Initial Problem

Start: n_f
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_f, n_g___5, n_g___6, n_h___1, n_h___2, n_h___3, n_h___4
Transitions:
0:n_f(Arg_0,Arg_1) -> n_g___6(Arg_0,1)
1:n_g___5(Arg_0,Arg_1) -> n_g___5(Arg_0-1,2*Arg_1):|:0<Arg_1 && 0<Arg_0
2:n_g___5(Arg_0,Arg_1) -> n_h___3(Arg_0,Arg_1):|:0<Arg_1 && Arg_0<=0
3:n_g___6(Arg_0,Arg_1) -> n_g___5(Arg_0-1,2*Arg_1):|:0<Arg_1 && Arg_1<=1 && 1<=Arg_1 && 0<Arg_0
4:n_g___6(Arg_0,Arg_1) -> n_h___4(Arg_0,Arg_1):|:0<Arg_1 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=0
5:n_h___1(Arg_0,Arg_1) -> n_h___2(Arg_0,Arg_1-1):|:Arg_0<=0 && 0<=Arg_1 && 0<Arg_1
6:n_h___2(Arg_0,Arg_1) -> n_h___2(Arg_0,Arg_1-1):|:Arg_0<=0 && 0<Arg_1
7:n_h___3(Arg_0,Arg_1) -> n_h___2(Arg_0,Arg_1-1):|:0<Arg_1 && Arg_0<=0 && 0<=Arg_1 && 0<Arg_1
8:n_h___4(Arg_0,Arg_1) -> n_h___1(Arg_0,Arg_1-1):|:0<Arg_1 && Arg_0<=0 && 1<=Arg_1 && 0<=Arg_1 && 0<Arg_1

Preprocessing

Found invariant Arg_1<=1 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 for location n_h___4

Found invariant Arg_1<=0 && Arg_0+Arg_1<=0 && 0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 for location n_h___1

Found invariant 0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_h___2

Found invariant 2<=Arg_1 && 2<=Arg_0+Arg_1 && 0<=Arg_0 for location n_g___5

Found invariant Arg_1<=1 && 1<=Arg_1 for location n_g___6

Found invariant 2<=Arg_1 && 2<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_h___3

Cut unsatisfiable transition 5: n_h___1->n_h___2

Problem after Preprocessing

Start: n_f
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_f, n_g___5, n_g___6, n_h___1, n_h___2, n_h___3, n_h___4
Transitions:
0:n_f(Arg_0,Arg_1) -> n_g___6(Arg_0,1)
1:n_g___5(Arg_0,Arg_1) -> n_g___5(Arg_0-1,2*Arg_1):|:2<=Arg_1 && 2<=Arg_0+Arg_1 && 0<=Arg_0 && 0<Arg_1 && 0<Arg_0
2:n_g___5(Arg_0,Arg_1) -> n_h___3(Arg_0,Arg_1):|:2<=Arg_1 && 2<=Arg_0+Arg_1 && 0<=Arg_0 && 0<Arg_1 && Arg_0<=0
3:n_g___6(Arg_0,Arg_1) -> n_g___5(Arg_0-1,2*Arg_1):|:Arg_1<=1 && 1<=Arg_1 && 0<Arg_1 && Arg_1<=1 && 1<=Arg_1 && 0<Arg_0
4:n_g___6(Arg_0,Arg_1) -> n_h___4(Arg_0,Arg_1):|:Arg_1<=1 && 1<=Arg_1 && 0<Arg_1 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=0
6:n_h___2(Arg_0,Arg_1) -> n_h___2(Arg_0,Arg_1-1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<Arg_1
7:n_h___3(Arg_0,Arg_1) -> n_h___2(Arg_0,Arg_1-1):|:2<=Arg_1 && 2<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && 0<Arg_1 && Arg_0<=0 && 0<=Arg_1 && 0<Arg_1
8:n_h___4(Arg_0,Arg_1) -> n_h___1(Arg_0,Arg_1-1):|:Arg_1<=1 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<Arg_1 && Arg_0<=0 && 1<=Arg_1 && 0<=Arg_1 && 0<Arg_1

MPRF for transition 1:n_g___5(Arg_0,Arg_1) -> n_g___5(Arg_0-1,2*Arg_1):|:2<=Arg_1 && 2<=Arg_0+Arg_1 && 0<=Arg_0 && 0<Arg_1 && 0<Arg_0 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

n_g___5 [Arg_0+1 ]

MPRF for transition 6:n_h___2(Arg_0,Arg_1) -> n_h___2(Arg_0,Arg_1-1):|:0<=Arg_1 && 0<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<Arg_1 of depth 1:

new bound:

2*2^(Arg_0+1)+3 {O(EXP)}

MPRF:

n_h___2 [Arg_1+1 ]

All Bounds

Timebounds

Overall timebound:2*2^(Arg_0+1)+Arg_0+10 {O(EXP)}
0: n_f->n_g___6: 1 {O(1)}
1: n_g___5->n_g___5: Arg_0+1 {O(n)}
2: n_g___5->n_h___3: 1 {O(1)}
3: n_g___6->n_g___5: 1 {O(1)}
4: n_g___6->n_h___4: 1 {O(1)}
6: n_h___2->n_h___2: 2*2^(Arg_0+1)+3 {O(EXP)}
7: n_h___3->n_h___2: 1 {O(1)}
8: n_h___4->n_h___1: 1 {O(1)}

Costbounds

Overall costbound: 2*2^(Arg_0+1)+Arg_0+10 {O(EXP)}
0: n_f->n_g___6: 1 {O(1)}
1: n_g___5->n_g___5: Arg_0+1 {O(n)}
2: n_g___5->n_h___3: 1 {O(1)}
3: n_g___6->n_g___5: 1 {O(1)}
4: n_g___6->n_h___4: 1 {O(1)}
6: n_h___2->n_h___2: 2*2^(Arg_0+1)+3 {O(EXP)}
7: n_h___3->n_h___2: 1 {O(1)}
8: n_h___4->n_h___1: 1 {O(1)}

Sizebounds

0: n_f->n_g___6, Arg_0: Arg_0 {O(n)}
0: n_f->n_g___6, Arg_1: 1 {O(1)}
1: n_g___5->n_g___5, Arg_0: Arg_0 {O(n)}
1: n_g___5->n_g___5, Arg_1: 2*2^(Arg_0+1) {O(EXP)}
2: n_g___5->n_h___3, Arg_0: 0 {O(1)}
2: n_g___5->n_h___3, Arg_1: 2*2^(Arg_0+1)+2 {O(EXP)}
3: n_g___6->n_g___5, Arg_0: Arg_0 {O(n)}
3: n_g___6->n_g___5, Arg_1: 2 {O(1)}
4: n_g___6->n_h___4, Arg_0: Arg_0 {O(n)}
4: n_g___6->n_h___4, Arg_1: 1 {O(1)}
6: n_h___2->n_h___2, Arg_0: 0 {O(1)}
6: n_h___2->n_h___2, Arg_1: 2*2^(Arg_0+1)+2 {O(EXP)}
7: n_h___3->n_h___2, Arg_0: 0 {O(1)}
7: n_h___3->n_h___2, Arg_1: 2*2^(Arg_0+1)+2 {O(EXP)}
8: n_h___4->n_h___1, Arg_0: Arg_0 {O(n)}
8: n_h___4->n_h___1, Arg_1: 0 {O(1)}