Initial Problem

Start: n_f1
Program_Vars: Arg_0
Temp_Vars:
Locations: n_f0___1, n_f0___2, n_f1
Transitions:
0:n_f0___1(Arg_0) -> n_f0___1(Arg_0-1):|:0<=1+Arg_0 && 0<=Arg_0
1:n_f0___2(Arg_0) -> n_f0___1(Arg_0-1):|:0<=Arg_0
2:n_f1(Arg_0) -> n_f0___2(Arg_0)

Preprocessing

Found invariant 0<=1+Arg_0 for location n_f0___1

Problem after Preprocessing

Start: n_f1
Program_Vars: Arg_0
Temp_Vars:
Locations: n_f0___1, n_f0___2, n_f1
Transitions:
0:n_f0___1(Arg_0) -> n_f0___1(Arg_0-1):|:0<=1+Arg_0 && 0<=1+Arg_0 && 0<=Arg_0
1:n_f0___2(Arg_0) -> n_f0___1(Arg_0-1):|:0<=Arg_0
2:n_f1(Arg_0) -> n_f0___2(Arg_0)

MPRF for transition 0:n_f0___1(Arg_0) -> n_f0___1(Arg_0-1):|:0<=1+Arg_0 && 0<=1+Arg_0 && 0<=Arg_0 of depth 1:

new bound:

Arg_0+2 {O(n)}

MPRF:

n_f0___1 [Arg_0+1 ]

All Bounds

Timebounds

Overall timebound:Arg_0+4 {O(n)}
0: n_f0___1->n_f0___1: Arg_0+2 {O(n)}
1: n_f0___2->n_f0___1: 1 {O(1)}
2: n_f1->n_f0___2: 1 {O(1)}

Costbounds

Overall costbound: Arg_0+4 {O(n)}
0: n_f0___1->n_f0___1: Arg_0+2 {O(n)}
1: n_f0___2->n_f0___1: 1 {O(1)}
2: n_f1->n_f0___2: 1 {O(1)}

Sizebounds

0: n_f0___1->n_f0___1, Arg_0: Arg_0+2 {O(n)}
1: n_f0___2->n_f0___1, Arg_0: Arg_0+1 {O(n)}
2: n_f1->n_f0___2, Arg_0: Arg_0 {O(n)}