Initial Problem

Start: n_f3
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars: NoDet0
Locations: n_f0___2, n_f0___3, n_f0___4, n_f0___5, n_f3, n_f4___1
Transitions:
0:n_f0___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f0___2(Arg_0+1,Arg_1,Arg_0,Arg_3):|:Arg_0<=1+Arg_2 && 1+Arg_2<=Arg_0 && Arg_0<=10 && Arg_0<=9
1:n_f0___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f4___1(Arg_0,NoDet0,Arg_2,Arg_3):|:Arg_0<=1+Arg_2 && 1+Arg_2<=Arg_0 && Arg_0<=10 && 10<=Arg_0
2:n_f0___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f0___2(Arg_0+1,Arg_1,Arg_0,Arg_3):|:Arg_0<=9 && Arg_0<=9 && Arg_0<=1+Arg_2 && 1+Arg_2<=Arg_0 && Arg_0<=10 && Arg_0<=9
3:n_f0___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f0___3(Arg_0+1,Arg_1,Arg_0,Arg_3):|:Arg_0<=9 && Arg_0<=9 && Arg_0<=1+Arg_2 && 1+Arg_2<=Arg_0 && Arg_0<=10 && Arg_0<=1 && 1<=Arg_0 && Arg_0<=9
4:n_f0___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f0___4(Arg_0+1,Arg_1,Arg_0,Arg_3):|:Arg_0<=9 && Arg_0<=9 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=9
5:n_f3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_f0___5(0,Arg_1,Arg_2,Arg_3)

Preprocessing

Eliminate variables {NoDet0,Arg_1,Arg_3} that do not contribute to the problem

Found invariant Arg_2<=9 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=19 && 9<=Arg_2 && 19<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && Arg_0<=10 && 10<=Arg_0 for location n_f4___1

Found invariant Arg_2<=1 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=3 && 1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && Arg_0<=2 && 2<=Arg_0 for location n_f0___3

Found invariant Arg_2<=0 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=1 && 0<=Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && Arg_0<=1 && 1<=Arg_0 for location n_f0___4

Found invariant Arg_2<=9 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=19 && 2<=Arg_2 && 5<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && Arg_0<=10 && 3<=Arg_0 for location n_f0___2

Found invariant Arg_0<=0 && 0<=Arg_0 for location n_f0___5

Problem after Preprocessing

Start: n_f3
Program_Vars: Arg_0, Arg_2
Temp_Vars:
Locations: n_f0___2, n_f0___3, n_f0___4, n_f0___5, n_f3, n_f4___1
Transitions:
12:n_f0___2(Arg_0,Arg_2) -> n_f0___2(Arg_0+1,Arg_0):|:Arg_2<=9 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=19 && 2<=Arg_2 && 5<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && Arg_0<=10 && 3<=Arg_0 && Arg_0<=1+Arg_2 && 1+Arg_2<=Arg_0 && Arg_0<=10 && Arg_0<=9
13:n_f0___2(Arg_0,Arg_2) -> n_f4___1(Arg_0,Arg_2):|:Arg_2<=9 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=19 && 2<=Arg_2 && 5<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && Arg_0<=10 && 3<=Arg_0 && Arg_0<=1+Arg_2 && 1+Arg_2<=Arg_0 && Arg_0<=10 && 10<=Arg_0
14:n_f0___3(Arg_0,Arg_2) -> n_f0___2(Arg_0+1,Arg_0):|:Arg_2<=1 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=3 && 1<=Arg_2 && 3<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && Arg_0<=2 && 2<=Arg_0 && Arg_0<=9 && Arg_0<=9 && Arg_0<=1+Arg_2 && 1+Arg_2<=Arg_0 && Arg_0<=10 && Arg_0<=9
15:n_f0___4(Arg_0,Arg_2) -> n_f0___3(Arg_0+1,Arg_0):|:Arg_2<=0 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=1 && 0<=Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && Arg_0<=1 && 1<=Arg_0 && Arg_0<=9 && Arg_0<=9 && Arg_0<=1+Arg_2 && 1+Arg_2<=Arg_0 && Arg_0<=10 && Arg_0<=1 && 1<=Arg_0 && Arg_0<=9
16:n_f0___5(Arg_0,Arg_2) -> n_f0___4(Arg_0+1,Arg_0):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=9 && Arg_0<=9 && Arg_0<=0 && 0<=Arg_0 && Arg_0<=9
17:n_f3(Arg_0,Arg_2) -> n_f0___5(0,Arg_2)

MPRF for transition 12:n_f0___2(Arg_0,Arg_2) -> n_f0___2(Arg_0+1,Arg_0):|:Arg_2<=9 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=19 && 2<=Arg_2 && 5<=Arg_0+Arg_2 && Arg_0<=1+Arg_2 && Arg_0<=10 && 3<=Arg_0 && Arg_0<=1+Arg_2 && 1+Arg_2<=Arg_0 && Arg_0<=10 && Arg_0<=9 of depth 1:

new bound:

14 {O(1)}

MPRF:

n_f0___2 [11-Arg_0 ]

All Bounds

Timebounds

Overall timebound:19 {O(1)}
12: n_f0___2->n_f0___2: 14 {O(1)}
13: n_f0___2->n_f4___1: 1 {O(1)}
14: n_f0___3->n_f0___2: 1 {O(1)}
15: n_f0___4->n_f0___3: 1 {O(1)}
16: n_f0___5->n_f0___4: 1 {O(1)}
17: n_f3->n_f0___5: 1 {O(1)}

Costbounds

Overall costbound: 19 {O(1)}
12: n_f0___2->n_f0___2: 14 {O(1)}
13: n_f0___2->n_f4___1: 1 {O(1)}
14: n_f0___3->n_f0___2: 1 {O(1)}
15: n_f0___4->n_f0___3: 1 {O(1)}
16: n_f0___5->n_f0___4: 1 {O(1)}
17: n_f3->n_f0___5: 1 {O(1)}

Sizebounds

12: n_f0___2->n_f0___2, Arg_0: 10 {O(1)}
12: n_f0___2->n_f0___2, Arg_2: 9 {O(1)}
13: n_f0___2->n_f4___1, Arg_0: 10 {O(1)}
13: n_f0___2->n_f4___1, Arg_2: 9 {O(1)}
14: n_f0___3->n_f0___2, Arg_0: 3 {O(1)}
14: n_f0___3->n_f0___2, Arg_2: 2 {O(1)}
15: n_f0___4->n_f0___3, Arg_0: 2 {O(1)}
15: n_f0___4->n_f0___3, Arg_2: 1 {O(1)}
16: n_f0___5->n_f0___4, Arg_0: 1 {O(1)}
16: n_f0___5->n_f0___4, Arg_2: 0 {O(1)}
17: n_f3->n_f0___5, Arg_0: 0 {O(1)}
17: n_f3->n_f0___5, Arg_2: Arg_2 {O(n)}