Initial Problem
Start: n_f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: B_P, C_P, NoDet0
Locations: n_f0, n_f1___4, n_f1___5, n_f1___6, n_f4___1, n_f4___2, n_f4___3
Transitions:
0:n_f0(Arg_0,Arg_1,Arg_2) -> n_f1___6(0,Arg_1,Arg_2)
1:n_f1___4(Arg_0,Arg_1,Arg_2) -> n_f1___4(Arg_0,B_P,C_P):|:Arg_0<=0 && 0<=Arg_0 && 0<=1+Arg_1 && Arg_2<=0 && C_P<=0 && 0<=1+B_P && Arg_1<=B_P+2 && 2+B_P<=Arg_1
2:n_f1___4(Arg_0,Arg_1,Arg_2) -> n_f1___5(Arg_0,B_P,C_P):|:Arg_0<=0 && 0<=Arg_0 && 0<=1+Arg_1 && Arg_2<=0 && 1<=C_P && 0<=B_P && Arg_1<=B_P+1 && 1+B_P<=Arg_1
3:n_f1___4(Arg_0,Arg_1,Arg_2) -> n_f4___3(Arg_0,B_P,NoDet0):|:Arg_0<=0 && 0<=Arg_0 && 0<=1+Arg_1 && Arg_2<=0 && B_P<=0 && Arg_1<=B_P && B_P<=Arg_1
4:n_f1___5(Arg_0,Arg_1,Arg_2) -> n_f1___4(Arg_0,B_P,C_P):|:Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_2 && C_P<=0 && 0<=1+B_P && Arg_1<=B_P+2 && 2+B_P<=Arg_1
5:n_f1___5(Arg_0,Arg_1,Arg_2) -> n_f1___5(Arg_0,B_P,C_P):|:Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_2 && 1<=C_P && 0<=B_P && Arg_1<=B_P+1 && 1+B_P<=Arg_1
6:n_f1___5(Arg_0,Arg_1,Arg_2) -> n_f4___3(Arg_0,B_P,NoDet0):|:Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_2 && B_P<=0 && Arg_1<=B_P && B_P<=Arg_1
7:n_f1___6(Arg_0,Arg_1,Arg_2) -> n_f1___4(Arg_0,B_P,C_P):|:Arg_0<=0 && 0<=Arg_0 && C_P<=0 && 0<=1+B_P && Arg_1<=B_P+2 && 2+B_P<=Arg_1
8:n_f1___6(Arg_0,Arg_1,Arg_2) -> n_f1___5(Arg_0,B_P,C_P):|:Arg_0<=0 && 0<=Arg_0 && 1<=C_P && 0<=B_P && Arg_1<=B_P+1 && 1+B_P<=Arg_1
9:n_f1___6(Arg_0,Arg_1,Arg_2) -> n_f4___3(Arg_0,B_P,NoDet0):|:Arg_0<=0 && 0<=Arg_0 && B_P<=0 && Arg_1<=B_P && B_P<=Arg_1
10:n_f4___1(Arg_0,Arg_1,Arg_2) -> n_f4___1(2,Arg_1,NoDet0):|:Arg_1<=0 && Arg_0<=2 && 2<=Arg_0 && Arg_2<=0
11:n_f4___1(Arg_0,Arg_1,Arg_2) -> n_f4___2(1,Arg_1,NoDet0):|:Arg_1<=0 && Arg_0<=2 && 2<=Arg_0 && 1<=Arg_2
12:n_f4___2(Arg_0,Arg_1,Arg_2) -> n_f4___1(2,Arg_1,NoDet0):|:Arg_1<=0 && Arg_0<=1 && 1<=Arg_0 && Arg_2<=0
13:n_f4___2(Arg_0,Arg_1,Arg_2) -> n_f4___2(1,Arg_1,NoDet0):|:Arg_1<=0 && Arg_0<=1 && 1<=Arg_0 && 1<=Arg_2
14:n_f4___3(Arg_0,Arg_1,Arg_2) -> n_f4___1(2,Arg_1,NoDet0):|:Arg_1<=0 && Arg_2<=0
15:n_f4___3(Arg_0,Arg_1,Arg_2) -> n_f4___2(1,Arg_1,NoDet0):|:Arg_1<=0 && 1<=Arg_2
Preprocessing
Found invariant Arg_1<=0 && 2+Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && Arg_0<=2 && 2<=Arg_0 for location n_f4___1
Found invariant Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=0 && 0<=Arg_0 for location n_f4___3
Found invariant Arg_2<=0 && Arg_2<=1+Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && Arg_0<=1+Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_f1___4
Found invariant Arg_1<=0 && 1+Arg_1<=Arg_0 && Arg_0+Arg_1<=1 && Arg_0<=1 && 1<=Arg_0 for location n_f4___2
Found invariant 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_f1___5
Found invariant Arg_0<=0 && 0<=Arg_0 for location n_f1___6
Problem after Preprocessing
Start: n_f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: B_P, C_P, NoDet0
Locations: n_f0, n_f1___4, n_f1___5, n_f1___6, n_f4___1, n_f4___2, n_f4___3
Transitions:
0:n_f0(Arg_0,Arg_1,Arg_2) -> n_f1___6(0,Arg_1,Arg_2)
1:n_f1___4(Arg_0,Arg_1,Arg_2) -> n_f1___4(Arg_0,B_P,C_P):|:Arg_2<=0 && Arg_2<=1+Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && Arg_0<=1+Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 0<=1+Arg_1 && Arg_2<=0 && C_P<=0 && 0<=1+B_P && Arg_1<=B_P+2 && 2+B_P<=Arg_1
2:n_f1___4(Arg_0,Arg_1,Arg_2) -> n_f1___5(Arg_0,B_P,C_P):|:Arg_2<=0 && Arg_2<=1+Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && Arg_0<=1+Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 0<=1+Arg_1 && Arg_2<=0 && 1<=C_P && 0<=B_P && Arg_1<=B_P+1 && 1+B_P<=Arg_1
3:n_f1___4(Arg_0,Arg_1,Arg_2) -> n_f4___3(Arg_0,B_P,NoDet0):|:Arg_2<=0 && Arg_2<=1+Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && Arg_0<=1+Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 0<=1+Arg_1 && Arg_2<=0 && B_P<=0 && Arg_1<=B_P && B_P<=Arg_1
4:n_f1___5(Arg_0,Arg_1,Arg_2) -> n_f1___4(Arg_0,B_P,C_P):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_2 && C_P<=0 && 0<=1+B_P && Arg_1<=B_P+2 && 2+B_P<=Arg_1
5:n_f1___5(Arg_0,Arg_1,Arg_2) -> n_f1___5(Arg_0,B_P,C_P):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_2 && 1<=C_P && 0<=B_P && Arg_1<=B_P+1 && 1+B_P<=Arg_1
6:n_f1___5(Arg_0,Arg_1,Arg_2) -> n_f4___3(Arg_0,B_P,NoDet0):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_2 && B_P<=0 && Arg_1<=B_P && B_P<=Arg_1
7:n_f1___6(Arg_0,Arg_1,Arg_2) -> n_f1___4(Arg_0,B_P,C_P):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && C_P<=0 && 0<=1+B_P && Arg_1<=B_P+2 && 2+B_P<=Arg_1
8:n_f1___6(Arg_0,Arg_1,Arg_2) -> n_f1___5(Arg_0,B_P,C_P):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 1<=C_P && 0<=B_P && Arg_1<=B_P+1 && 1+B_P<=Arg_1
9:n_f1___6(Arg_0,Arg_1,Arg_2) -> n_f4___3(Arg_0,B_P,NoDet0):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && B_P<=0 && Arg_1<=B_P && B_P<=Arg_1
10:n_f4___1(Arg_0,Arg_1,Arg_2) -> n_f4___1(2,Arg_1,NoDet0):|:Arg_1<=0 && 2+Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && Arg_0<=2 && 2<=Arg_0 && Arg_1<=0 && Arg_0<=2 && 2<=Arg_0 && Arg_2<=0
11:n_f4___1(Arg_0,Arg_1,Arg_2) -> n_f4___2(1,Arg_1,NoDet0):|:Arg_1<=0 && 2+Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && Arg_0<=2 && 2<=Arg_0 && Arg_1<=0 && Arg_0<=2 && 2<=Arg_0 && 1<=Arg_2
12:n_f4___2(Arg_0,Arg_1,Arg_2) -> n_f4___1(2,Arg_1,NoDet0):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && Arg_0+Arg_1<=1 && Arg_0<=1 && 1<=Arg_0 && Arg_1<=0 && Arg_0<=1 && 1<=Arg_0 && Arg_2<=0
13:n_f4___2(Arg_0,Arg_1,Arg_2) -> n_f4___2(1,Arg_1,NoDet0):|:Arg_1<=0 && 1+Arg_1<=Arg_0 && Arg_0+Arg_1<=1 && Arg_0<=1 && 1<=Arg_0 && Arg_1<=0 && Arg_0<=1 && 1<=Arg_0 && 1<=Arg_2
14:n_f4___3(Arg_0,Arg_1,Arg_2) -> n_f4___1(2,Arg_1,NoDet0):|:Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=0 && Arg_2<=0
15:n_f4___3(Arg_0,Arg_1,Arg_2) -> n_f4___2(1,Arg_1,NoDet0):|:Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=0 && 1<=Arg_2
MPRF for transition 1:n_f1___4(Arg_0,Arg_1,Arg_2) -> n_f1___4(Arg_0,B_P,C_P):|:Arg_2<=0 && Arg_2<=1+Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && Arg_0<=1+Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 0<=1+Arg_1 && Arg_2<=0 && C_P<=0 && 0<=1+B_P && Arg_1<=B_P+2 && 2+B_P<=Arg_1 of depth 1:
new bound:
2*Arg_1+2 {O(n)}
MPRF:
n_f1___4 [Arg_1+2 ]
n_f1___5 [Arg_1 ]
MPRF for transition 2:n_f1___4(Arg_0,Arg_1,Arg_2) -> n_f1___5(Arg_0,B_P,C_P):|:Arg_2<=0 && Arg_2<=1+Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && 0<=1+Arg_1 && 0<=1+Arg_0+Arg_1 && Arg_0<=1+Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 0<=1+Arg_1 && Arg_2<=0 && 1<=C_P && 0<=B_P && Arg_1<=B_P+1 && 1+B_P<=Arg_1 of depth 1:
new bound:
2*Arg_1+2 {O(n)}
MPRF:
n_f1___4 [Arg_1+2 ]
n_f1___5 [Arg_1 ]
MPRF for transition 4:n_f1___5(Arg_0,Arg_1,Arg_2) -> n_f1___4(Arg_0,B_P,C_P):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_2 && C_P<=0 && 0<=1+B_P && Arg_1<=B_P+2 && 2+B_P<=Arg_1 of depth 1:
new bound:
2*Arg_1+1 {O(n)}
MPRF:
n_f1___4 [Arg_1 ]
n_f1___5 [Arg_1+1 ]
MPRF for transition 5:n_f1___5(Arg_0,Arg_1,Arg_2) -> n_f1___5(Arg_0,B_P,C_P):|:1<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_2 && 1<=C_P && 0<=B_P && Arg_1<=B_P+1 && 1+B_P<=Arg_1 of depth 1:
new bound:
2*Arg_1+1 {O(n)}
MPRF:
n_f1___4 [Arg_1 ]
n_f1___5 [Arg_1+1 ]
All Bounds
Timebounds
Overall timebound:inf {Infinity}
0: n_f0->n_f1___6: 1 {O(1)}
1: n_f1___4->n_f1___4: 2*Arg_1+2 {O(n)}
2: n_f1___4->n_f1___5: 2*Arg_1+2 {O(n)}
3: n_f1___4->n_f4___3: 1 {O(1)}
4: n_f1___5->n_f1___4: 2*Arg_1+1 {O(n)}
5: n_f1___5->n_f1___5: 2*Arg_1+1 {O(n)}
6: n_f1___5->n_f4___3: 1 {O(1)}
7: n_f1___6->n_f1___4: 1 {O(1)}
8: n_f1___6->n_f1___5: 1 {O(1)}
9: n_f1___6->n_f4___3: 1 {O(1)}
10: n_f4___1->n_f4___1: inf {Infinity}
11: n_f4___1->n_f4___2: inf {Infinity}
12: n_f4___2->n_f4___1: inf {Infinity}
13: n_f4___2->n_f4___2: inf {Infinity}
14: n_f4___3->n_f4___1: 1 {O(1)}
15: n_f4___3->n_f4___2: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
0: n_f0->n_f1___6: 1 {O(1)}
1: n_f1___4->n_f1___4: 2*Arg_1+2 {O(n)}
2: n_f1___4->n_f1___5: 2*Arg_1+2 {O(n)}
3: n_f1___4->n_f4___3: 1 {O(1)}
4: n_f1___5->n_f1___4: 2*Arg_1+1 {O(n)}
5: n_f1___5->n_f1___5: 2*Arg_1+1 {O(n)}
6: n_f1___5->n_f4___3: 1 {O(1)}
7: n_f1___6->n_f1___4: 1 {O(1)}
8: n_f1___6->n_f1___5: 1 {O(1)}
9: n_f1___6->n_f4___3: 1 {O(1)}
10: n_f4___1->n_f4___1: inf {Infinity}
11: n_f4___1->n_f4___2: inf {Infinity}
12: n_f4___2->n_f4___1: inf {Infinity}
13: n_f4___2->n_f4___2: inf {Infinity}
14: n_f4___3->n_f4___1: 1 {O(1)}
15: n_f4___3->n_f4___2: 1 {O(1)}
Sizebounds
0: n_f0->n_f1___6, Arg_0: 0 {O(1)}
0: n_f0->n_f1___6, Arg_1: Arg_1 {O(n)}
0: n_f0->n_f1___6, Arg_2: Arg_2 {O(n)}
1: n_f1___4->n_f1___4, Arg_0: 0 {O(1)}
1: n_f1___4->n_f1___4, Arg_1: 4*Arg_1 {O(n)}
2: n_f1___4->n_f1___5, Arg_0: 0 {O(1)}
2: n_f1___4->n_f1___5, Arg_1: 4*Arg_1 {O(n)}
3: n_f1___4->n_f4___3, Arg_0: 0 {O(1)}
3: n_f1___4->n_f4___3, Arg_1: 1 {O(1)}
4: n_f1___5->n_f1___4, Arg_0: 0 {O(1)}
4: n_f1___5->n_f1___4, Arg_1: 4*Arg_1 {O(n)}
5: n_f1___5->n_f1___5, Arg_0: 0 {O(1)}
5: n_f1___5->n_f1___5, Arg_1: 4*Arg_1 {O(n)}
6: n_f1___5->n_f4___3, Arg_0: 0 {O(1)}
6: n_f1___5->n_f4___3, Arg_1: 0 {O(1)}
7: n_f1___6->n_f1___4, Arg_0: 0 {O(1)}
7: n_f1___6->n_f1___4, Arg_1: Arg_1 {O(n)}
8: n_f1___6->n_f1___5, Arg_0: 0 {O(1)}
8: n_f1___6->n_f1___5, Arg_1: Arg_1 {O(n)}
9: n_f1___6->n_f4___3, Arg_0: 0 {O(1)}
9: n_f1___6->n_f4___3, Arg_1: Arg_1 {O(n)}
10: n_f4___1->n_f4___1, Arg_0: 2 {O(1)}
10: n_f4___1->n_f4___1, Arg_1: 4*Arg_1+4 {O(n)}
11: n_f4___1->n_f4___2, Arg_0: 1 {O(1)}
11: n_f4___1->n_f4___2, Arg_1: 4*Arg_1+4 {O(n)}
12: n_f4___2->n_f4___1, Arg_0: 2 {O(1)}
12: n_f4___2->n_f4___1, Arg_1: 4*Arg_1+4 {O(n)}
13: n_f4___2->n_f4___2, Arg_0: 1 {O(1)}
13: n_f4___2->n_f4___2, Arg_1: 4*Arg_1+4 {O(n)}
14: n_f4___3->n_f4___1, Arg_0: 2 {O(1)}
14: n_f4___3->n_f4___1, Arg_1: Arg_1+1 {O(n)}
15: n_f4___3->n_f4___2, Arg_0: 1 {O(1)}
15: n_f4___3->n_f4___2, Arg_1: Arg_1+1 {O(n)}