Initial Problem

Start: n_f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_f0, n_f1___1, n_f1___2, n_f1___3
Transitions:
0:n_f0(Arg_0,Arg_1,Arg_2) -> n_f1___3(Arg_0,Arg_1,Arg_2)
1:n_f1___1(Arg_0,Arg_1,Arg_2) -> n_f1___1(Arg_0+Arg_2,Arg_1,Arg_2-1):|:2+Arg_2<=Arg_0 && 1<=Arg_0
2:n_f1___1(Arg_0,Arg_1,Arg_2) -> n_f1___2(Arg_0+Arg_1,Arg_1-1,Arg_2):|:2+Arg_2<=Arg_0 && 1<=Arg_0
3:n_f1___2(Arg_0,Arg_1,Arg_2) -> n_f1___1(Arg_0+Arg_2,Arg_1,Arg_2-1):|:2+Arg_1<=Arg_0 && 1<=Arg_0
4:n_f1___2(Arg_0,Arg_1,Arg_2) -> n_f1___2(Arg_0+Arg_1,Arg_1-1,Arg_2):|:2+Arg_1<=Arg_0 && 1<=Arg_0
5:n_f1___3(Arg_0,Arg_1,Arg_2) -> n_f1___1(Arg_0+Arg_2,Arg_1,Arg_2-1):|:1<=Arg_0
6:n_f1___3(Arg_0,Arg_1,Arg_2) -> n_f1___2(Arg_0+Arg_1,Arg_1-1,Arg_2):|:1<=Arg_0

Preprocessing

Found invariant 2+Arg_1<=Arg_0 for location n_f1___2

Found invariant 2+Arg_2<=Arg_0 for location n_f1___1

Problem after Preprocessing

Start: n_f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_f0, n_f1___1, n_f1___2, n_f1___3
Transitions:
0:n_f0(Arg_0,Arg_1,Arg_2) -> n_f1___3(Arg_0,Arg_1,Arg_2)
1:n_f1___1(Arg_0,Arg_1,Arg_2) -> n_f1___1(Arg_0+Arg_2,Arg_1,Arg_2-1):|:2+Arg_2<=Arg_0 && 2+Arg_2<=Arg_0 && 1<=Arg_0
2:n_f1___1(Arg_0,Arg_1,Arg_2) -> n_f1___2(Arg_0+Arg_1,Arg_1-1,Arg_2):|:2+Arg_2<=Arg_0 && 2+Arg_2<=Arg_0 && 1<=Arg_0
3:n_f1___2(Arg_0,Arg_1,Arg_2) -> n_f1___1(Arg_0+Arg_2,Arg_1,Arg_2-1):|:2+Arg_1<=Arg_0 && 2+Arg_1<=Arg_0 && 1<=Arg_0
4:n_f1___2(Arg_0,Arg_1,Arg_2) -> n_f1___2(Arg_0+Arg_1,Arg_1-1,Arg_2):|:2+Arg_1<=Arg_0 && 2+Arg_1<=Arg_0 && 1<=Arg_0
5:n_f1___3(Arg_0,Arg_1,Arg_2) -> n_f1___1(Arg_0+Arg_2,Arg_1,Arg_2-1):|:1<=Arg_0
6:n_f1___3(Arg_0,Arg_1,Arg_2) -> n_f1___2(Arg_0+Arg_1,Arg_1-1,Arg_2):|:1<=Arg_0

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: n_f0->n_f1___3: 1 {O(1)}
1: n_f1___1->n_f1___1: inf {Infinity}
2: n_f1___1->n_f1___2: inf {Infinity}
3: n_f1___2->n_f1___1: inf {Infinity}
4: n_f1___2->n_f1___2: inf {Infinity}
5: n_f1___3->n_f1___1: 1 {O(1)}
6: n_f1___3->n_f1___2: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
0: n_f0->n_f1___3: 1 {O(1)}
1: n_f1___1->n_f1___1: inf {Infinity}
2: n_f1___1->n_f1___2: inf {Infinity}
3: n_f1___2->n_f1___1: inf {Infinity}
4: n_f1___2->n_f1___2: inf {Infinity}
5: n_f1___3->n_f1___1: 1 {O(1)}
6: n_f1___3->n_f1___2: 1 {O(1)}

Sizebounds

0: n_f0->n_f1___3, Arg_0: Arg_0 {O(n)}
0: n_f0->n_f1___3, Arg_1: Arg_1 {O(n)}
0: n_f0->n_f1___3, Arg_2: Arg_2 {O(n)}
5: n_f1___3->n_f1___1, Arg_0: Arg_0+Arg_2 {O(n)}
5: n_f1___3->n_f1___1, Arg_1: Arg_1 {O(n)}
5: n_f1___3->n_f1___1, Arg_2: Arg_2+1 {O(n)}
6: n_f1___3->n_f1___2, Arg_0: Arg_0+Arg_1 {O(n)}
6: n_f1___3->n_f1___2, Arg_1: Arg_1+1 {O(n)}
6: n_f1___3->n_f1___2, Arg_2: Arg_2 {O(n)}