Initial Problem

Start: n_f3
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: B_P, NoDet0
Locations: n_f2___3, n_f2___5, n_f3, n_f4___1, n_f4___2, n_f4___4
Transitions:
0:n_f2___3(Arg_0,Arg_1,Arg_2) -> n_f2___3(Arg_0-Arg_1,Arg_1+1,Arg_2):|:2<=Arg_0+Arg_1 && 1<=Arg_1 && 1<=Arg_0
1:n_f2___3(Arg_0,Arg_1,Arg_2) -> n_f4___1(Arg_0,Arg_1,NoDet0):|:2<=Arg_0+Arg_1 && 1<=Arg_1 && Arg_0<=0
2:n_f2___5(Arg_0,Arg_1,Arg_2) -> n_f2___3(Arg_0-Arg_1,Arg_1+1,Arg_2):|:1<=Arg_1 && 1<=Arg_0
3:n_f2___5(Arg_0,Arg_1,Arg_2) -> n_f4___2(Arg_0,Arg_1,NoDet0):|:1<=Arg_1 && Arg_0<=0
4:n_f3(Arg_0,Arg_1,Arg_2) -> n_f2___5(Arg_0,Arg_1,Arg_2):|:1<=Arg_1
5:n_f3(Arg_0,Arg_1,Arg_2) -> n_f4___4(Arg_0,B_P,NoDet0):|:B_P<=0 && Arg_1<=B_P && B_P<=Arg_1

Preprocessing

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

Found invariant 2<=Arg_1 && 2<=Arg_0+Arg_1 && 2+Arg_0<=Arg_1 && Arg_0<=0 for location n_f4___1

Found invariant 1<=Arg_1 for location n_f2___5

Found invariant 1<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 for location n_f4___2

Found invariant Arg_1<=0 for location n_f4___4

Found invariant 2<=Arg_1 && 2<=Arg_0+Arg_1 for location n_f2___3

Problem after Preprocessing

Start: n_f3
Program_Vars: Arg_0, Arg_1
Temp_Vars: B_P
Locations: n_f2___3, n_f2___5, n_f3, n_f4___1, n_f4___2, n_f4___4
Transitions:
11:n_f2___3(Arg_0,Arg_1) -> n_f2___3(Arg_0-Arg_1,Arg_1+1):|:2<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_1 && 1<=Arg_0
12:n_f2___3(Arg_0,Arg_1) -> n_f4___1(Arg_0,Arg_1):|:2<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_1 && Arg_0<=0
13:n_f2___5(Arg_0,Arg_1) -> n_f2___3(Arg_0-Arg_1,Arg_1+1):|:1<=Arg_1 && 1<=Arg_1 && 1<=Arg_0
14:n_f2___5(Arg_0,Arg_1) -> n_f4___2(Arg_0,Arg_1):|:1<=Arg_1 && 1<=Arg_1 && Arg_0<=0
15:n_f3(Arg_0,Arg_1) -> n_f2___5(Arg_0,Arg_1):|:1<=Arg_1
16:n_f3(Arg_0,Arg_1) -> n_f4___4(Arg_0,B_P):|:B_P<=0 && Arg_1<=B_P && B_P<=Arg_1

MPRF for transition 11:n_f2___3(Arg_0,Arg_1) -> n_f2___3(Arg_0-Arg_1,Arg_1+1):|:2<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0+Arg_1 && 1<=Arg_1 && 1<=Arg_0 of depth 1:

new bound:

Arg_0+Arg_1 {O(n)}

MPRF:

n_f2___3 [Arg_0 ]

All Bounds

Timebounds

Overall timebound:Arg_0+Arg_1+5 {O(n)}
11: n_f2___3->n_f2___3: Arg_0+Arg_1 {O(n)}
12: n_f2___3->n_f4___1: 1 {O(1)}
13: n_f2___5->n_f2___3: 1 {O(1)}
14: n_f2___5->n_f4___2: 1 {O(1)}
15: n_f3->n_f2___5: 1 {O(1)}
16: n_f3->n_f4___4: 1 {O(1)}

Costbounds

Overall costbound: Arg_0+Arg_1+5 {O(n)}
11: n_f2___3->n_f2___3: Arg_0+Arg_1 {O(n)}
12: n_f2___3->n_f4___1: 1 {O(1)}
13: n_f2___5->n_f2___3: 1 {O(1)}
14: n_f2___5->n_f4___2: 1 {O(1)}
15: n_f3->n_f2___5: 1 {O(1)}
16: n_f3->n_f4___4: 1 {O(1)}

Sizebounds

11: n_f2___3->n_f2___3, Arg_0: 2*Arg_0+4*Arg_1+2 {O(n)}
11: n_f2___3->n_f2___3, Arg_1: 2*Arg_1+Arg_0+1 {O(n)}
12: n_f2___3->n_f4___1, Arg_0: 3*Arg_0+5*Arg_1+2 {O(n)}
12: n_f2___3->n_f4___1, Arg_1: 3*Arg_1+Arg_0+2 {O(n)}
13: n_f2___5->n_f2___3, Arg_0: Arg_0+Arg_1 {O(n)}
13: n_f2___5->n_f2___3, Arg_1: Arg_1+1 {O(n)}
14: n_f2___5->n_f4___2, Arg_0: Arg_0 {O(n)}
14: n_f2___5->n_f4___2, Arg_1: Arg_1 {O(n)}
15: n_f3->n_f2___5, Arg_0: Arg_0 {O(n)}
15: n_f3->n_f2___5, Arg_1: Arg_1 {O(n)}
16: n_f3->n_f4___4, Arg_0: Arg_0 {O(n)}
16: n_f3->n_f4___4, Arg_1: Arg_1 {O(n)}