Initial Problem
Start: n_f
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_f, n_g___4, n_g___6, n_g___7, n_h___1, n_h___2, n_h___3, n_h___5
Transitions:
0:n_f(Arg_0,Arg_1,Arg_2) -> n_g___7(1,1,Arg_2)
1:n_g___4(Arg_0,Arg_1,Arg_2) -> n_g___4(Arg_0+Arg_1,Arg_0+Arg_1,Arg_2-1):|:0<Arg_2
2:n_g___4(Arg_0,Arg_1,Arg_2) -> n_h___2(Arg_0,Arg_1,Arg_2):|:Arg_2<=0
3:n_g___6(Arg_0,Arg_1,Arg_2) -> n_g___4(Arg_0+Arg_1,Arg_0+Arg_1,Arg_2-1):|:0<Arg_1 && 0<Arg_2
4:n_g___6(Arg_0,Arg_1,Arg_2) -> n_h___3(Arg_0,Arg_1,Arg_2):|:0<Arg_1 && Arg_2<=0
5:n_g___7(Arg_0,Arg_1,Arg_2) -> n_g___6(Arg_0+Arg_1,Arg_0+Arg_1,Arg_2-1):|:0<Arg_1 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && 0<Arg_2
6:n_g___7(Arg_0,Arg_1,Arg_2) -> n_h___5(Arg_0,Arg_1,Arg_2):|:0<Arg_1 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && Arg_2<=0
7:n_h___1(Arg_0,Arg_1,Arg_2) -> n_h___2(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=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_2<=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_2<=0 && 0<=Arg_1 && 0<Arg_1
10:n_h___5(Arg_0,Arg_1,Arg_2) -> n_h___1(Arg_0,Arg_1-1,Arg_2):|:0<Arg_1 && Arg_2<=0 && 1<=Arg_1 && 0<=Arg_1 && 0<Arg_1
Preprocessing
Found invariant 0<=Arg_2 && 4<=Arg_1+Arg_2 && 4<=Arg_0+Arg_2 && 4<=Arg_1 && 8<=Arg_0+Arg_1 && 4<=Arg_0 for location n_g___4
Found invariant Arg_2<=0 && Arg_2<=Arg_1 && Arg_1+Arg_2<=0 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=1 && Arg_1<=0 && 1+Arg_1<=Arg_0 && Arg_0+Arg_1<=1 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && Arg_0<=1+Arg_1 && Arg_0<=1 && 1<=Arg_0 for location n_h___1
Found invariant Arg_2<=0 && Arg_2<=Arg_1 && 2+Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 for location n_h___2
Found invariant Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 1<=Arg_0 for location n_g___7
Found invariant 0<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=2+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=2+Arg_2 && Arg_1<=2 && Arg_1<=Arg_0 && Arg_0+Arg_1<=4 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=2 && 2<=Arg_0 for location n_g___6
Found invariant Arg_2<=0 && 2+Arg_2<=Arg_1 && Arg_1+Arg_2<=2 && 2+Arg_2<=Arg_0 && Arg_0+Arg_2<=2 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=2+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=2+Arg_2 && Arg_1<=2 && Arg_1<=Arg_0 && Arg_0+Arg_1<=4 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=2 && 2<=Arg_0 for location n_h___3
Found invariant Arg_2<=0 && 1+Arg_2<=Arg_1 && Arg_1+Arg_2<=1 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=1 && Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 1<=Arg_0 for location n_h___5
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_g___4, n_g___6, n_g___7, n_h___1, n_h___2, n_h___3, n_h___5
Transitions:
0:n_f(Arg_0,Arg_1,Arg_2) -> n_g___7(1,1,Arg_2)
1:n_g___4(Arg_0,Arg_1,Arg_2) -> n_g___4(Arg_0+Arg_1,Arg_0+Arg_1,Arg_2-1):|:0<=Arg_2 && 4<=Arg_1+Arg_2 && 4<=Arg_0+Arg_2 && 4<=Arg_1 && 8<=Arg_0+Arg_1 && 4<=Arg_0 && 0<Arg_2
2:n_g___4(Arg_0,Arg_1,Arg_2) -> n_h___2(Arg_0,Arg_1,Arg_2):|:0<=Arg_2 && 4<=Arg_1+Arg_2 && 4<=Arg_0+Arg_2 && 4<=Arg_1 && 8<=Arg_0+Arg_1 && 4<=Arg_0 && Arg_2<=0
3:n_g___6(Arg_0,Arg_1,Arg_2) -> n_g___4(Arg_0+Arg_1,Arg_0+Arg_1,Arg_2-1):|:0<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=2+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=2+Arg_2 && Arg_1<=2 && Arg_1<=Arg_0 && Arg_0+Arg_1<=4 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=2 && 2<=Arg_0 && 0<Arg_1 && 0<Arg_2
4:n_g___6(Arg_0,Arg_1,Arg_2) -> n_h___3(Arg_0,Arg_1,Arg_2):|:0<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=2+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=2+Arg_2 && Arg_1<=2 && Arg_1<=Arg_0 && Arg_0+Arg_1<=4 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=2 && 2<=Arg_0 && 0<Arg_1 && Arg_2<=0
5:n_g___7(Arg_0,Arg_1,Arg_2) -> n_g___6(Arg_0+Arg_1,Arg_0+Arg_1,Arg_2-1):|:Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && 0<Arg_1 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && 0<Arg_2
6:n_g___7(Arg_0,Arg_1,Arg_2) -> n_h___5(Arg_0,Arg_1,Arg_2):|:Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && 0<Arg_1 && Arg_1<=1 && 1<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && Arg_2<=0
8:n_h___2(Arg_0,Arg_1,Arg_2) -> n_h___2(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_1 && 2+Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_2<=0 && 0<Arg_1
9:n_h___3(Arg_0,Arg_1,Arg_2) -> n_h___2(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && 2+Arg_2<=Arg_1 && Arg_1+Arg_2<=2 && 2+Arg_2<=Arg_0 && Arg_0+Arg_2<=2 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=2+Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=2+Arg_2 && Arg_1<=2 && Arg_1<=Arg_0 && Arg_0+Arg_1<=4 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=2 && 2<=Arg_0 && 0<Arg_1 && Arg_2<=0 && 0<=Arg_1 && 0<Arg_1
10:n_h___5(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 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=1 && Arg_1<=1 && Arg_1<=Arg_0 && Arg_0+Arg_1<=2 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=1 && 1<=Arg_0 && 0<Arg_1 && Arg_2<=0 && 1<=Arg_1 && 0<=Arg_1 && 0<Arg_1
MPRF for transition 1:n_g___4(Arg_0,Arg_1,Arg_2) -> n_g___4(Arg_0+Arg_1,Arg_0+Arg_1,Arg_2-1):|:0<=Arg_2 && 4<=Arg_1+Arg_2 && 4<=Arg_0+Arg_2 && 4<=Arg_1 && 8<=Arg_0+Arg_1 && 4<=Arg_0 && 0<Arg_2 of depth 1:
new bound:
Arg_2+1 {O(n)}
MPRF:
n_g___4 [Arg_2+1 ]
MPRF for transition 8:n_h___2(Arg_0,Arg_1,Arg_2) -> n_h___2(Arg_0,Arg_1-1,Arg_2):|:Arg_2<=0 && Arg_2<=Arg_1 && 2+Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_2<=0 && 0<Arg_1 of depth 1:
new bound:
16*2^(Arg_2+1)+7 {O(EXP)}
MPRF:
n_h___2 [Arg_1+1 ]
All Bounds
Timebounds
Overall timebound:16*2^(Arg_2+1)+Arg_2+16 {O(EXP)}
0: n_f->n_g___7: 1 {O(1)}
1: n_g___4->n_g___4: Arg_2+1 {O(n)}
2: n_g___4->n_h___2: 1 {O(1)}
3: n_g___6->n_g___4: 1 {O(1)}
4: n_g___6->n_h___3: 1 {O(1)}
5: n_g___7->n_g___6: 1 {O(1)}
6: n_g___7->n_h___5: 1 {O(1)}
8: n_h___2->n_h___2: 16*2^(Arg_2+1)+7 {O(EXP)}
9: n_h___3->n_h___2: 1 {O(1)}
10: n_h___5->n_h___1: 1 {O(1)}
Costbounds
Overall costbound: 16*2^(Arg_2+1)+Arg_2+16 {O(EXP)}
0: n_f->n_g___7: 1 {O(1)}
1: n_g___4->n_g___4: Arg_2+1 {O(n)}
2: n_g___4->n_h___2: 1 {O(1)}
3: n_g___6->n_g___4: 1 {O(1)}
4: n_g___6->n_h___3: 1 {O(1)}
5: n_g___7->n_g___6: 1 {O(1)}
6: n_g___7->n_h___5: 1 {O(1)}
8: n_h___2->n_h___2: 16*2^(Arg_2+1)+7 {O(EXP)}
9: n_h___3->n_h___2: 1 {O(1)}
10: n_h___5->n_h___1: 1 {O(1)}
Sizebounds
0: n_f->n_g___7, Arg_0: 1 {O(1)}
0: n_f->n_g___7, Arg_1: 1 {O(1)}
0: n_f->n_g___7, Arg_2: Arg_2 {O(n)}
1: n_g___4->n_g___4, Arg_0: 16*2^(Arg_2+1) {O(EXP)}
1: n_g___4->n_g___4, Arg_1: 16*2^(Arg_2+1) {O(EXP)}
1: n_g___4->n_g___4, Arg_2: Arg_2 {O(n)}
2: n_g___4->n_h___2, Arg_0: 16*2^(Arg_2+1)+4 {O(EXP)}
2: n_g___4->n_h___2, Arg_1: 16*2^(Arg_2+1)+4 {O(EXP)}
2: n_g___4->n_h___2, Arg_2: 0 {O(1)}
3: n_g___6->n_g___4, Arg_0: 4 {O(1)}
3: n_g___6->n_g___4, Arg_1: 4 {O(1)}
3: n_g___6->n_g___4, Arg_2: Arg_2 {O(n)}
4: n_g___6->n_h___3, Arg_0: 2 {O(1)}
4: n_g___6->n_h___3, Arg_1: 2 {O(1)}
4: n_g___6->n_h___3, Arg_2: 0 {O(1)}
5: n_g___7->n_g___6, Arg_0: 2 {O(1)}
5: n_g___7->n_g___6, Arg_1: 2 {O(1)}
5: n_g___7->n_g___6, Arg_2: Arg_2 {O(n)}
6: n_g___7->n_h___5, Arg_0: 1 {O(1)}
6: n_g___7->n_h___5, Arg_1: 1 {O(1)}
6: n_g___7->n_h___5, Arg_2: Arg_2 {O(n)}
8: n_h___2->n_h___2, Arg_0: 16*2^(Arg_2+1)+6 {O(EXP)}
8: n_h___2->n_h___2, Arg_1: 16*2^(Arg_2+1)+5 {O(EXP)}
8: n_h___2->n_h___2, Arg_2: 0 {O(1)}
9: n_h___3->n_h___2, Arg_0: 2 {O(1)}
9: n_h___3->n_h___2, Arg_1: 1 {O(1)}
9: n_h___3->n_h___2, Arg_2: 0 {O(1)}
10: n_h___5->n_h___1, Arg_0: 1 {O(1)}
10: n_h___5->n_h___1, Arg_1: 0 {O(1)}
10: n_h___5->n_h___1, Arg_2: Arg_2 {O(n)}