Initial Problem

Start: n_f2
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: B_P, NoDet0
Locations: n_f1___3, n_f1___4, n_f1___5, n_f2, n_f300___1, n_f300___2
Transitions:
0:n_f1___3(Arg_0,Arg_1,Arg_2) -> n_f300___1(Arg_0,B_P,NoDet0):|:Arg_0<=1+Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+B_P<=Arg_0 && Arg_1<=B_P && B_P<=Arg_1
1:n_f1___4(Arg_0,Arg_1,Arg_2) -> n_f1___3(Arg_0+1,Arg_0,Arg_2):|:Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0
2:n_f1___4(Arg_0,Arg_1,Arg_2) -> n_f1___4(Arg_0+1,Arg_1,Arg_2):|:Arg_0<=Arg_1 && 1+Arg_0<=Arg_1
3:n_f1___5(Arg_0,Arg_1,Arg_2) -> n_f1___3(Arg_0+1,Arg_0,Arg_2):|:Arg_0<=Arg_1 && Arg_1<=Arg_0
4:n_f1___5(Arg_0,Arg_1,Arg_2) -> n_f1___4(Arg_0+1,Arg_1,Arg_2):|:1+Arg_0<=Arg_1
5:n_f1___5(Arg_0,Arg_1,Arg_2) -> n_f300___2(Arg_0,B_P,NoDet0):|:1+B_P<=Arg_0 && Arg_1<=B_P && B_P<=Arg_1
6:n_f2(Arg_0,Arg_1,Arg_2) -> n_f1___5(Arg_0,Arg_1,Arg_2)

Preprocessing

Eliminate variables {NoDet0,Arg_2} that do not contribute to the problem

Found invariant 1+Arg_1<=Arg_0 && Arg_0<=1+Arg_1 for location n_f300___1

Found invariant 1+Arg_1<=Arg_0 for location n_f300___2

Found invariant Arg_0<=Arg_1 for location n_f1___4

Found invariant 1+Arg_1<=Arg_0 && Arg_0<=1+Arg_1 for location n_f1___3

Problem after Preprocessing

Start: n_f2
Program_Vars: Arg_0, Arg_1
Temp_Vars: B_P
Locations: n_f1___3, n_f1___4, n_f1___5, n_f2, n_f300___1, n_f300___2
Transitions:
14:n_f1___3(Arg_0,Arg_1) -> n_f300___1(Arg_0,B_P):|:1+Arg_1<=Arg_0 && Arg_0<=1+Arg_1 && Arg_0<=1+Arg_1 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+B_P<=Arg_0 && Arg_1<=B_P && B_P<=Arg_1
15:n_f1___4(Arg_0,Arg_1) -> n_f1___3(Arg_0+1,Arg_0):|:Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0
16:n_f1___4(Arg_0,Arg_1) -> n_f1___4(Arg_0+1,Arg_1):|:Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1+Arg_0<=Arg_1
17:n_f1___5(Arg_0,Arg_1) -> n_f1___3(Arg_0+1,Arg_0):|:Arg_0<=Arg_1 && Arg_1<=Arg_0
18:n_f1___5(Arg_0,Arg_1) -> n_f1___4(Arg_0+1,Arg_1):|:1+Arg_0<=Arg_1
19:n_f1___5(Arg_0,Arg_1) -> n_f300___2(Arg_0,B_P):|:1+B_P<=Arg_0 && Arg_1<=B_P && B_P<=Arg_1
20:n_f2(Arg_0,Arg_1) -> n_f1___5(Arg_0,Arg_1)

MPRF for transition 16:n_f1___4(Arg_0,Arg_1) -> n_f1___4(Arg_0+1,Arg_1):|:Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1+Arg_0<=Arg_1 of depth 1:

new bound:

Arg_0+Arg_1+2 {O(n)}

MPRF:

n_f1___4 [Arg_1+1-Arg_0 ]

All Bounds

Timebounds

Overall timebound:Arg_0+Arg_1+8 {O(n)}
14: n_f1___3->n_f300___1: 1 {O(1)}
15: n_f1___4->n_f1___3: 1 {O(1)}
16: n_f1___4->n_f1___4: Arg_0+Arg_1+2 {O(n)}
17: n_f1___5->n_f1___3: 1 {O(1)}
18: n_f1___5->n_f1___4: 1 {O(1)}
19: n_f1___5->n_f300___2: 1 {O(1)}
20: n_f2->n_f1___5: 1 {O(1)}

Costbounds

Overall costbound: Arg_0+Arg_1+8 {O(n)}
14: n_f1___3->n_f300___1: 1 {O(1)}
15: n_f1___4->n_f1___3: 1 {O(1)}
16: n_f1___4->n_f1___4: Arg_0+Arg_1+2 {O(n)}
17: n_f1___5->n_f1___3: 1 {O(1)}
18: n_f1___5->n_f1___4: 1 {O(1)}
19: n_f1___5->n_f300___2: 1 {O(1)}
20: n_f2->n_f1___5: 1 {O(1)}

Sizebounds

14: n_f1___3->n_f300___1, Arg_0: 4*Arg_0+Arg_1+7 {O(n)}
14: n_f1___3->n_f300___1, Arg_1: 4*Arg_0+Arg_1+4 {O(n)}
15: n_f1___4->n_f1___3, Arg_0: 3*Arg_0+Arg_1+6 {O(n)}
15: n_f1___4->n_f1___3, Arg_1: 3*Arg_0+Arg_1+4 {O(n)}
16: n_f1___4->n_f1___4, Arg_0: 2*Arg_0+Arg_1+3 {O(n)}
16: n_f1___4->n_f1___4, Arg_1: Arg_1 {O(n)}
17: n_f1___5->n_f1___3, Arg_0: Arg_0+1 {O(n)}
17: n_f1___5->n_f1___3, Arg_1: Arg_0 {O(n)}
18: n_f1___5->n_f1___4, Arg_0: Arg_0+1 {O(n)}
18: n_f1___5->n_f1___4, Arg_1: Arg_1 {O(n)}
19: n_f1___5->n_f300___2, Arg_0: Arg_0 {O(n)}
19: n_f1___5->n_f300___2, Arg_1: Arg_1 {O(n)}
20: n_f2->n_f1___5, Arg_0: Arg_0 {O(n)}
20: n_f2->n_f1___5, Arg_1: Arg_1 {O(n)}