Initial Problem

Start: n_f0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: n_f0, n_f19___5, n_f19___6, n_f19___7, n_f28___2, n_f28___3, n_f28___4, n_f36___1
Transitions:
0:n_f0(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f19___7(Arg_0,999,Arg_2,1)
1:n_f19___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f19___5(Arg_0,Arg_1-1,Arg_2,Arg_3):|:0<=1+Arg_1 && 0<=Arg_1
2:n_f19___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f28___4(Arg_0,Arg_1,999,Arg_3):|:0<=1+Arg_1 && 1+Arg_1<=0
3:n_f19___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f19___5(Arg_0,Arg_1-1,Arg_2,Arg_3):|:0<=Arg_1 && 0<=Arg_1 && 0<=1+Arg_1 && 0<=Arg_1
4:n_f19___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f19___6(Arg_0,Arg_1-1,Arg_2,Arg_3):|:0<=Arg_1 && 0<=Arg_1 && 0<=1+Arg_1 && Arg_1<=999 && 999<=Arg_1 && Arg_3<=1 && 1<=Arg_3 && 0<=Arg_1
5:n_f28___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f28___2(Arg_0,Arg_1,Arg_2-1,Arg_3):|:0<=1+Arg_2 && 0<=Arg_2
6:n_f28___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f36___1(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=1+Arg_2 && 1+Arg_2<=0
7:n_f28___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f28___2(Arg_0,Arg_1,Arg_2-1,Arg_3):|:0<=Arg_2 && 0<=Arg_2 && 0<=1+Arg_2 && 0<=Arg_2
8:n_f28___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f28___3(Arg_0,Arg_1,Arg_2-1,Arg_3):|:0<=Arg_2 && 0<=Arg_2 && 0<=1+Arg_2 && Arg_2<=999 && 999<=Arg_2 && 1+Arg_1<=0 && 0<=Arg_2

Preprocessing

Eliminate variables {Arg_0} that do not contribute to the problem

Found invariant Arg_3<=1 && 997+Arg_3<=Arg_2 && Arg_2+Arg_3<=999 && Arg_3<=2+Arg_1 && Arg_1+Arg_3<=0 && 1<=Arg_3 && 999<=Arg_2+Arg_3 && Arg_2<=997+Arg_3 && 0<=Arg_1+Arg_3 && 2+Arg_1<=Arg_3 && Arg_2<=998 && Arg_2<=999+Arg_1 && Arg_1+Arg_2<=997 && 998<=Arg_2 && 997<=Arg_1+Arg_2 && 999+Arg_1<=Arg_2 && 1+Arg_1<=0 && 0<=1+Arg_1 for location n_f28___3

Found invariant Arg_3<=1 && Arg_3<=2+Arg_1 && Arg_1+Arg_3<=998 && 1<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=996+Arg_3 && Arg_1<=997 && 0<=1+Arg_1 for location n_f19___5

Found invariant Arg_3<=1 && Arg_3<=2+Arg_2 && Arg_2+Arg_3<=998 && Arg_3<=2+Arg_1 && Arg_1+Arg_3<=0 && 1<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=996+Arg_3 && 0<=Arg_1+Arg_3 && 2+Arg_1<=Arg_3 && Arg_2<=997 && Arg_2<=998+Arg_1 && Arg_1+Arg_2<=996 && 0<=1+Arg_2 && 0<=2+Arg_1+Arg_2 && Arg_1<=Arg_2 && 1+Arg_1<=0 && 0<=1+Arg_1 for location n_f28___2

Found invariant Arg_3<=1 && Arg_3<=2+Arg_2 && Arg_2+Arg_3<=0 && Arg_3<=2+Arg_1 && Arg_1+Arg_3<=0 && 1<=Arg_3 && 0<=Arg_2+Arg_3 && 2+Arg_2<=Arg_3 && 0<=Arg_1+Arg_3 && 2+Arg_1<=Arg_3 && 1+Arg_2<=0 && Arg_2<=Arg_1 && 2+Arg_1+Arg_2<=0 && 0<=1+Arg_2 && 0<=2+Arg_1+Arg_2 && Arg_1<=Arg_2 && 1+Arg_1<=0 && 0<=1+Arg_1 for location n_f36___1

Found invariant Arg_3<=1 && 997+Arg_3<=Arg_1 && Arg_1+Arg_3<=999 && 1<=Arg_3 && 999<=Arg_1+Arg_3 && Arg_1<=997+Arg_3 && Arg_1<=998 && 998<=Arg_1 for location n_f19___6

Found invariant Arg_3<=1 && 998+Arg_3<=Arg_2 && Arg_2+Arg_3<=1000 && Arg_3<=2+Arg_1 && Arg_1+Arg_3<=0 && 1<=Arg_3 && 1000<=Arg_2+Arg_3 && Arg_2<=998+Arg_3 && 0<=Arg_1+Arg_3 && 2+Arg_1<=Arg_3 && Arg_2<=999 && Arg_2<=1000+Arg_1 && Arg_1+Arg_2<=998 && 999<=Arg_2 && 998<=Arg_1+Arg_2 && 1000+Arg_1<=Arg_2 && 1+Arg_1<=0 && 0<=1+Arg_1 for location n_f28___4

Found invariant Arg_3<=1 && 998+Arg_3<=Arg_1 && Arg_1+Arg_3<=1000 && 1<=Arg_3 && 1000<=Arg_1+Arg_3 && Arg_1<=998+Arg_3 && Arg_1<=999 && 999<=Arg_1 for location n_f19___7

Problem after Preprocessing

Start: n_f0
Program_Vars: Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: n_f0, n_f19___5, n_f19___6, n_f19___7, n_f28___2, n_f28___3, n_f28___4, n_f36___1
Transitions:
18:n_f0(Arg_1,Arg_2,Arg_3) -> n_f19___7(999,Arg_2,1)
19:n_f19___5(Arg_1,Arg_2,Arg_3) -> n_f19___5(Arg_1-1,Arg_2,Arg_3):|:Arg_3<=1 && Arg_3<=2+Arg_1 && Arg_1+Arg_3<=998 && 1<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=996+Arg_3 && Arg_1<=997 && 0<=1+Arg_1 && 0<=1+Arg_1 && 0<=Arg_1
20:n_f19___5(Arg_1,Arg_2,Arg_3) -> n_f28___4(Arg_1,999,Arg_3):|:Arg_3<=1 && Arg_3<=2+Arg_1 && Arg_1+Arg_3<=998 && 1<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=996+Arg_3 && Arg_1<=997 && 0<=1+Arg_1 && 0<=1+Arg_1 && 1+Arg_1<=0
21:n_f19___6(Arg_1,Arg_2,Arg_3) -> n_f19___5(Arg_1-1,Arg_2,Arg_3):|:Arg_3<=1 && 997+Arg_3<=Arg_1 && Arg_1+Arg_3<=999 && 1<=Arg_3 && 999<=Arg_1+Arg_3 && Arg_1<=997+Arg_3 && Arg_1<=998 && 998<=Arg_1 && 0<=Arg_1 && 0<=Arg_1 && 0<=1+Arg_1 && 0<=Arg_1
22:n_f19___7(Arg_1,Arg_2,Arg_3) -> n_f19___6(Arg_1-1,Arg_2,Arg_3):|:Arg_3<=1 && 998+Arg_3<=Arg_1 && Arg_1+Arg_3<=1000 && 1<=Arg_3 && 1000<=Arg_1+Arg_3 && Arg_1<=998+Arg_3 && Arg_1<=999 && 999<=Arg_1 && 0<=Arg_1 && 0<=Arg_1 && 0<=1+Arg_1 && Arg_1<=999 && 999<=Arg_1 && Arg_3<=1 && 1<=Arg_3 && 0<=Arg_1
23:n_f28___2(Arg_1,Arg_2,Arg_3) -> n_f28___2(Arg_1,Arg_2-1,Arg_3):|:Arg_3<=1 && Arg_3<=2+Arg_2 && Arg_2+Arg_3<=998 && Arg_3<=2+Arg_1 && Arg_1+Arg_3<=0 && 1<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=996+Arg_3 && 0<=Arg_1+Arg_3 && 2+Arg_1<=Arg_3 && Arg_2<=997 && Arg_2<=998+Arg_1 && Arg_1+Arg_2<=996 && 0<=1+Arg_2 && 0<=2+Arg_1+Arg_2 && Arg_1<=Arg_2 && 1+Arg_1<=0 && 0<=1+Arg_1 && 0<=1+Arg_2 && 0<=Arg_2
24:n_f28___2(Arg_1,Arg_2,Arg_3) -> n_f36___1(Arg_1,Arg_2,Arg_3):|:Arg_3<=1 && Arg_3<=2+Arg_2 && Arg_2+Arg_3<=998 && Arg_3<=2+Arg_1 && Arg_1+Arg_3<=0 && 1<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=996+Arg_3 && 0<=Arg_1+Arg_3 && 2+Arg_1<=Arg_3 && Arg_2<=997 && Arg_2<=998+Arg_1 && Arg_1+Arg_2<=996 && 0<=1+Arg_2 && 0<=2+Arg_1+Arg_2 && Arg_1<=Arg_2 && 1+Arg_1<=0 && 0<=1+Arg_1 && 0<=1+Arg_2 && 1+Arg_2<=0
25:n_f28___3(Arg_1,Arg_2,Arg_3) -> n_f28___2(Arg_1,Arg_2-1,Arg_3):|:Arg_3<=1 && 997+Arg_3<=Arg_2 && Arg_2+Arg_3<=999 && Arg_3<=2+Arg_1 && Arg_1+Arg_3<=0 && 1<=Arg_3 && 999<=Arg_2+Arg_3 && Arg_2<=997+Arg_3 && 0<=Arg_1+Arg_3 && 2+Arg_1<=Arg_3 && Arg_2<=998 && Arg_2<=999+Arg_1 && Arg_1+Arg_2<=997 && 998<=Arg_2 && 997<=Arg_1+Arg_2 && 999+Arg_1<=Arg_2 && 1+Arg_1<=0 && 0<=1+Arg_1 && 0<=Arg_2 && 0<=Arg_2 && 0<=1+Arg_2 && 0<=Arg_2
26:n_f28___4(Arg_1,Arg_2,Arg_3) -> n_f28___3(Arg_1,Arg_2-1,Arg_3):|:Arg_3<=1 && 998+Arg_3<=Arg_2 && Arg_2+Arg_3<=1000 && Arg_3<=2+Arg_1 && Arg_1+Arg_3<=0 && 1<=Arg_3 && 1000<=Arg_2+Arg_3 && Arg_2<=998+Arg_3 && 0<=Arg_1+Arg_3 && 2+Arg_1<=Arg_3 && Arg_2<=999 && Arg_2<=1000+Arg_1 && Arg_1+Arg_2<=998 && 999<=Arg_2 && 998<=Arg_1+Arg_2 && 1000+Arg_1<=Arg_2 && 1+Arg_1<=0 && 0<=1+Arg_1 && 0<=Arg_2 && 0<=Arg_2 && 0<=1+Arg_2 && Arg_2<=999 && 999<=Arg_2 && 1+Arg_1<=0 && 0<=Arg_2

MPRF for transition 19:n_f19___5(Arg_1,Arg_2,Arg_3) -> n_f19___5(Arg_1-1,Arg_2,Arg_3):|:Arg_3<=1 && Arg_3<=2+Arg_1 && Arg_1+Arg_3<=998 && 1<=Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=996+Arg_3 && Arg_1<=997 && 0<=1+Arg_1 && 0<=1+Arg_1 && 0<=Arg_1 of depth 1:

new bound:

998 {O(1)}

MPRF:

n_f19___5 [Arg_1+1 ]

MPRF for transition 23:n_f28___2(Arg_1,Arg_2,Arg_3) -> n_f28___2(Arg_1,Arg_2-1,Arg_3):|:Arg_3<=1 && Arg_3<=2+Arg_2 && Arg_2+Arg_3<=998 && Arg_3<=2+Arg_1 && Arg_1+Arg_3<=0 && 1<=Arg_3 && 0<=Arg_2+Arg_3 && Arg_2<=996+Arg_3 && 0<=Arg_1+Arg_3 && 2+Arg_1<=Arg_3 && Arg_2<=997 && Arg_2<=998+Arg_1 && Arg_1+Arg_2<=996 && 0<=1+Arg_2 && 0<=2+Arg_1+Arg_2 && Arg_1<=Arg_2 && 1+Arg_1<=0 && 0<=1+Arg_1 && 0<=1+Arg_2 && 0<=Arg_2 of depth 1:

new bound:

998 {O(1)}

MPRF:

n_f28___2 [Arg_2+1 ]

All Bounds

Timebounds

Overall timebound:2003 {O(1)}
18: n_f0->n_f19___7: 1 {O(1)}
19: n_f19___5->n_f19___5: 998 {O(1)}
20: n_f19___5->n_f28___4: 1 {O(1)}
21: n_f19___6->n_f19___5: 1 {O(1)}
22: n_f19___7->n_f19___6: 1 {O(1)}
23: n_f28___2->n_f28___2: 998 {O(1)}
24: n_f28___2->n_f36___1: 1 {O(1)}
25: n_f28___3->n_f28___2: 1 {O(1)}
26: n_f28___4->n_f28___3: 1 {O(1)}

Costbounds

Overall costbound: 2003 {O(1)}
18: n_f0->n_f19___7: 1 {O(1)}
19: n_f19___5->n_f19___5: 998 {O(1)}
20: n_f19___5->n_f28___4: 1 {O(1)}
21: n_f19___6->n_f19___5: 1 {O(1)}
22: n_f19___7->n_f19___6: 1 {O(1)}
23: n_f28___2->n_f28___2: 998 {O(1)}
24: n_f28___2->n_f36___1: 1 {O(1)}
25: n_f28___3->n_f28___2: 1 {O(1)}
26: n_f28___4->n_f28___3: 1 {O(1)}

Sizebounds

18: n_f0->n_f19___7, Arg_1: 999 {O(1)}
18: n_f0->n_f19___7, Arg_2: Arg_2 {O(n)}
18: n_f0->n_f19___7, Arg_3: 1 {O(1)}
19: n_f19___5->n_f19___5, Arg_1: 996 {O(1)}
19: n_f19___5->n_f19___5, Arg_2: Arg_2 {O(n)}
19: n_f19___5->n_f19___5, Arg_3: 1 {O(1)}
20: n_f19___5->n_f28___4, Arg_1: 1 {O(1)}
20: n_f19___5->n_f28___4, Arg_2: 999 {O(1)}
20: n_f19___5->n_f28___4, Arg_3: 1 {O(1)}
21: n_f19___6->n_f19___5, Arg_1: 997 {O(1)}
21: n_f19___6->n_f19___5, Arg_2: Arg_2 {O(n)}
21: n_f19___6->n_f19___5, Arg_3: 1 {O(1)}
22: n_f19___7->n_f19___6, Arg_1: 998 {O(1)}
22: n_f19___7->n_f19___6, Arg_2: Arg_2 {O(n)}
22: n_f19___7->n_f19___6, Arg_3: 1 {O(1)}
23: n_f28___2->n_f28___2, Arg_1: 1 {O(1)}
23: n_f28___2->n_f28___2, Arg_2: 996 {O(1)}
23: n_f28___2->n_f28___2, Arg_3: 1 {O(1)}
24: n_f28___2->n_f36___1, Arg_1: 1 {O(1)}
24: n_f28___2->n_f36___1, Arg_2: 1 {O(1)}
24: n_f28___2->n_f36___1, Arg_3: 1 {O(1)}
25: n_f28___3->n_f28___2, Arg_1: 1 {O(1)}
25: n_f28___3->n_f28___2, Arg_2: 997 {O(1)}
25: n_f28___3->n_f28___2, Arg_3: 1 {O(1)}
26: n_f28___4->n_f28___3, Arg_1: 1 {O(1)}
26: n_f28___4->n_f28___3, Arg_2: 998 {O(1)}
26: n_f28___4->n_f28___3, Arg_3: 1 {O(1)}