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___5, n_f2, n_f300___2, n_f300___3, n_f300___4, n_f300___6
Transitions:
0:n_f2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___6(Arg_0,Arg_1,Arg_2,Arg_3)
1:n_f300___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f1___1(Arg_0,B_P,Arg_2,NoDet0):|:Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && B_P<=Arg_0 && Arg_1<=B_P && B_P<=Arg_1
2:n_f300___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___2(Arg_0,Arg_1-1,0,Arg_3):|:Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && 1+Arg_0<=Arg_1
3:n_f300___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___3(Arg_0,B_P,C_P,Arg_3):|:Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && 1+C_P<=0 && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
4:n_f300___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___4(Arg_0,B_P,C_P,Arg_3):|:Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && 1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
5:n_f300___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___2(Arg_0,Arg_1-1,0,Arg_3):|:1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_2<=0 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1
6:n_f300___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___3(Arg_0,B_P,C_P,Arg_3):|:1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_2<=0 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+C_P<=0 && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
7:n_f300___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___4(Arg_0,B_P,C_P,Arg_3):|:1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_2<=0 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
8:n_f300___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___2(Arg_0,Arg_1-1,0,Arg_3):|:1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1
9:n_f300___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___3(Arg_0,B_P,C_P,Arg_3):|:1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+C_P<=0 && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
10:n_f300___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___4(Arg_0,B_P,C_P,Arg_3):|:1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
11:n_f300___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f1___5(Arg_0,B_P,Arg_2,NoDet0):|:B_P<=Arg_0 && Arg_1<=B_P && B_P<=Arg_1
12:n_f300___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___2(Arg_0,Arg_1-1,0,Arg_3):|:1+Arg_0<=Arg_1
13:n_f300___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___3(Arg_0,B_P,C_P,Arg_3):|:1+C_P<=0 && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
14:n_f300___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f300___4(Arg_0,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 Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 for location n_f300___2

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

Found invariant Arg_1<=Arg_0 for location n_f1___5

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

Found invariant 1<=Arg_2 && 1+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___5, n_f2, n_f300___2, n_f300___3, n_f300___4, n_f300___6
Transitions:
30:n_f2(Arg_0,Arg_1,Arg_2) -> n_f300___6(Arg_0,Arg_1,Arg_2)
31:n_f300___2(Arg_0,Arg_1,Arg_2) -> n_f1___1(Arg_0,B_P,Arg_2):|:Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && B_P<=Arg_0 && Arg_1<=B_P && B_P<=Arg_1
32:n_f300___2(Arg_0,Arg_1,Arg_2) -> n_f300___2(Arg_0,Arg_1-1,0):|:Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && 1+Arg_0<=Arg_1
33:n_f300___2(Arg_0,Arg_1,Arg_2) -> n_f300___3(Arg_0,B_P,C_P):|:Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && 1+C_P<=0 && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
34:n_f300___2(Arg_0,Arg_1,Arg_2) -> n_f300___4(Arg_0,B_P,C_P):|:Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && 1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
35:n_f300___3(Arg_0,Arg_1,Arg_2) -> n_f300___2(Arg_0,Arg_1-1,0):|:1+Arg_2<=0 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_2<=0 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1
36:n_f300___3(Arg_0,Arg_1,Arg_2) -> n_f300___3(Arg_0,B_P,C_P):|:1+Arg_2<=0 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_2<=0 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+C_P<=0 && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
37:n_f300___3(Arg_0,Arg_1,Arg_2) -> n_f300___4(Arg_0,B_P,C_P):|:1+Arg_2<=0 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_2<=0 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
38:n_f300___4(Arg_0,Arg_1,Arg_2) -> n_f300___2(Arg_0,Arg_1-1,0):|:1<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1
39:n_f300___4(Arg_0,Arg_1,Arg_2) -> n_f300___3(Arg_0,B_P,C_P):|:1<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+C_P<=0 && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
40:n_f300___4(Arg_0,Arg_1,Arg_2) -> n_f300___4(Arg_0,B_P,C_P):|:1<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
41:n_f300___6(Arg_0,Arg_1,Arg_2) -> n_f1___5(Arg_0,B_P,Arg_2):|:B_P<=Arg_0 && Arg_1<=B_P && B_P<=Arg_1
42:n_f300___6(Arg_0,Arg_1,Arg_2) -> n_f300___2(Arg_0,Arg_1-1,0):|:1+Arg_0<=Arg_1
43:n_f300___6(Arg_0,Arg_1,Arg_2) -> n_f300___3(Arg_0,B_P,C_P):|:1+C_P<=0 && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1
44:n_f300___6(Arg_0,Arg_1,Arg_2) -> n_f300___4(Arg_0,B_P,C_P):|:1<=C_P && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1

MPRF for transition 32:n_f300___2(Arg_0,Arg_1,Arg_2) -> n_f300___2(Arg_0,Arg_1-1,0):|:Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 of depth 1:

new bound:

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

MPRF:

n_f300___2 [Arg_1+1-Arg_0 ]
n_f300___3 [Arg_1-Arg_0 ]
n_f300___4 [Arg_1-Arg_0 ]

MPRF for transition 33:n_f300___2(Arg_0,Arg_1,Arg_2) -> n_f300___3(Arg_0,B_P,C_P):|:Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && 1+C_P<=0 && 1+Arg_0<=B_P && Arg_1<=B_P && B_P<=Arg_1 of depth 1:

new bound:

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

MPRF:

n_f300___2 [Arg_1+1-Arg_0 ]
n_f300___3 [Arg_1-Arg_0 ]
n_f300___4 [Arg_1-Arg_0 ]

MPRF for transition 34:n_f300___2(Arg_0,Arg_1,Arg_2) -> n_f300___4(Arg_0,B_P,C_P):|:Arg_2<=0 && 0<=Arg_2 && Arg_0<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && 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+2 {O(n)}

MPRF:

n_f300___2 [Arg_1+1-Arg_0 ]
n_f300___3 [Arg_1-Arg_0 ]
n_f300___4 [Arg_1-Arg_0 ]

MPRF for transition 35:n_f300___3(Arg_0,Arg_1,Arg_2) -> n_f300___2(Arg_0,Arg_1-1,0):|:1+Arg_2<=0 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_2<=0 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 of depth 1:

new bound:

3*Arg_0+3*Arg_1+1 {O(n)}

MPRF:

n_f300___2 [Arg_1-Arg_0 ]
n_f300___3 [Arg_1-Arg_0 ]
n_f300___4 [Arg_1-Arg_0 ]

MPRF for transition 38:n_f300___4(Arg_0,Arg_1,Arg_2) -> n_f300___2(Arg_0,Arg_1-1,0):|:1<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1<=Arg_2 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 of depth 1:

new bound:

3*Arg_0+3*Arg_1+1 {O(n)}

MPRF:

n_f300___2 [Arg_1-Arg_0 ]
n_f300___3 [Arg_1-Arg_0 ]
n_f300___4 [Arg_1-Arg_0 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
30: n_f2->n_f300___6: 1 {O(1)}
31: n_f300___2->n_f1___1: 1 {O(1)}
32: n_f300___2->n_f300___2: 3*Arg_0+3*Arg_1+2 {O(n)}
33: n_f300___2->n_f300___3: 3*Arg_0+3*Arg_1+2 {O(n)}
34: n_f300___2->n_f300___4: 3*Arg_0+3*Arg_1+2 {O(n)}
35: n_f300___3->n_f300___2: 3*Arg_0+3*Arg_1+1 {O(n)}
36: n_f300___3->n_f300___3: inf {Infinity}
37: n_f300___3->n_f300___4: inf {Infinity}
38: n_f300___4->n_f300___2: 3*Arg_0+3*Arg_1+1 {O(n)}
39: n_f300___4->n_f300___3: inf {Infinity}
40: n_f300___4->n_f300___4: inf {Infinity}
41: n_f300___6->n_f1___5: 1 {O(1)}
42: n_f300___6->n_f300___2: 1 {O(1)}
43: n_f300___6->n_f300___3: 1 {O(1)}
44: n_f300___6->n_f300___4: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
30: n_f2->n_f300___6: 1 {O(1)}
31: n_f300___2->n_f1___1: 1 {O(1)}
32: n_f300___2->n_f300___2: 3*Arg_0+3*Arg_1+2 {O(n)}
33: n_f300___2->n_f300___3: 3*Arg_0+3*Arg_1+2 {O(n)}
34: n_f300___2->n_f300___4: 3*Arg_0+3*Arg_1+2 {O(n)}
35: n_f300___3->n_f300___2: 3*Arg_0+3*Arg_1+1 {O(n)}
36: n_f300___3->n_f300___3: inf {Infinity}
37: n_f300___3->n_f300___4: inf {Infinity}
38: n_f300___4->n_f300___2: 3*Arg_0+3*Arg_1+1 {O(n)}
39: n_f300___4->n_f300___3: inf {Infinity}
40: n_f300___4->n_f300___4: inf {Infinity}
41: n_f300___6->n_f1___5: 1 {O(1)}
42: n_f300___6->n_f300___2: 1 {O(1)}
43: n_f300___6->n_f300___3: 1 {O(1)}
44: n_f300___6->n_f300___4: 1 {O(1)}

Sizebounds

30: n_f2->n_f300___6, Arg_0: Arg_0 {O(n)}
30: n_f2->n_f300___6, Arg_1: Arg_1 {O(n)}
30: n_f2->n_f300___6, Arg_2: Arg_2 {O(n)}
31: n_f300___2->n_f1___1, Arg_0: 28*Arg_0 {O(n)}
31: n_f300___2->n_f1___1, Arg_1: 27*Arg_0+55*Arg_1+22 {O(n)}
31: n_f300___2->n_f1___1, Arg_2: 0 {O(1)}
32: n_f300___2->n_f300___2, Arg_0: 9*Arg_0 {O(n)}
32: n_f300___2->n_f300___2, Arg_1: 18*Arg_1+9*Arg_0+7 {O(n)}
32: n_f300___2->n_f300___2, Arg_2: 0 {O(1)}
33: n_f300___2->n_f300___3, Arg_0: 9*Arg_0 {O(n)}
33: n_f300___2->n_f300___3, Arg_1: 18*Arg_1+9*Arg_0+7 {O(n)}
34: n_f300___2->n_f300___4, Arg_0: 9*Arg_0 {O(n)}
34: n_f300___2->n_f300___4, Arg_1: 18*Arg_1+9*Arg_0+7 {O(n)}
35: n_f300___3->n_f300___2, Arg_0: 9*Arg_0 {O(n)}
35: n_f300___3->n_f300___2, Arg_1: 18*Arg_1+9*Arg_0+7 {O(n)}
35: n_f300___3->n_f300___2, Arg_2: 0 {O(1)}
36: n_f300___3->n_f300___3, Arg_0: 9*Arg_0 {O(n)}
36: n_f300___3->n_f300___3, Arg_1: 18*Arg_1+9*Arg_0+7 {O(n)}
37: n_f300___3->n_f300___4, Arg_0: 9*Arg_0 {O(n)}
37: n_f300___3->n_f300___4, Arg_1: 18*Arg_1+9*Arg_0+7 {O(n)}
38: n_f300___4->n_f300___2, Arg_0: 9*Arg_0 {O(n)}
38: n_f300___4->n_f300___2, Arg_1: 18*Arg_1+9*Arg_0+7 {O(n)}
38: n_f300___4->n_f300___2, Arg_2: 0 {O(1)}
39: n_f300___4->n_f300___3, Arg_0: 9*Arg_0 {O(n)}
39: n_f300___4->n_f300___3, Arg_1: 18*Arg_1+9*Arg_0+7 {O(n)}
40: n_f300___4->n_f300___4, Arg_0: 9*Arg_0 {O(n)}
40: n_f300___4->n_f300___4, Arg_1: 18*Arg_1+9*Arg_0+7 {O(n)}
41: n_f300___6->n_f1___5, Arg_0: Arg_0 {O(n)}
41: n_f300___6->n_f1___5, Arg_1: Arg_1 {O(n)}
41: n_f300___6->n_f1___5, Arg_2: Arg_2 {O(n)}
42: n_f300___6->n_f300___2, Arg_0: Arg_0 {O(n)}
42: n_f300___6->n_f300___2, Arg_1: Arg_1+1 {O(n)}
42: n_f300___6->n_f300___2, Arg_2: 0 {O(1)}
43: n_f300___6->n_f300___3, Arg_0: Arg_0 {O(n)}
43: n_f300___6->n_f300___3, Arg_1: Arg_1 {O(n)}
44: n_f300___6->n_f300___4, Arg_0: Arg_0 {O(n)}
44: n_f300___6->n_f300___4, Arg_1: Arg_1 {O(n)}