Initial Problem

Start: n_f1
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4
Temp_Vars:
Locations: n_f1, n_f2___1, n_f2___4, n_f300___2, n_f300___3, n_f300___5
Transitions:
0:n_f1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_f300___5(1000,Arg_1,Arg_2,Arg_3,Arg_4)
1:n_f300___2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_f2___1(Arg_0,Arg_1,0,0,0):|:Arg_1<=9 && 100<=Arg_0 && Arg_1<=9 && Arg_1<=9 && Arg_0<=100
2:n_f300___2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_f300___2(Arg_0-1,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=9 && 100<=Arg_0 && Arg_1<=9 && 101<=Arg_0 && Arg_1<=9
3:n_f300___3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_f300___2(Arg_0-1,Arg_1,Arg_2,Arg_3,Arg_4):|:Arg_1<=9 && 101<=Arg_0 && 101<=Arg_0 && Arg_1<=9 && 100<=Arg_0 && Arg_1<=9 && 101<=Arg_0 && Arg_1<=9
4:n_f300___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_f2___4(Arg_0,Arg_1,0,0,0):|:101<=Arg_0 && Arg_0<=1000 && 1000<=Arg_0 && 10<=Arg_1
5:n_f300___5(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4) -> n_f300___3(Arg_0-1,Arg_1,Arg_2,Arg_3,Arg_4):|:101<=Arg_0 && Arg_0<=1000 && 1000<=Arg_0 && 101<=Arg_0 && Arg_1<=9

Preprocessing

Eliminate variables {Arg_2,Arg_3,Arg_4} that do not contribute to the problem

Found invariant Arg_1<=9 && 91+Arg_1<=Arg_0 && Arg_0+Arg_1<=109 && Arg_0<=100 && 100<=Arg_0 for location n_f2___1

Found invariant Arg_1<=9 && 91+Arg_1<=Arg_0 && Arg_0+Arg_1<=1007 && Arg_0<=998 && 100<=Arg_0 for location n_f300___2

Found invariant Arg_1<=9 && 990+Arg_1<=Arg_0 && Arg_0+Arg_1<=1008 && Arg_0<=999 && 999<=Arg_0 for location n_f300___3

Found invariant Arg_0<=1000 && 1000<=Arg_0 for location n_f300___5

Found invariant 10<=Arg_1 && 1010<=Arg_0+Arg_1 && Arg_0<=990+Arg_1 && Arg_0<=1000 && 1000<=Arg_0 for location n_f2___4

Problem after Preprocessing

Start: n_f1
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_f1, n_f2___1, n_f2___4, n_f300___2, n_f300___3, n_f300___5
Transitions:
12:n_f1(Arg_0,Arg_1) -> n_f300___5(1000,Arg_1)
13:n_f300___2(Arg_0,Arg_1) -> n_f2___1(Arg_0,Arg_1):|:Arg_1<=9 && 91+Arg_1<=Arg_0 && Arg_0+Arg_1<=1007 && Arg_0<=998 && 100<=Arg_0 && Arg_1<=9 && 100<=Arg_0 && Arg_1<=9 && Arg_1<=9 && Arg_0<=100
14:n_f300___2(Arg_0,Arg_1) -> n_f300___2(Arg_0-1,Arg_1):|:Arg_1<=9 && 91+Arg_1<=Arg_0 && Arg_0+Arg_1<=1007 && Arg_0<=998 && 100<=Arg_0 && Arg_1<=9 && 100<=Arg_0 && Arg_1<=9 && 101<=Arg_0 && Arg_1<=9
15:n_f300___3(Arg_0,Arg_1) -> n_f300___2(Arg_0-1,Arg_1):|:Arg_1<=9 && 990+Arg_1<=Arg_0 && Arg_0+Arg_1<=1008 && Arg_0<=999 && 999<=Arg_0 && Arg_1<=9 && 101<=Arg_0 && 101<=Arg_0 && Arg_1<=9 && 100<=Arg_0 && Arg_1<=9 && 101<=Arg_0 && Arg_1<=9
16:n_f300___5(Arg_0,Arg_1) -> n_f2___4(Arg_0,Arg_1):|:Arg_0<=1000 && 1000<=Arg_0 && 101<=Arg_0 && Arg_0<=1000 && 1000<=Arg_0 && 10<=Arg_1
17:n_f300___5(Arg_0,Arg_1) -> n_f300___3(Arg_0-1,Arg_1):|:Arg_0<=1000 && 1000<=Arg_0 && 101<=Arg_0 && Arg_0<=1000 && 1000<=Arg_0 && 101<=Arg_0 && Arg_1<=9

MPRF for transition 14:n_f300___2(Arg_0,Arg_1) -> n_f300___2(Arg_0-1,Arg_1):|:Arg_1<=9 && 91+Arg_1<=Arg_0 && Arg_0+Arg_1<=1007 && Arg_0<=998 && 100<=Arg_0 && Arg_1<=9 && 100<=Arg_0 && Arg_1<=9 && 101<=Arg_0 && Arg_1<=9 of depth 1:

new bound:

998 {O(1)}

MPRF:

n_f300___2 [Arg_0 ]

All Bounds

Timebounds

Overall timebound:1003 {O(1)}
12: n_f1->n_f300___5: 1 {O(1)}
13: n_f300___2->n_f2___1: 1 {O(1)}
14: n_f300___2->n_f300___2: 998 {O(1)}
15: n_f300___3->n_f300___2: 1 {O(1)}
16: n_f300___5->n_f2___4: 1 {O(1)}
17: n_f300___5->n_f300___3: 1 {O(1)}

Costbounds

Overall costbound: 1003 {O(1)}
12: n_f1->n_f300___5: 1 {O(1)}
13: n_f300___2->n_f2___1: 1 {O(1)}
14: n_f300___2->n_f300___2: 998 {O(1)}
15: n_f300___3->n_f300___2: 1 {O(1)}
16: n_f300___5->n_f2___4: 1 {O(1)}
17: n_f300___5->n_f300___3: 1 {O(1)}

Sizebounds

12: n_f1->n_f300___5, Arg_0: 1000 {O(1)}
12: n_f1->n_f300___5, Arg_1: Arg_1 {O(n)}
13: n_f300___2->n_f2___1, Arg_0: 100 {O(1)}
13: n_f300___2->n_f2___1, Arg_1: Arg_1 {O(n)}
14: n_f300___2->n_f300___2, Arg_0: 997 {O(1)}
14: n_f300___2->n_f300___2, Arg_1: Arg_1 {O(n)}
15: n_f300___3->n_f300___2, Arg_0: 998 {O(1)}
15: n_f300___3->n_f300___2, Arg_1: Arg_1 {O(n)}
16: n_f300___5->n_f2___4, Arg_0: 1000 {O(1)}
16: n_f300___5->n_f2___4, Arg_1: Arg_1 {O(n)}
17: n_f300___5->n_f300___3, Arg_0: 999 {O(1)}
17: n_f300___5->n_f300___3, Arg_1: Arg_1 {O(n)}