Initial Problem

Start: n_f3
Program_Vars: Arg_0
Temp_Vars:
Locations: n_f2___1, n_f2___2, n_f2___3, n_f3
Transitions:
0:n_f2___1(Arg_0) -> n_f2___1(Arg_0-1):|:Arg_0<=1 && Arg_0<=1 && Arg_0<=0 && Arg_0<=1
1:n_f2___2(Arg_0) -> n_f2___1(Arg_0-1):|:1<=Arg_0 && Arg_0<=1
2:n_f2___2(Arg_0) -> n_f2___2(Arg_0-1):|:1<=Arg_0 && 2<=Arg_0
3:n_f2___3(Arg_0) -> n_f2___1(Arg_0-1):|:Arg_0<=1
4:n_f2___3(Arg_0) -> n_f2___2(Arg_0-1):|:2<=Arg_0
5:n_f3(Arg_0) -> n_f2___3(Arg_0)

Preprocessing

Found invariant Arg_0<=0 for location n_f2___1

Found invariant 1<=Arg_0 for location n_f2___2

Problem after Preprocessing

Start: n_f3
Program_Vars: Arg_0
Temp_Vars:
Locations: n_f2___1, n_f2___2, n_f2___3, n_f3
Transitions:
0:n_f2___1(Arg_0) -> n_f2___1(Arg_0-1):|:Arg_0<=0 && Arg_0<=1 && Arg_0<=1 && Arg_0<=0 && Arg_0<=1
1:n_f2___2(Arg_0) -> n_f2___1(Arg_0-1):|:1<=Arg_0 && 1<=Arg_0 && Arg_0<=1
2:n_f2___2(Arg_0) -> n_f2___2(Arg_0-1):|:1<=Arg_0 && 1<=Arg_0 && 2<=Arg_0
3:n_f2___3(Arg_0) -> n_f2___1(Arg_0-1):|:Arg_0<=1
4:n_f2___3(Arg_0) -> n_f2___2(Arg_0-1):|:2<=Arg_0
5:n_f3(Arg_0) -> n_f2___3(Arg_0)

MPRF for transition 2:n_f2___2(Arg_0) -> n_f2___2(Arg_0-1):|:1<=Arg_0 && 1<=Arg_0 && 2<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_f2___2 [Arg_0 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: n_f2___1->n_f2___1: inf {Infinity}
1: n_f2___2->n_f2___1: 1 {O(1)}
2: n_f2___2->n_f2___2: Arg_0 {O(n)}
3: n_f2___3->n_f2___1: 1 {O(1)}
4: n_f2___3->n_f2___2: 1 {O(1)}
5: n_f3->n_f2___3: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
0: n_f2___1->n_f2___1: inf {Infinity}
1: n_f2___2->n_f2___1: 1 {O(1)}
2: n_f2___2->n_f2___2: Arg_0 {O(n)}
3: n_f2___3->n_f2___1: 1 {O(1)}
4: n_f2___3->n_f2___2: 1 {O(1)}
5: n_f3->n_f2___3: 1 {O(1)}

Sizebounds

1: n_f2___2->n_f2___1, Arg_0: 0 {O(1)}
2: n_f2___2->n_f2___2, Arg_0: Arg_0 {O(n)}
3: n_f2___3->n_f2___1, Arg_0: Arg_0+1 {O(n)}
4: n_f2___3->n_f2___2, Arg_0: Arg_0 {O(n)}
5: n_f3->n_f2___3, Arg_0: Arg_0 {O(n)}