Initial Problem

Start: n_f0
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: NoDet0
Locations: n_f0, n_f15___3, n_f15___5, n_f18___2, n_f18___4, n_f28___1
Transitions:
0:n_f0(Arg_0,Arg_1,Arg_2) -> n_f15___5(2,Arg_1,Arg_2)
1:n_f15___3(Arg_0,Arg_1,Arg_2) -> n_f18___4(Arg_0,Arg_0,Arg_2):|:Arg_0<=10
2:n_f15___3(Arg_0,Arg_1,Arg_2) -> n_f28___1(Arg_0,Arg_1,Arg_2):|:11<=Arg_0
3:n_f15___5(Arg_0,Arg_1,Arg_2) -> n_f18___4(Arg_0,Arg_0,Arg_2):|:Arg_0<=10 && Arg_0<=2 && 2<=Arg_0 && Arg_0<=10 && Arg_0<=10
4:n_f18___2(Arg_0,Arg_1,Arg_2) -> n_f15___3(Arg_0+1,Arg_1,Arg_2)
5:n_f18___2(Arg_0,Arg_1,Arg_2) -> n_f18___2(Arg_0,Arg_1-1,NoDet0)
6:n_f18___4(Arg_0,Arg_1,Arg_2) -> n_f15___3(Arg_0+1,Arg_1,Arg_2):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=10
7:n_f18___4(Arg_0,Arg_1,Arg_2) -> n_f18___2(Arg_0,Arg_1-1,NoDet0):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=10

Preprocessing

Eliminate variables {NoDet0,Arg_2} that do not contribute to the problem

Found invariant Arg_1<=10 && Arg_1<=Arg_0 && Arg_0+Arg_1<=20 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=10 && 2<=Arg_0 for location n_f18___4

Found invariant Arg_1<=9 && 1+Arg_1<=Arg_0 && Arg_0+Arg_1<=19 && Arg_0<=10 && 2<=Arg_0 for location n_f18___2

Found invariant 1+Arg_1<=Arg_0 && 3<=Arg_0 for location n_f15___3

Found invariant 1+Arg_1<=Arg_0 && 11<=Arg_0 for location n_f28___1

Found invariant Arg_0<=2 && 2<=Arg_0 for location n_f15___5

Problem after Preprocessing

Start: n_f0
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: n_f0, n_f15___3, n_f15___5, n_f18___2, n_f18___4, n_f28___1
Transitions:
16:n_f0(Arg_0,Arg_1) -> n_f15___5(2,Arg_1)
17:n_f15___3(Arg_0,Arg_1) -> n_f18___4(Arg_0,Arg_0):|:1+Arg_1<=Arg_0 && 3<=Arg_0 && Arg_0<=10
18:n_f15___3(Arg_0,Arg_1) -> n_f28___1(Arg_0,Arg_1):|:1+Arg_1<=Arg_0 && 3<=Arg_0 && 11<=Arg_0
19:n_f15___5(Arg_0,Arg_1) -> n_f18___4(Arg_0,Arg_0):|:Arg_0<=2 && 2<=Arg_0 && Arg_0<=10 && Arg_0<=2 && 2<=Arg_0 && Arg_0<=10 && Arg_0<=10
20:n_f18___2(Arg_0,Arg_1) -> n_f15___3(Arg_0+1,Arg_1):|:Arg_1<=9 && 1+Arg_1<=Arg_0 && Arg_0+Arg_1<=19 && Arg_0<=10 && 2<=Arg_0
21:n_f18___2(Arg_0,Arg_1) -> n_f18___2(Arg_0,Arg_1-1):|:Arg_1<=9 && 1+Arg_1<=Arg_0 && Arg_0+Arg_1<=19 && Arg_0<=10 && 2<=Arg_0
22:n_f18___4(Arg_0,Arg_1) -> n_f15___3(Arg_0+1,Arg_1):|:Arg_1<=10 && Arg_1<=Arg_0 && Arg_0+Arg_1<=20 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=10 && 2<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=10
23:n_f18___4(Arg_0,Arg_1) -> n_f18___2(Arg_0,Arg_1-1):|:Arg_1<=10 && Arg_1<=Arg_0 && Arg_0+Arg_1<=20 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=10 && 2<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=10

MPRF for transition 17:n_f15___3(Arg_0,Arg_1) -> n_f18___4(Arg_0,Arg_0):|:1+Arg_1<=Arg_0 && 3<=Arg_0 && Arg_0<=10 of depth 1:

new bound:

12 {O(1)}

MPRF:

n_f15___3 [11-Arg_0 ]
n_f18___4 [10-Arg_1 ]
n_f18___2 [10-Arg_0 ]

MPRF for transition 20:n_f18___2(Arg_0,Arg_1) -> n_f15___3(Arg_0+1,Arg_1):|:Arg_1<=9 && 1+Arg_1<=Arg_0 && Arg_0+Arg_1<=19 && Arg_0<=10 && 2<=Arg_0 of depth 1:

new bound:

97 {O(1)}

MPRF:

n_f15___3 [81-8*Arg_0 ]
n_f18___4 [81-8*Arg_0 ]
n_f18___2 [81-8*Arg_0 ]

MPRF for transition 22:n_f18___4(Arg_0,Arg_1) -> n_f15___3(Arg_0+1,Arg_1):|:Arg_1<=10 && Arg_1<=Arg_0 && Arg_0+Arg_1<=20 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=10 && 2<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=10 of depth 1:

new bound:

13 {O(1)}

MPRF:

n_f15___3 [11-Arg_0 ]
n_f18___4 [11-Arg_0 ]
n_f18___2 [10-Arg_0 ]

MPRF for transition 23:n_f18___4(Arg_0,Arg_1) -> n_f18___2(Arg_0,Arg_1-1):|:Arg_1<=10 && Arg_1<=Arg_0 && Arg_0+Arg_1<=20 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && Arg_0<=Arg_1 && Arg_0<=10 && 2<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=10 of depth 1:

new bound:

13 {O(1)}

MPRF:

n_f15___3 [11-Arg_0 ]
n_f18___4 [11-Arg_1 ]
n_f18___2 [10-Arg_0 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
16: n_f0->n_f15___5: 1 {O(1)}
17: n_f15___3->n_f18___4: 12 {O(1)}
18: n_f15___3->n_f28___1: 1 {O(1)}
19: n_f15___5->n_f18___4: 1 {O(1)}
20: n_f18___2->n_f15___3: 97 {O(1)}
21: n_f18___2->n_f18___2: inf {Infinity}
22: n_f18___4->n_f15___3: 13 {O(1)}
23: n_f18___4->n_f18___2: 13 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
16: n_f0->n_f15___5: 1 {O(1)}
17: n_f15___3->n_f18___4: 12 {O(1)}
18: n_f15___3->n_f28___1: 1 {O(1)}
19: n_f15___5->n_f18___4: 1 {O(1)}
20: n_f18___2->n_f15___3: 97 {O(1)}
21: n_f18___2->n_f18___2: inf {Infinity}
22: n_f18___4->n_f15___3: 13 {O(1)}
23: n_f18___4->n_f18___2: 13 {O(1)}

Sizebounds

16: n_f0->n_f15___5, Arg_0: 2 {O(1)}
16: n_f0->n_f15___5, Arg_1: Arg_1 {O(n)}
17: n_f15___3->n_f18___4, Arg_0: 10 {O(1)}
17: n_f15___3->n_f18___4, Arg_1: 10 {O(1)}
18: n_f15___3->n_f28___1, Arg_0: 22 {O(1)}
19: n_f15___5->n_f18___4, Arg_0: 2 {O(1)}
19: n_f15___5->n_f18___4, Arg_1: 2 {O(1)}
20: n_f18___2->n_f15___3, Arg_0: 11 {O(1)}
21: n_f18___2->n_f18___2, Arg_0: 10 {O(1)}
22: n_f18___4->n_f15___3, Arg_0: 11 {O(1)}
22: n_f18___4->n_f15___3, Arg_1: 10 {O(1)}
23: n_f18___4->n_f18___2, Arg_0: 10 {O(1)}
23: n_f18___4->n_f18___2, Arg_1: 9 {O(1)}