Initial Problem

Start: n_f3
Program_Vars: Arg_0, Arg_1
Temp_Vars: NoDet0
Locations: n_f2___3, n_f2___4, n_f3, n_f300___1, n_f300___2
Transitions:
0:n_f2___3(Arg_0,Arg_1) -> n_f2___3(Arg_0-1,Arg_1):|:0<=Arg_0 && 1<=Arg_0
1:n_f2___3(Arg_0,Arg_1) -> n_f300___1(Arg_0-1,NoDet0):|:0<=Arg_0 && Arg_0<=0
2:n_f2___4(Arg_0,Arg_1) -> n_f2___3(Arg_0-1,Arg_1):|:1<=Arg_0
3:n_f2___4(Arg_0,Arg_1) -> n_f300___2(Arg_0-1,NoDet0):|:Arg_0<=0
4:n_f3(Arg_0,Arg_1) -> n_f2___4(Arg_0,Arg_1)

Preprocessing

Eliminate variables {NoDet0,Arg_1} that do not contribute to the problem

Found invariant 1+Arg_0<=0 && 0<=1+Arg_0 for location n_f300___1

Found invariant 1+Arg_0<=0 for location n_f300___2

Found invariant 0<=Arg_0 for location n_f2___3

Problem after Preprocessing

Start: n_f3
Program_Vars: Arg_0
Temp_Vars:
Locations: n_f2___3, n_f2___4, n_f3, n_f300___1, n_f300___2
Transitions:
10:n_f2___3(Arg_0) -> n_f2___3(Arg_0-1):|:0<=Arg_0 && 0<=Arg_0 && 1<=Arg_0
11:n_f2___3(Arg_0) -> n_f300___1(Arg_0-1):|:0<=Arg_0 && 0<=Arg_0 && Arg_0<=0
12:n_f2___4(Arg_0) -> n_f2___3(Arg_0-1):|:1<=Arg_0
13:n_f2___4(Arg_0) -> n_f300___2(Arg_0-1):|:Arg_0<=0
14:n_f3(Arg_0) -> n_f2___4(Arg_0)

MPRF for transition 10:n_f2___3(Arg_0) -> n_f2___3(Arg_0-1):|:0<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

n_f2___3 [Arg_0+1 ]

All Bounds

Timebounds

Overall timebound:Arg_0+5 {O(n)}
10: n_f2___3->n_f2___3: Arg_0+1 {O(n)}
11: n_f2___3->n_f300___1: 1 {O(1)}
12: n_f2___4->n_f2___3: 1 {O(1)}
13: n_f2___4->n_f300___2: 1 {O(1)}
14: n_f3->n_f2___4: 1 {O(1)}

Costbounds

Overall costbound: Arg_0+5 {O(n)}
10: n_f2___3->n_f2___3: Arg_0+1 {O(n)}
11: n_f2___3->n_f300___1: 1 {O(1)}
12: n_f2___4->n_f2___3: 1 {O(1)}
13: n_f2___4->n_f300___2: 1 {O(1)}
14: n_f3->n_f2___4: 1 {O(1)}

Sizebounds

10: n_f2___3->n_f2___3, Arg_0: Arg_0 {O(n)}
11: n_f2___3->n_f300___1, Arg_0: 1 {O(1)}
12: n_f2___4->n_f2___3, Arg_0: Arg_0 {O(n)}
13: n_f2___4->n_f300___2, Arg_0: Arg_0+1 {O(n)}
14: n_f3->n_f2___4, Arg_0: Arg_0 {O(n)}