Initial Problem

Start: n_f
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_f, n_g1___4, n_g1___7, n_g___5, n_g___8, n_h___1, n_h___2, n_h___3, n_h___6
Transitions:
0:n_f(Arg_0,Arg_1,Arg_2) -> n_g___8(Arg_0,1,0)
1:n_g1___4(Arg_0,Arg_1,Arg_2) -> n_g___5(Arg_0,Arg_1+Arg_2,Arg_2):|:0<Arg_1 && 0<1+Arg_0 && Arg_1<=Arg_2 && Arg_2<=Arg_1
2:n_g1___7(Arg_0,Arg_1,Arg_2) -> n_g___5(Arg_0,Arg_1+Arg_2,Arg_2):|:0<1+Arg_0 && Arg_1<=1 && 1<=Arg_1 && Arg_2<=1 && 1<=Arg_2
3:n_g___5(Arg_0,Arg_1,Arg_2) -> n_g1___4(Arg_0-1,Arg_1,Arg_1):|:0<Arg_1 && 0<Arg_0
4:n_g___5(Arg_0,Arg_1,Arg_2) -> n_h___3(Arg_0,Arg_1,Arg_2):|:0<Arg_1 && Arg_0<=0
5:n_g___8(Arg_0,Arg_1,Arg_2) -> n_g1___7(Arg_0-1,Arg_1,Arg_1):|:0<Arg_1 && Arg_1<=1 && 1<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && 0<Arg_0
6:n_g___8(Arg_0,Arg_1,Arg_2) -> n_h___6(Arg_0,Arg_1,Arg_2):|:0<Arg_1 && Arg_1<=1 && 1<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=0
7:n_h___1(Arg_0,Arg_1,Arg_2) -> n_h___2(Arg_0,Arg_1-1,Arg_2):|:Arg_0<=0 && 0<=Arg_1 && 0<Arg_1
8:n_h___2(Arg_0,Arg_1,Arg_2) -> n_h___2(Arg_0,Arg_1-1,Arg_2):|:Arg_0<=0 && 0<Arg_1
9:n_h___3(Arg_0,Arg_1,Arg_2) -> n_h___2(Arg_0,Arg_1-1,Arg_2):|:0<Arg_1 && Arg_0<=0 && 0<=Arg_1 && 0<Arg_1
10:n_h___6(Arg_0,Arg_1,Arg_2) -> n_h___1(Arg_0,Arg_1-1,Arg_2):|:0<Arg_1 && Arg_0<=0 && 1<=Arg_1 && 0<=Arg_1 && 0<Arg_1

Preprocessing

Found invariant Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_1+Arg_2<=1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && Arg_1<=1 && 1<=Arg_1 for location n_g___8

Found invariant Arg_2<=Arg_1 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 2<=Arg_0+Arg_1 && 0<=Arg_0 for location n_g1___4

Found invariant Arg_2<=0 && Arg_2<=Arg_1 && Arg_1+Arg_2<=0 && Arg_0+Arg_2<=0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && Arg_0<=Arg_2 && 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 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_h___2

Found invariant Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_1+Arg_2<=1 && Arg_0+Arg_2<=0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && Arg_0<=Arg_2 && Arg_1<=1 && Arg_0+Arg_1<=1 && 1<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 for location n_h___6

Found invariant 1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 2<=Arg_1 && 2<=Arg_0+Arg_1 && 0<=Arg_0 for location n_g___5

Found invariant Arg_2<=1 && Arg_2<=Arg_1 && Arg_1+Arg_2<=2 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=1 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location n_g1___7

Found invariant 1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 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 7: n_h___1->n_h___2

Problem after Preprocessing

Start: n_f
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_f, n_g1___4, n_g1___7, n_g___5, n_g___8, n_h___1, n_h___2, n_h___3, n_h___6
Transitions:
0:n_f(Arg_0,Arg_1,Arg_2) -> n_g___8(Arg_0,1,0)
1:n_g1___4(Arg_0,Arg_1,Arg_2) -> n_g___5(Arg_0,Arg_1+Arg_2,Arg_2):|:Arg_2<=Arg_1 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 2<=Arg_0+Arg_1 && 0<=Arg_0 && 0<Arg_1 && 0<1+Arg_0 && Arg_1<=Arg_2 && Arg_2<=Arg_1
2:n_g1___7(Arg_0,Arg_1,Arg_2) -> n_g___5(Arg_0,Arg_1+Arg_2,Arg_2):|:Arg_2<=1 && Arg_2<=Arg_1 && Arg_1+Arg_2<=2 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=1 && Arg_1<=1+Arg_0 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 0<1+Arg_0 && Arg_1<=1 && 1<=Arg_1 && Arg_2<=1 && 1<=Arg_2
3:n_g___5(Arg_0,Arg_1,Arg_2) -> n_g1___4(Arg_0-1,Arg_1,Arg_1):|:1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 2<=Arg_1 && 2<=Arg_0+Arg_1 && 0<=Arg_0 && 0<Arg_1 && 0<Arg_0
4:n_g___5(Arg_0,Arg_1,Arg_2) -> n_h___3(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 2<=Arg_1 && 2<=Arg_0+Arg_1 && 0<=Arg_0 && 0<Arg_1 && Arg_0<=0
5:n_g___8(Arg_0,Arg_1,Arg_2) -> n_g1___7(Arg_0-1,Arg_1,Arg_1):|:Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_1+Arg_2<=1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && Arg_1<=1 && 1<=Arg_1 && 0<Arg_1 && Arg_1<=1 && 1<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && 0<Arg_0
6:n_g___8(Arg_0,Arg_1,Arg_2) -> n_h___6(Arg_0,Arg_1,Arg_2):|:Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_1+Arg_2<=1 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && Arg_1<=1 && 1<=Arg_1 && 0<Arg_1 && Arg_1<=1 && 1<=Arg_1 && Arg_2<=0 && 0<=Arg_2 && Arg_0<=0
8:n_h___2(Arg_0,Arg_1,Arg_2) -> n_h___2(Arg_0,Arg_1-1,Arg_2):|: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_1
9:n_h___3(Arg_0,Arg_1,Arg_2) -> n_h___2(Arg_0,Arg_1-1,Arg_2):|:1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 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
10:n_h___6(Arg_0,Arg_1,Arg_2) -> n_h___1(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_1+Arg_2<=1 && Arg_0+Arg_2<=0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && Arg_1<=1+Arg_2 && Arg_0<=Arg_2 && 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_g1___4(Arg_0,Arg_1,Arg_2) -> n_g___5(Arg_0,Arg_1+Arg_2,Arg_2):|:Arg_2<=Arg_1 && 2<=Arg_2 && 4<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 2<=Arg_0+Arg_1 && 0<=Arg_0 && 0<Arg_1 && 0<1+Arg_0 && Arg_1<=Arg_2 && Arg_2<=Arg_1 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_g___5 [Arg_0 ]
n_g1___4 [Arg_0+1 ]

MPRF for transition 3:n_g___5(Arg_0,Arg_1,Arg_2) -> n_g1___4(Arg_0-1,Arg_1,Arg_1):|:1+Arg_2<=Arg_1 && 1<=Arg_2 && 3<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 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 ]
n_g1___4 [Arg_0+1 ]

MPRF for transition 8:n_h___2(Arg_0,Arg_1,Arg_2) -> n_h___2(Arg_0,Arg_1-1,Arg_2):|: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_1 of depth 1:

new bound:

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

MPRF:

n_h___2 [Arg_1+1 ]

All Bounds

Timebounds

Overall timebound:2*2^(Arg_0)+2*Arg_0+11 {O(EXP)}
0: n_f->n_g___8: 1 {O(1)}
1: n_g1___4->n_g___5: Arg_0 {O(n)}
2: n_g1___7->n_g___5: 1 {O(1)}
3: n_g___5->n_g1___4: Arg_0+1 {O(n)}
4: n_g___5->n_h___3: 1 {O(1)}
5: n_g___8->n_g1___7: 1 {O(1)}
6: n_g___8->n_h___6: 1 {O(1)}
8: n_h___2->n_h___2: 2*2^(Arg_0)+3 {O(EXP)}
9: n_h___3->n_h___2: 1 {O(1)}
10: n_h___6->n_h___1: 1 {O(1)}

Costbounds

Overall costbound: 2*2^(Arg_0)+2*Arg_0+11 {O(EXP)}
0: n_f->n_g___8: 1 {O(1)}
1: n_g1___4->n_g___5: Arg_0 {O(n)}
2: n_g1___7->n_g___5: 1 {O(1)}
3: n_g___5->n_g1___4: Arg_0+1 {O(n)}
4: n_g___5->n_h___3: 1 {O(1)}
5: n_g___8->n_g1___7: 1 {O(1)}
6: n_g___8->n_h___6: 1 {O(1)}
8: n_h___2->n_h___2: 2*2^(Arg_0)+3 {O(EXP)}
9: n_h___3->n_h___2: 1 {O(1)}
10: n_h___6->n_h___1: 1 {O(1)}

Sizebounds

0: n_f->n_g___8, Arg_0: Arg_0 {O(n)}
0: n_f->n_g___8, Arg_1: 1 {O(1)}
0: n_f->n_g___8, Arg_2: 0 {O(1)}
1: n_g1___4->n_g___5, Arg_0: Arg_0 {O(n)}
1: n_g1___4->n_g___5, Arg_1: 2*2^(Arg_0) {O(EXP)}
1: n_g1___4->n_g___5, Arg_2: 2*2^(Arg_0)+2 {O(EXP)}
2: n_g1___7->n_g___5, Arg_0: Arg_0 {O(n)}
2: n_g1___7->n_g___5, Arg_1: 2 {O(1)}
2: n_g1___7->n_g___5, Arg_2: 1 {O(1)}
3: n_g___5->n_g1___4, Arg_0: Arg_0 {O(n)}
3: n_g___5->n_g1___4, Arg_1: 2*2^(Arg_0) {O(EXP)}
3: n_g___5->n_g1___4, Arg_2: 2*2^(Arg_0)+2 {O(EXP)}
4: n_g___5->n_h___3, Arg_0: 0 {O(1)}
4: n_g___5->n_h___3, Arg_1: 2*2^(Arg_0)+2 {O(EXP)}
4: n_g___5->n_h___3, Arg_2: 2*2^(Arg_0)+3 {O(EXP)}
5: n_g___8->n_g1___7, Arg_0: Arg_0 {O(n)}
5: n_g___8->n_g1___7, Arg_1: 1 {O(1)}
5: n_g___8->n_g1___7, Arg_2: 1 {O(1)}
6: n_g___8->n_h___6, Arg_0: Arg_0 {O(n)}
6: n_g___8->n_h___6, Arg_1: 1 {O(1)}
6: n_g___8->n_h___6, Arg_2: 0 {O(1)}
8: n_h___2->n_h___2, Arg_0: 0 {O(1)}
8: n_h___2->n_h___2, Arg_1: 2*2^(Arg_0)+2 {O(EXP)}
8: n_h___2->n_h___2, Arg_2: 2*2^(Arg_0)+3 {O(EXP)}
9: n_h___3->n_h___2, Arg_0: 0 {O(1)}
9: n_h___3->n_h___2, Arg_1: 2*2^(Arg_0)+2 {O(EXP)}
9: n_h___3->n_h___2, Arg_2: 2*2^(Arg_0)+3 {O(EXP)}
10: n_h___6->n_h___1, Arg_0: Arg_0 {O(n)}
10: n_h___6->n_h___1, Arg_1: 0 {O(1)}
10: n_h___6->n_h___1, Arg_2: 0 {O(1)}