Initial Problem

Start: n_f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: NoDet0
Locations: n_f0, n_f19___2, n_f19___3, n_f19___4, n_f29___1, n_f8___5, n_f8___6, n_f8___7
Transitions:
0:n_f0(Arg_0,Arg_1,Arg_2) -> n_f8___7(NoDet0,0,Arg_2)
1:n_f19___2(Arg_0,Arg_1,Arg_2) -> n_f19___2(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=10 && Arg_2<=9
2:n_f19___2(Arg_0,Arg_1,Arg_2) -> n_f29___1(Arg_0,Arg_1,Arg_2):|:Arg_2<=10 && 10<=Arg_2
3:n_f19___3(Arg_0,Arg_1,Arg_2) -> n_f19___2(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=9 && Arg_2<=9 && Arg_2<=10 && Arg_2<=9
4:n_f19___4(Arg_0,Arg_1,Arg_2) -> n_f19___3(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=9 && Arg_2<=9 && Arg_2<=10 && Arg_2<=0 && 0<=Arg_2 && 10<=Arg_1 && Arg_2<=9
5:n_f8___5(Arg_0,Arg_1,Arg_2) -> n_f19___4(Arg_0,Arg_1,0):|:Arg_1<=10 && 10<=Arg_1
6:n_f8___5(Arg_0,Arg_1,Arg_2) -> n_f8___5(Arg_0,Arg_1+1,Arg_2):|:Arg_1<=10 && Arg_1<=9
7:n_f8___6(Arg_0,Arg_1,Arg_2) -> n_f8___5(Arg_0,Arg_1+1,Arg_2):|:Arg_1<=9 && Arg_1<=9 && Arg_1<=10 && Arg_1<=9
8:n_f8___7(Arg_0,Arg_1,Arg_2) -> n_f8___6(Arg_0,Arg_1+1,Arg_2):|:Arg_1<=9 && Arg_1<=0 && 0<=Arg_1 && Arg_1<=9 && Arg_1<=10 && Arg_1<=9

Preprocessing

Eliminate variables {NoDet0,Arg_0} that do not contribute to the problem

Found invariant Arg_1<=0 && 0<=Arg_1 for location n_f8___7

Found invariant Arg_2<=10 && Arg_2<=Arg_1 && Arg_1+Arg_2<=20 && 10<=Arg_2 && 20<=Arg_1+Arg_2 && Arg_1<=Arg_2 && Arg_1<=10 && 10<=Arg_1 for location n_f29___1

Found invariant Arg_2<=1 && 9+Arg_2<=Arg_1 && Arg_1+Arg_2<=11 && 1<=Arg_2 && 11<=Arg_1+Arg_2 && Arg_1<=9+Arg_2 && Arg_1<=10 && 10<=Arg_1 for location n_f19___3

Found invariant Arg_1<=10 && 2<=Arg_1 for location n_f8___5

Found invariant Arg_1<=1 && 1<=Arg_1 for location n_f8___6

Found invariant Arg_2<=0 && 10+Arg_2<=Arg_1 && Arg_1+Arg_2<=10 && 0<=Arg_2 && 10<=Arg_1+Arg_2 && Arg_1<=10+Arg_2 && Arg_1<=10 && 10<=Arg_1 for location n_f19___4

Found invariant Arg_2<=10 && Arg_2<=Arg_1 && Arg_1+Arg_2<=20 && 2<=Arg_2 && 12<=Arg_1+Arg_2 && Arg_1<=8+Arg_2 && Arg_1<=10 && 10<=Arg_1 for location n_f19___2

Problem after Preprocessing

Start: n_f0
Program_Vars: Arg_1, Arg_2
Temp_Vars:
Locations: n_f0, n_f19___2, n_f19___3, n_f19___4, n_f29___1, n_f8___5, n_f8___6, n_f8___7
Transitions:
18:n_f0(Arg_1,Arg_2) -> n_f8___7(0,Arg_2)
19:n_f19___2(Arg_1,Arg_2) -> n_f19___2(Arg_1,Arg_2+1):|:Arg_2<=10 && Arg_2<=Arg_1 && Arg_1+Arg_2<=20 && 2<=Arg_2 && 12<=Arg_1+Arg_2 && Arg_1<=8+Arg_2 && Arg_1<=10 && 10<=Arg_1 && Arg_2<=10 && Arg_2<=9
20:n_f19___2(Arg_1,Arg_2) -> n_f29___1(Arg_1,Arg_2):|:Arg_2<=10 && Arg_2<=Arg_1 && Arg_1+Arg_2<=20 && 2<=Arg_2 && 12<=Arg_1+Arg_2 && Arg_1<=8+Arg_2 && Arg_1<=10 && 10<=Arg_1 && Arg_2<=10 && 10<=Arg_2
21:n_f19___3(Arg_1,Arg_2) -> n_f19___2(Arg_1,Arg_2+1):|:Arg_2<=1 && 9+Arg_2<=Arg_1 && Arg_1+Arg_2<=11 && 1<=Arg_2 && 11<=Arg_1+Arg_2 && Arg_1<=9+Arg_2 && Arg_1<=10 && 10<=Arg_1 && Arg_2<=9 && Arg_2<=9 && Arg_2<=10 && Arg_2<=9
22:n_f19___4(Arg_1,Arg_2) -> n_f19___3(Arg_1,Arg_2+1):|:Arg_2<=0 && 10+Arg_2<=Arg_1 && Arg_1+Arg_2<=10 && 0<=Arg_2 && 10<=Arg_1+Arg_2 && Arg_1<=10+Arg_2 && Arg_1<=10 && 10<=Arg_1 && Arg_2<=9 && Arg_2<=9 && Arg_2<=10 && Arg_2<=0 && 0<=Arg_2 && 10<=Arg_1 && Arg_2<=9
23:n_f8___5(Arg_1,Arg_2) -> n_f19___4(Arg_1,0):|:Arg_1<=10 && 2<=Arg_1 && Arg_1<=10 && 10<=Arg_1
24:n_f8___5(Arg_1,Arg_2) -> n_f8___5(Arg_1+1,Arg_2):|:Arg_1<=10 && 2<=Arg_1 && Arg_1<=10 && Arg_1<=9
25:n_f8___6(Arg_1,Arg_2) -> n_f8___5(Arg_1+1,Arg_2):|:Arg_1<=1 && 1<=Arg_1 && Arg_1<=9 && Arg_1<=9 && Arg_1<=10 && Arg_1<=9
26:n_f8___7(Arg_1,Arg_2) -> n_f8___6(Arg_1+1,Arg_2):|:Arg_1<=0 && 0<=Arg_1 && Arg_1<=9 && Arg_1<=0 && 0<=Arg_1 && Arg_1<=9 && Arg_1<=10 && Arg_1<=9

MPRF for transition 24:n_f8___5(Arg_1,Arg_2) -> n_f8___5(Arg_1+1,Arg_2):|:Arg_1<=10 && 2<=Arg_1 && Arg_1<=10 && Arg_1<=9 of depth 1:

new bound:

13 {O(1)}

MPRF:

n_f8___5 [11-Arg_1 ]

MPRF for transition 19:n_f19___2(Arg_1,Arg_2) -> n_f19___2(Arg_1,Arg_2+1):|:Arg_2<=10 && Arg_2<=Arg_1 && Arg_1+Arg_2<=20 && 2<=Arg_2 && 12<=Arg_1+Arg_2 && Arg_1<=8+Arg_2 && Arg_1<=10 && 10<=Arg_1 && Arg_2<=10 && Arg_2<=9 of depth 1:

new bound:

13 {O(1)}

MPRF:

n_f19___2 [11-Arg_2 ]

All Bounds

Timebounds

Overall timebound:33 {O(1)}
18: n_f0->n_f8___7: 1 {O(1)}
19: n_f19___2->n_f19___2: 13 {O(1)}
20: n_f19___2->n_f29___1: 1 {O(1)}
21: n_f19___3->n_f19___2: 1 {O(1)}
22: n_f19___4->n_f19___3: 1 {O(1)}
23: n_f8___5->n_f19___4: 1 {O(1)}
24: n_f8___5->n_f8___5: 13 {O(1)}
25: n_f8___6->n_f8___5: 1 {O(1)}
26: n_f8___7->n_f8___6: 1 {O(1)}

Costbounds

Overall costbound: 33 {O(1)}
18: n_f0->n_f8___7: 1 {O(1)}
19: n_f19___2->n_f19___2: 13 {O(1)}
20: n_f19___2->n_f29___1: 1 {O(1)}
21: n_f19___3->n_f19___2: 1 {O(1)}
22: n_f19___4->n_f19___3: 1 {O(1)}
23: n_f8___5->n_f19___4: 1 {O(1)}
24: n_f8___5->n_f8___5: 13 {O(1)}
25: n_f8___6->n_f8___5: 1 {O(1)}
26: n_f8___7->n_f8___6: 1 {O(1)}

Sizebounds

18: n_f0->n_f8___7, Arg_1: 0 {O(1)}
18: n_f0->n_f8___7, Arg_2: Arg_2 {O(n)}
19: n_f19___2->n_f19___2, Arg_1: 10 {O(1)}
19: n_f19___2->n_f19___2, Arg_2: 10 {O(1)}
20: n_f19___2->n_f29___1, Arg_1: 10 {O(1)}
20: n_f19___2->n_f29___1, Arg_2: 10 {O(1)}
21: n_f19___3->n_f19___2, Arg_1: 10 {O(1)}
21: n_f19___3->n_f19___2, Arg_2: 2 {O(1)}
22: n_f19___4->n_f19___3, Arg_1: 10 {O(1)}
22: n_f19___4->n_f19___3, Arg_2: 1 {O(1)}
23: n_f8___5->n_f19___4, Arg_1: 10 {O(1)}
23: n_f8___5->n_f19___4, Arg_2: 0 {O(1)}
24: n_f8___5->n_f8___5, Arg_1: 10 {O(1)}
24: n_f8___5->n_f8___5, Arg_2: Arg_2 {O(n)}
25: n_f8___6->n_f8___5, Arg_1: 2 {O(1)}
25: n_f8___6->n_f8___5, Arg_2: Arg_2 {O(n)}
26: n_f8___7->n_f8___6, Arg_1: 1 {O(1)}
26: n_f8___7->n_f8___6, Arg_2: Arg_2 {O(n)}