Initial Problem

Start: n_f3
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_f1___1, n_f1___2, n_f1___3, n_f1___4, n_f3
Transitions:
0:n_f1___1(Arg_0,Arg_1,Arg_2) -> n_f1___1(Arg_0,Arg_1,Arg_2+1):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_1 && Arg_0<=Arg_1 && 2+Arg_2<=Arg_1 && Arg_0<=Arg_1
1:n_f1___2(Arg_0,Arg_1,Arg_2) -> n_f1___2(Arg_0,Arg_1,Arg_2+1):|:Arg_0<=Arg_1 && 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_1 && Arg_0<=Arg_1 && 2+Arg_2<=Arg_1 && Arg_0<=Arg_1
2:n_f1___3(Arg_0,Arg_1,Arg_2) -> n_f1___1(Arg_0,Arg_1,Arg_2+1):|:2+Arg_2<=Arg_1 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_1 && 2+Arg_2<=Arg_1 && Arg_0<=Arg_1
3:n_f1___3(Arg_0,Arg_1,Arg_2) -> n_f1___3(Arg_0,Arg_1+1,Arg_2):|:2+Arg_2<=Arg_1 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_1 && 1+Arg_1<=Arg_0
4:n_f1___4(Arg_0,Arg_1,Arg_2) -> n_f1___2(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && 2+Arg_2<=Arg_1 && Arg_0<=Arg_1
5:n_f1___4(Arg_0,Arg_1,Arg_2) -> n_f1___3(Arg_0,Arg_1+1,Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_1<=Arg_0
6:n_f3(Arg_0,Arg_1,Arg_2) -> n_f1___4(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1

Preprocessing

Found invariant 1+Arg_2<=Arg_1 && Arg_0<=Arg_1 for location n_f1___2

Found invariant 1+Arg_2<=Arg_1 for location n_f1___4

Found invariant 2+Arg_2<=Arg_1 && 2+Arg_2<=Arg_0 && Arg_1<=Arg_0 for location n_f1___3

Found invariant 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && Arg_1<=Arg_0 && Arg_0<=Arg_1 for location n_f1___1

Problem after Preprocessing

Start: n_f3
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_f1___1, n_f1___2, n_f1___3, n_f1___4, n_f3
Transitions:
0:n_f1___1(Arg_0,Arg_1,Arg_2) -> n_f1___1(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_1 && Arg_0<=Arg_1 && 2+Arg_2<=Arg_1 && Arg_0<=Arg_1
1:n_f1___2(Arg_0,Arg_1,Arg_2) -> n_f1___2(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_1 && Arg_0<=Arg_1 && 2+Arg_2<=Arg_1 && Arg_0<=Arg_1
2:n_f1___3(Arg_0,Arg_1,Arg_2) -> n_f1___1(Arg_0,Arg_1,Arg_2+1):|:2+Arg_2<=Arg_1 && 2+Arg_2<=Arg_0 && Arg_1<=Arg_0 && 2+Arg_2<=Arg_1 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_1 && 2+Arg_2<=Arg_1 && Arg_0<=Arg_1
3:n_f1___3(Arg_0,Arg_1,Arg_2) -> n_f1___3(Arg_0,Arg_1+1,Arg_2):|:2+Arg_2<=Arg_1 && 2+Arg_2<=Arg_0 && Arg_1<=Arg_0 && 2+Arg_2<=Arg_1 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_1 && 1+Arg_1<=Arg_0
4:n_f1___4(Arg_0,Arg_1,Arg_2) -> n_f1___2(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_1 && 2+Arg_2<=Arg_1 && Arg_0<=Arg_1
5:n_f1___4(Arg_0,Arg_1,Arg_2) -> n_f1___3(Arg_0,Arg_1+1,Arg_2):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_1 && 1+Arg_1<=Arg_0
6:n_f3(Arg_0,Arg_1,Arg_2) -> n_f1___4(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_1

MPRF for transition 3:n_f1___3(Arg_0,Arg_1,Arg_2) -> n_f1___3(Arg_0,Arg_1+1,Arg_2):|:2+Arg_2<=Arg_1 && 2+Arg_2<=Arg_0 && Arg_1<=Arg_0 && 2+Arg_2<=Arg_1 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_1 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

Arg_0+Arg_1+2 {O(n)}

MPRF:

n_f1___3 [Arg_0+1-Arg_1 ]

MPRF for transition 1:n_f1___2(Arg_0,Arg_1,Arg_2) -> n_f1___2(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_1 && Arg_0<=Arg_1 && 2+Arg_2<=Arg_1 && Arg_0<=Arg_1 of depth 1:

new bound:

Arg_1+Arg_2+1 {O(n)}

MPRF:

n_f1___2 [Arg_1-Arg_2 ]

MPRF for transition 0:n_f1___1(Arg_0,Arg_1,Arg_2) -> n_f1___1(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_0 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_1 && 1+Arg_2<=Arg_1 && Arg_0<=Arg_1 && 2+Arg_2<=Arg_1 && Arg_0<=Arg_1 of depth 1:

new bound:

2*Arg_2+3*Arg_1+Arg_0+6 {O(n)}

MPRF:

n_f1___1 [Arg_1-Arg_2 ]

All Bounds

Timebounds

Overall timebound:2*Arg_0+3*Arg_2+5*Arg_1+13 {O(n)}
0: n_f1___1->n_f1___1: 2*Arg_2+3*Arg_1+Arg_0+6 {O(n)}
1: n_f1___2->n_f1___2: Arg_1+Arg_2+1 {O(n)}
2: n_f1___3->n_f1___1: 1 {O(1)}
3: n_f1___3->n_f1___3: Arg_0+Arg_1+2 {O(n)}
4: n_f1___4->n_f1___2: 1 {O(1)}
5: n_f1___4->n_f1___3: 1 {O(1)}
6: n_f3->n_f1___4: 1 {O(1)}

Costbounds

Overall costbound: 2*Arg_0+3*Arg_2+5*Arg_1+13 {O(n)}
0: n_f1___1->n_f1___1: 2*Arg_2+3*Arg_1+Arg_0+6 {O(n)}
1: n_f1___2->n_f1___2: Arg_1+Arg_2+1 {O(n)}
2: n_f1___3->n_f1___1: 1 {O(1)}
3: n_f1___3->n_f1___3: Arg_0+Arg_1+2 {O(n)}
4: n_f1___4->n_f1___2: 1 {O(1)}
5: n_f1___4->n_f1___3: 1 {O(1)}
6: n_f3->n_f1___4: 1 {O(1)}

Sizebounds

0: n_f1___1->n_f1___1, Arg_0: 2*Arg_0 {O(n)}
0: n_f1___1->n_f1___1, Arg_1: 3*Arg_1+Arg_0+4 {O(n)}
0: n_f1___1->n_f1___1, Arg_2: 3*Arg_1+4*Arg_2+Arg_0+8 {O(n)}
1: n_f1___2->n_f1___2, Arg_0: Arg_0 {O(n)}
1: n_f1___2->n_f1___2, Arg_1: Arg_1 {O(n)}
1: n_f1___2->n_f1___2, Arg_2: 2*Arg_2+Arg_1+2 {O(n)}
2: n_f1___3->n_f1___1, Arg_0: 2*Arg_0 {O(n)}
2: n_f1___3->n_f1___1, Arg_1: 3*Arg_1+Arg_0+4 {O(n)}
2: n_f1___3->n_f1___1, Arg_2: 2*Arg_2+2 {O(n)}
3: n_f1___3->n_f1___3, Arg_0: Arg_0 {O(n)}
3: n_f1___3->n_f1___3, Arg_1: 2*Arg_1+Arg_0+3 {O(n)}
3: n_f1___3->n_f1___3, Arg_2: Arg_2 {O(n)}
4: n_f1___4->n_f1___2, Arg_0: Arg_0 {O(n)}
4: n_f1___4->n_f1___2, Arg_1: Arg_1 {O(n)}
4: n_f1___4->n_f1___2, Arg_2: Arg_2+1 {O(n)}
5: n_f1___4->n_f1___3, Arg_0: Arg_0 {O(n)}
5: n_f1___4->n_f1___3, Arg_1: Arg_1+1 {O(n)}
5: n_f1___4->n_f1___3, Arg_2: Arg_2 {O(n)}
6: n_f3->n_f1___4, Arg_0: Arg_0 {O(n)}
6: n_f3->n_f1___4, Arg_1: Arg_1 {O(n)}
6: n_f3->n_f1___4, Arg_2: Arg_2 {O(n)}