Initial Problem

Start: n_f3
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
Temp_Vars: B_P, NoDet0
Locations: n_f2___5, n_f2___6, n_f3, n_f4___1, n_f4___2, n_f4___3, n_f4___4
Transitions:
0:n_f2___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f2___5(Arg_0-1,Arg_1-1,Arg_0,Arg_1,Arg_0-2,Arg_5):|:Arg_2<=2+Arg_4 && 2+Arg_4<=Arg_2 && Arg_0<=1+Arg_4 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_3<=1+Arg_1 && 0<=1+Arg_4 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1
1:n_f2___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f4___1(Arg_0,B_P,Arg_2,Arg_3,Arg_4,NoDet0):|:Arg_2<=2+Arg_4 && 2+Arg_4<=Arg_2 && Arg_0<=1+Arg_4 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_3<=1+Arg_1 && 0<=1+Arg_4 && 0<=Arg_1 && Arg_0<=0 && 1<=B_P && Arg_1<=B_P && B_P<=Arg_1
2:n_f2___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f4___2(Arg_0,B_P,Arg_2,Arg_3,Arg_4,NoDet0):|:Arg_2<=2+Arg_4 && 2+Arg_4<=Arg_2 && Arg_0<=1+Arg_4 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_3<=1+Arg_1 && 0<=1+Arg_4 && 0<=Arg_1 && Arg_1<=0 && B_P<=0
3:n_f2___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f2___5(Arg_0-1,Arg_1-1,Arg_0,Arg_1,Arg_0-2,Arg_5):|:1<=Arg_0 && 1<=Arg_1
4:n_f2___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f4___3(Arg_0,B_P,Arg_2,Arg_3,Arg_4,NoDet0):|:Arg_0<=0 && 1<=B_P && Arg_1<=B_P && B_P<=Arg_1
5:n_f2___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f4___4(Arg_0,B_P,Arg_2,Arg_3,Arg_4,NoDet0):|:Arg_1<=0 && B_P<=0
6:n_f3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> n_f2___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5)

Preprocessing

Eliminate variables {NoDet0,Arg_5} that do not contribute to the problem

Found invariant 1+Arg_4<=0 && 3+Arg_4<=Arg_3 && 2+Arg_4<=Arg_2 && Arg_2+Arg_4<=0 && 2+Arg_4<=Arg_1 && 1+Arg_4<=Arg_0 && 1+Arg_0+Arg_4<=0 && 0<=1+Arg_4 && 1<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && Arg_2<=2+Arg_4 && 0<=Arg_1+Arg_4 && 0<=1+Arg_0+Arg_4 && Arg_0<=1+Arg_4 && Arg_3<=1+Arg_1 && 2<=Arg_3 && 3<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && 2+Arg_0<=Arg_3 && Arg_2<=1 && Arg_2<=Arg_1 && Arg_2<=1+Arg_0 && Arg_0+Arg_2<=1 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 && 0<=Arg_0 for location n_f4___1

Found invariant 1<=Arg_1 && 1+Arg_0<=Arg_1 && Arg_0<=0 for location n_f4___3

Found invariant 2+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=1+Arg_4 && 0<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && Arg_2<=2+Arg_4 && 0<=1+Arg_1+Arg_4 && 0<=1+Arg_0+Arg_4 && Arg_0<=1+Arg_4 && Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location n_f2___5

Found invariant 2+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=1+Arg_4 && 0<=Arg_3+Arg_4 && Arg_3<=2+Arg_4 && 0<=Arg_2+Arg_4 && Arg_2<=2+Arg_4 && Arg_1<=1+Arg_4 && 0<=1+Arg_0+Arg_4 && Arg_0<=1+Arg_4 && Arg_3<=1 && Arg_3<=Arg_2 && Arg_1+Arg_3<=1 && Arg_3<=1+Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 1+Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 1+Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_0 for location n_f4___2

Found invariant Arg_1<=0 for location n_f4___4

Problem after Preprocessing

Start: n_f3
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars: B_P
Locations: n_f2___5, n_f2___6, n_f3, n_f4___1, n_f4___2, n_f4___3, n_f4___4
Transitions:
14:n_f2___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_f2___5(Arg_0-1,Arg_1-1,Arg_0,Arg_1,Arg_0-2):|:2+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=1+Arg_4 && 0<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && Arg_2<=2+Arg_4 && 0<=1+Arg_1+Arg_4 && 0<=1+Arg_0+Arg_4 && Arg_0<=1+Arg_4 && Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<=2+Arg_4 && 2+Arg_4<=Arg_2 && Arg_0<=1+Arg_4 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_3<=1+Arg_1 && 0<=1+Arg_4 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1
15:n_f2___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_f4___1(Arg_0,B_P,Arg_2,Arg_3,Arg_4):|:2+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=1+Arg_4 && 0<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && Arg_2<=2+Arg_4 && 0<=1+Arg_1+Arg_4 && 0<=1+Arg_0+Arg_4 && Arg_0<=1+Arg_4 && Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<=2+Arg_4 && 2+Arg_4<=Arg_2 && Arg_0<=1+Arg_4 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_3<=1+Arg_1 && 0<=1+Arg_4 && 0<=Arg_1 && Arg_0<=0 && 1<=B_P && Arg_1<=B_P && B_P<=Arg_1
16:n_f2___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_f4___2(Arg_0,B_P,Arg_2,Arg_3,Arg_4):|:2+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=1+Arg_4 && 0<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && Arg_2<=2+Arg_4 && 0<=1+Arg_1+Arg_4 && 0<=1+Arg_0+Arg_4 && Arg_0<=1+Arg_4 && Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<=2+Arg_4 && 2+Arg_4<=Arg_2 && Arg_0<=1+Arg_4 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_3<=1+Arg_1 && 0<=1+Arg_4 && 0<=Arg_1 && Arg_1<=0 && B_P<=0
17:n_f2___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_f2___5(Arg_0-1,Arg_1-1,Arg_0,Arg_1,Arg_0-2):|:1<=Arg_0 && 1<=Arg_1
18:n_f2___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_f4___3(Arg_0,B_P,Arg_2,Arg_3,Arg_4):|:Arg_0<=0 && 1<=B_P && Arg_1<=B_P && B_P<=Arg_1
19:n_f2___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_f4___4(Arg_0,B_P,Arg_2,Arg_3,Arg_4):|:Arg_1<=0 && B_P<=0
20:n_f3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_f2___6(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4)

MPRF for transition 14:n_f2___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_f2___5(Arg_0-1,Arg_1-1,Arg_0,Arg_1,Arg_0-2):|:2+Arg_4<=Arg_2 && 1+Arg_4<=Arg_0 && 0<=1+Arg_4 && 0<=Arg_3+Arg_4 && 0<=Arg_2+Arg_4 && Arg_2<=2+Arg_4 && 0<=1+Arg_1+Arg_4 && 0<=1+Arg_0+Arg_4 && Arg_0<=1+Arg_4 && Arg_3<=1+Arg_1 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=1+Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1<=Arg_0+Arg_2 && 1+Arg_0<=Arg_2 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 && Arg_2<=2+Arg_4 && 2+Arg_4<=Arg_2 && Arg_0<=1+Arg_4 && 1+Arg_4<=Arg_0 && 1+Arg_1<=Arg_3 && Arg_3<=1+Arg_1 && 0<=1+Arg_4 && 0<=Arg_1 && 1<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

Arg_0+1 {O(n)}

MPRF:

n_f2___5 [Arg_0+1 ]

All Bounds

Timebounds

Overall timebound:Arg_0+7 {O(n)}
14: n_f2___5->n_f2___5: Arg_0+1 {O(n)}
15: n_f2___5->n_f4___1: 1 {O(1)}
16: n_f2___5->n_f4___2: 1 {O(1)}
17: n_f2___6->n_f2___5: 1 {O(1)}
18: n_f2___6->n_f4___3: 1 {O(1)}
19: n_f2___6->n_f4___4: 1 {O(1)}
20: n_f3->n_f2___6: 1 {O(1)}

Costbounds

Overall costbound: Arg_0+7 {O(n)}
14: n_f2___5->n_f2___5: Arg_0+1 {O(n)}
15: n_f2___5->n_f4___1: 1 {O(1)}
16: n_f2___5->n_f4___2: 1 {O(1)}
17: n_f2___6->n_f2___5: 1 {O(1)}
18: n_f2___6->n_f4___3: 1 {O(1)}
19: n_f2___6->n_f4___4: 1 {O(1)}
20: n_f3->n_f2___6: 1 {O(1)}

Sizebounds

14: n_f2___5->n_f2___5, Arg_0: Arg_0 {O(n)}
14: n_f2___5->n_f2___5, Arg_1: Arg_1 {O(n)}
14: n_f2___5->n_f2___5, Arg_2: 2*Arg_0 {O(n)}
14: n_f2___5->n_f2___5, Arg_3: 2*Arg_1 {O(n)}
14: n_f2___5->n_f2___5, Arg_4: 2*Arg_0 {O(n)}
15: n_f2___5->n_f4___1, Arg_0: 0 {O(1)}
15: n_f2___5->n_f4___1, Arg_1: 2*Arg_1 {O(n)}
15: n_f2___5->n_f4___1, Arg_2: 1 {O(1)}
15: n_f2___5->n_f4___1, Arg_3: 3*Arg_1 {O(n)}
15: n_f2___5->n_f4___1, Arg_4: 1 {O(1)}
16: n_f2___5->n_f4___2, Arg_0: 2*Arg_0 {O(n)}
16: n_f2___5->n_f4___2, Arg_2: 3*Arg_0 {O(n)}
16: n_f2___5->n_f4___2, Arg_3: 1 {O(1)}
16: n_f2___5->n_f4___2, Arg_4: 3*Arg_0 {O(n)}
17: n_f2___6->n_f2___5, Arg_0: Arg_0 {O(n)}
17: n_f2___6->n_f2___5, Arg_1: Arg_1 {O(n)}
17: n_f2___6->n_f2___5, Arg_2: Arg_0 {O(n)}
17: n_f2___6->n_f2___5, Arg_3: Arg_1 {O(n)}
17: n_f2___6->n_f2___5, Arg_4: Arg_0 {O(n)}
18: n_f2___6->n_f4___3, Arg_0: Arg_0 {O(n)}
18: n_f2___6->n_f4___3, Arg_1: Arg_1 {O(n)}
18: n_f2___6->n_f4___3, Arg_2: Arg_2 {O(n)}
18: n_f2___6->n_f4___3, Arg_3: Arg_3 {O(n)}
18: n_f2___6->n_f4___3, Arg_4: Arg_4 {O(n)}
19: n_f2___6->n_f4___4, Arg_0: Arg_0 {O(n)}
19: n_f2___6->n_f4___4, Arg_2: Arg_2 {O(n)}
19: n_f2___6->n_f4___4, Arg_3: Arg_3 {O(n)}
19: n_f2___6->n_f4___4, Arg_4: Arg_4 {O(n)}
20: n_f3->n_f2___6, Arg_0: Arg_0 {O(n)}
20: n_f3->n_f2___6, Arg_1: Arg_1 {O(n)}
20: n_f3->n_f2___6, Arg_2: Arg_2 {O(n)}
20: n_f3->n_f2___6, Arg_3: Arg_3 {O(n)}
20: n_f3->n_f2___6, Arg_4: Arg_4 {O(n)}