Initial Problem

Start: n_f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_f0, n_f2___4, n_f2___6, n_f3___3, n_f3___5, n_f5___1, n_f5___2
Transitions:
0:n_f0(Arg_0,Arg_1,Arg_2) -> n_f2___6(0,Arg_1,Arg_2):|:1<=Arg_2
1:n_f0(Arg_0,Arg_1,Arg_2) -> n_f3___5(0,Arg_1,Arg_2):|:Arg_2<=0
2:n_f2___4(Arg_0,Arg_1,Arg_2) -> n_f2___4(Arg_0+1,Arg_1,Arg_2)
3:n_f2___6(Arg_0,Arg_1,Arg_2) -> n_f2___4(Arg_0+1,Arg_1,Arg_2):|:Arg_0<=0 && 0<=Arg_0 && 1<=Arg_2
4:n_f3___3(Arg_0,Arg_1,Arg_2) -> n_f3___3(Arg_0,Arg_1-1,Arg_2):|:0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_2<=0 && 1<=Arg_1
5:n_f3___3(Arg_0,Arg_1,Arg_2) -> n_f5___2(0,Arg_1,Arg_2):|:0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_2<=0 && Arg_1<=0
6:n_f3___5(Arg_0,Arg_1,Arg_2) -> n_f3___3(Arg_0,Arg_1-1,Arg_2):|:Arg_0<=0 && 0<=Arg_0 && Arg_2<=0 && 1<=Arg_1
7:n_f3___5(Arg_0,Arg_1,Arg_2) -> n_f5___2(0,Arg_1,Arg_2):|:Arg_0<=0 && 0<=Arg_0 && Arg_2<=0 && Arg_1<=0
8:n_f5___1(Arg_0,Arg_1,Arg_2) -> n_f5___1(Arg_0,Arg_1,1):|:Arg_2<=1 && 1<=Arg_2 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=0
9:n_f5___2(Arg_0,Arg_1,Arg_2) -> n_f5___1(Arg_0,Arg_1,1):|:Arg_0<=0 && 0<=Arg_0 && Arg_1<=0

Preprocessing

Found invariant 1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_0<=0 && 0<=Arg_0 for location n_f2___6

Found invariant Arg_2<=0 && Arg_1+Arg_2<=0 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=0 && 0<=Arg_0 for location n_f5___2

Found invariant Arg_2<=0 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_f3___3

Found invariant Arg_2<=1 && Arg_1+Arg_2<=1 && Arg_2<=1+Arg_0 && Arg_0+Arg_2<=1 && 1<=Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=0 && 0<=Arg_0 for location n_f5___1

Found invariant 1<=Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_0 for location n_f2___4

Found invariant Arg_2<=0 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && Arg_0<=0 && 0<=Arg_0 for location n_f3___5

Problem after Preprocessing

Start: n_f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_f0, n_f2___4, n_f2___6, n_f3___3, n_f3___5, n_f5___1, n_f5___2
Transitions:
0:n_f0(Arg_0,Arg_1,Arg_2) -> n_f2___6(0,Arg_1,Arg_2):|:1<=Arg_2
1:n_f0(Arg_0,Arg_1,Arg_2) -> n_f3___5(0,Arg_1,Arg_2):|:Arg_2<=0
2:n_f2___4(Arg_0,Arg_1,Arg_2) -> n_f2___4(Arg_0+1,Arg_1,Arg_2):|:1<=Arg_2 && 2<=Arg_0+Arg_2 && 1<=Arg_0
3:n_f2___6(Arg_0,Arg_1,Arg_2) -> n_f2___4(Arg_0+1,Arg_1,Arg_2):|:1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 1<=Arg_2
4:n_f3___3(Arg_0,Arg_1,Arg_2) -> n_f3___3(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_2<=0 && 1<=Arg_1
5:n_f3___3(Arg_0,Arg_1,Arg_2) -> n_f5___2(0,Arg_1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_2<=0 && Arg_1<=0
6:n_f3___5(Arg_0,Arg_1,Arg_2) -> n_f3___3(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && Arg_2<=0 && 1<=Arg_1
7:n_f3___5(Arg_0,Arg_1,Arg_2) -> n_f5___2(0,Arg_1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && Arg_2<=0 && Arg_1<=0
8:n_f5___1(Arg_0,Arg_1,Arg_2) -> n_f5___1(Arg_0,Arg_1,1):|:Arg_2<=1 && Arg_1+Arg_2<=1 && Arg_2<=1+Arg_0 && Arg_0+Arg_2<=1 && 1<=Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=0 && 0<=Arg_0 && Arg_2<=1 && 1<=Arg_2 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=0
9:n_f5___2(Arg_0,Arg_1,Arg_2) -> n_f5___1(Arg_0,Arg_1,1):|:Arg_2<=0 && Arg_1+Arg_2<=0 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=0

MPRF for transition 4:n_f3___3(Arg_0,Arg_1,Arg_2) -> n_f3___3(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && 0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_2<=0 && 1<=Arg_1 of depth 1:

new bound:

Arg_1+1 {O(n)}

MPRF:

n_f3___3 [Arg_1+1 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: n_f0->n_f2___6: 1 {O(1)}
1: n_f0->n_f3___5: 1 {O(1)}
2: n_f2___4->n_f2___4: inf {Infinity}
3: n_f2___6->n_f2___4: 1 {O(1)}
4: n_f3___3->n_f3___3: Arg_1+1 {O(n)}
5: n_f3___3->n_f5___2: 1 {O(1)}
6: n_f3___5->n_f3___3: 1 {O(1)}
7: n_f3___5->n_f5___2: 1 {O(1)}
8: n_f5___1->n_f5___1: inf {Infinity}
9: n_f5___2->n_f5___1: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
0: n_f0->n_f2___6: 1 {O(1)}
1: n_f0->n_f3___5: 1 {O(1)}
2: n_f2___4->n_f2___4: inf {Infinity}
3: n_f2___6->n_f2___4: 1 {O(1)}
4: n_f3___3->n_f3___3: Arg_1+1 {O(n)}
5: n_f3___3->n_f5___2: 1 {O(1)}
6: n_f3___5->n_f3___3: 1 {O(1)}
7: n_f3___5->n_f5___2: 1 {O(1)}
8: n_f5___1->n_f5___1: inf {Infinity}
9: n_f5___2->n_f5___1: 1 {O(1)}

Sizebounds

0: n_f0->n_f2___6, Arg_0: 0 {O(1)}
0: n_f0->n_f2___6, Arg_1: Arg_1 {O(n)}
0: n_f0->n_f2___6, Arg_2: Arg_2 {O(n)}
1: n_f0->n_f3___5, Arg_0: 0 {O(1)}
1: n_f0->n_f3___5, Arg_1: Arg_1 {O(n)}
1: n_f0->n_f3___5, Arg_2: Arg_2 {O(n)}
2: n_f2___4->n_f2___4, Arg_1: Arg_1 {O(n)}
2: n_f2___4->n_f2___4, Arg_2: Arg_2 {O(n)}
3: n_f2___6->n_f2___4, Arg_0: 1 {O(1)}
3: n_f2___6->n_f2___4, Arg_1: Arg_1 {O(n)}
3: n_f2___6->n_f2___4, Arg_2: Arg_2 {O(n)}
4: n_f3___3->n_f3___3, Arg_0: 0 {O(1)}
4: n_f3___3->n_f3___3, Arg_1: Arg_1 {O(n)}
4: n_f3___3->n_f3___3, Arg_2: Arg_2 {O(n)}
5: n_f3___3->n_f5___2, Arg_0: 0 {O(1)}
5: n_f3___3->n_f5___2, Arg_1: 0 {O(1)}
5: n_f3___3->n_f5___2, Arg_2: 2*Arg_2 {O(n)}
6: n_f3___5->n_f3___3, Arg_0: 0 {O(1)}
6: n_f3___5->n_f3___3, Arg_1: Arg_1 {O(n)}
6: n_f3___5->n_f3___3, Arg_2: Arg_2 {O(n)}
7: n_f3___5->n_f5___2, Arg_0: 0 {O(1)}
7: n_f3___5->n_f5___2, Arg_1: Arg_1 {O(n)}
7: n_f3___5->n_f5___2, Arg_2: Arg_2 {O(n)}
8: n_f5___1->n_f5___1, Arg_0: 0 {O(1)}
8: n_f5___1->n_f5___1, Arg_1: Arg_1 {O(n)}
8: n_f5___1->n_f5___1, Arg_2: 1 {O(1)}
9: n_f5___2->n_f5___1, Arg_0: 0 {O(1)}
9: n_f5___2->n_f5___1, Arg_1: Arg_1 {O(n)}
9: n_f5___2->n_f5___1, Arg_2: 1 {O(1)}