Initial Problem

Start: n_f0
Program_Vars: Arg_0
Temp_Vars:
Locations: n_f0, n_f1___1, n_f1___2
Transitions:
0:n_f0(Arg_0) -> n_f1___2(Arg_0)
1:n_f1___1(Arg_0) -> n_f1___1(Arg_0-1000):|:1<=Arg_0 && 1001<=Arg_0
2:n_f1___2(Arg_0) -> n_f1___1(Arg_0-1000):|:1001<=Arg_0

Preprocessing

Found invariant 1<=Arg_0 for location n_f1___1

Problem after Preprocessing

Start: n_f0
Program_Vars: Arg_0
Temp_Vars:
Locations: n_f0, n_f1___1, n_f1___2
Transitions:
0:n_f0(Arg_0) -> n_f1___2(Arg_0)
1:n_f1___1(Arg_0) -> n_f1___1(Arg_0-1000):|:1<=Arg_0 && 1<=Arg_0 && 1001<=Arg_0
2:n_f1___2(Arg_0) -> n_f1___1(Arg_0-1000):|:1001<=Arg_0

MPRF for transition 1:n_f1___1(Arg_0) -> n_f1___1(Arg_0-1000):|:1<=Arg_0 && 1<=Arg_0 && 1001<=Arg_0 of depth 1:

new bound:

Arg_0 {O(n)}

MPRF:

n_f1___1 [Arg_0 ]

All Bounds

Timebounds

Overall timebound:Arg_0+2 {O(n)}
0: n_f0->n_f1___2: 1 {O(1)}
1: n_f1___1->n_f1___1: Arg_0 {O(n)}
2: n_f1___2->n_f1___1: 1 {O(1)}

Costbounds

Overall costbound: Arg_0+2 {O(n)}
0: n_f0->n_f1___2: 1 {O(1)}
1: n_f1___1->n_f1___1: Arg_0 {O(n)}
2: n_f1___2->n_f1___1: 1 {O(1)}

Sizebounds

0: n_f0->n_f1___2, Arg_0: Arg_0 {O(n)}
1: n_f1___1->n_f1___1, Arg_0: Arg_0 {O(n)}
2: n_f1___2->n_f1___1, Arg_0: Arg_0 {O(n)}