: n_f300___4->n_f300___4: 3*Arg_0+3*Arg_1+3 {O(n)}
39: n_f300___4->n_f300___5: 3*Arg_0+3*Arg_1+3 {O(n)}
40: n_f300___5->n_f1___2: 1 {O(1)}
41: n_f300___5->n_f300___3: 3*Arg_0+3*Arg_1+3 {O(n)}
42: n_f300___5->n_f300___4: 3*Arg_0+3*Arg_1+3 {O(n)}
43: n_f300___5->n_f300___5: 3*Arg_0+3*Arg_1+3 {O(n)}
44: n_f300___7->n_f1___6: 1 {O(1)}
45: n_f300___7->n_f300___3: 1 {O(1)}
46: n_f300___7->n_f300___4: 1 {O(1)}
47: n_f300___7->n_f300___5: 1 {O(1)}

Sizebounds

32: n_f2->n_f300___7, Arg_0: Arg_0 {O(n)}
32: n_f2->n_f300___7, Arg_1: Arg_1 {O(n)}
32: n_f2->n_f300___7, Arg_2: Arg_2 {O(n)}
33: n_f300___3->n_f300___3, Arg_0: 18*Arg_1+27*Arg_0+23 {O(n)}
33: n_f300___3->n_f300___3, Arg_1: 9*Arg_1 {O(n)}
33: n_f300___3->n_f300___3, Arg_2: 0 {O(1)}
34: n_f300___3->n_f300___4, Arg_0: 18*Arg_1+27*Arg_0+23 {O(n)}
34: n_f300___3->n_f300___4, Arg_1: 9*Arg_1 {O(n)}
35: n_f300___3->n_f300___5, Arg_0: 18*Arg_1+27*Arg_0+23 {O(n)}
35: n_f300___3->n_f300___5, Arg_1: 9*Arg_1 {O(n)}
36: n_f300___4->n_f1___1, Arg_0: 54*Arg_1+82*Arg_0+70 {O(n)}
36: n_f300___4->n_f1___1, Arg_1: 28*Arg_1 {O(n)}
37: n_f300___4->n_f300___3, Arg_0: 18*Arg_1+27*Arg_0+23 {O(n)}
37: n_f300___4->n_f300___3, Arg_1: 9*Arg_1 {O(n)}
37: n_f300___4->n_f300___3, Arg_2: 0 {O(1)}
38: n_f300___4->n_f300___4, Arg_0: 18*Arg_1+27*Arg_0+23 {O(n)}
38: n_f300___4->n_f300___4, Arg_1: 9*Arg_1 {O(n)}
39: n_f300___4->n_f300___5, Arg_0: 18*Arg_1+27*Arg_0+23 {O(n)}
39: n_f300___4->n_f300___5, Arg_1: 9*Arg_1 {O(n)}
40: n_f300___5->n_f1___2, Arg_0: 54*Arg_1+82*Arg_0+70 {O(n)}
40: n_f300___5->n_f1___2, Arg_1: 28*Arg_1 {O(n)}
41: n_f300___5->n_f300___3, Arg_0: 18*Arg_1+27*Arg_0+23 {O(n)}
41: n_f300___5->n_f300___3, Arg_1: 9*Arg_1 {O(n)}
41: n_f300___5->n_f300___3, Arg_2: 0 {O(1)}
42: n_f300___5->n_f300___4, Arg_0: 18*Arg_1+27*Arg_0+23 {O(n)}
42: n_f300___5->n_f300___4, Arg_1: 9*Arg_1 {O(n)}
43: n_f300___5->n_f300___5, Arg_0: 18*Arg_1+27*Arg_0+23 {O(n)}
43: n_f300___5->n_f300___5, Arg_1: 9*Arg_1 {O(n)}
44: n_f300___7->n_f1___6, Arg_0: Arg_0 {O(n)}
44: n_f300___7->n_f1___6, Arg_1: Arg_1 {O(n)}
44: n_f300___7->n_f1___6, Arg_2: Arg_2 {O(n)}
45: n_f300___7->n_f300___3, Arg_0: Arg_0 {O(n)}
45: n_f300___7->n_f300___3, Arg_1: Arg_1 {O(n)}
45: n_f300___7->n_f300___3, Arg_2: 0 {O(1)}
46: n_f300___7->n_f300___4, Arg_0: Arg_0+1 {O(n)}
46: n_f300___7->n_f300___4, Arg_1: Arg_1 {O(n)}
47: n_f300___7->n_f300___5, Arg_0: Arg_0+1 {O(n)}
47: n_f300___7->n_f300___5, Arg_1: Arg_1 {O(n)}