Initial Problem

Start: n_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_eval1___4, n_eval1___5, n_eval1___6, n_eval1___8, n_eval2___1, n_eval2___2, n_eval2___3, n_eval2___7, n_start
Transitions:
0:n_eval1___4(Arg_0,Arg_1,Arg_2) -> n_eval2___1(Arg_0,Arg_1,Arg_2):|:Arg_0<=Arg_2 && 1+Arg_0<=Arg_2 && 1+Arg_1<=Arg_0
1:n_eval1___5(Arg_0,Arg_1,Arg_2) -> n_eval2___2(Arg_0,Arg_1,Arg_2):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_1<=Arg_0
2:n_eval1___6(Arg_0,Arg_1,Arg_2) -> n_eval2___3(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_1<=Arg_0
3:n_eval1___8(Arg_0,Arg_1,Arg_2) -> n_eval2___7(Arg_0,Arg_1,Arg_2):|:1+Arg_1<=Arg_0
4:n_eval2___1(Arg_0,Arg_1,Arg_2) -> n_eval1___4(Arg_0-1,Arg_1,Arg_2):|:1+Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2
5:n_eval2___2(Arg_0,Arg_1,Arg_2) -> n_eval1___4(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && Arg_0<=Arg_2
6:n_eval2___2(Arg_0,Arg_1,Arg_2) -> n_eval1___5(Arg_0,Arg_1,Arg_2+1):|:1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_2<=Arg_0
7:n_eval2___2(Arg_0,Arg_1,Arg_2) -> n_eval1___6(Arg_0,Arg_1+1,Arg_2):|:1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_2<=Arg_0
8:n_eval2___3(Arg_0,Arg_1,Arg_2) -> n_eval1___5(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_2<=Arg_0
9:n_eval2___3(Arg_0,Arg_1,Arg_2) -> n_eval1___6(Arg_0,Arg_1+1,Arg_2):|:1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_2<=Arg_0
10:n_eval2___7(Arg_0,Arg_1,Arg_2) -> n_eval1___4(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_0 && Arg_0<=Arg_2
11:n_eval2___7(Arg_0,Arg_1,Arg_2) -> n_eval1___5(Arg_0,Arg_1,Arg_2+1):|:1+Arg_1<=Arg_0 && 1+Arg_2<=Arg_0
12:n_eval2___7(Arg_0,Arg_1,Arg_2) -> n_eval1___6(Arg_0,Arg_1+1,Arg_2):|:1+Arg_1<=Arg_0 && 1+Arg_2<=Arg_0
13:n_start(Arg_0,Arg_1,Arg_2) -> n_eval1___8(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant 1+Arg_1<=Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 for location n_eval1___4

Found invariant Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 for location n_eval2___2

Found invariant Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 for location n_eval1___5

Found invariant 1+Arg_1<=Arg_0 for location n_eval2___7

Found invariant 1+Arg_2<=Arg_0 && Arg_1<=Arg_0 for location n_eval1___6

Found invariant 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 for location n_eval2___3

Found invariant 2+Arg_1<=Arg_2 && 1+Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 for location n_eval2___1

Problem after Preprocessing

Start: n_start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars:
Locations: n_eval1___4, n_eval1___5, n_eval1___6, n_eval1___8, n_eval2___1, n_eval2___2, n_eval2___3, n_eval2___7, n_start
Transitions:
0:n_eval1___4(Arg_0,Arg_1,Arg_2) -> n_eval2___1(Arg_0,Arg_1,Arg_2):|:1+Arg_1<=Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && Arg_0<=Arg_2 && 1+Arg_0<=Arg_2 && 1+Arg_1<=Arg_0
1:n_eval1___5(Arg_0,Arg_1,Arg_2) -> n_eval2___2(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_1<=Arg_0
2:n_eval1___6(Arg_0,Arg_1,Arg_2) -> n_eval2___3(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_1<=Arg_0
3:n_eval1___8(Arg_0,Arg_1,Arg_2) -> n_eval2___7(Arg_0,Arg_1,Arg_2):|:1+Arg_1<=Arg_0
4:n_eval2___1(Arg_0,Arg_1,Arg_2) -> n_eval1___4(Arg_0-1,Arg_1,Arg_2):|:2+Arg_1<=Arg_2 && 1+Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2
5:n_eval2___2(Arg_0,Arg_1,Arg_2) -> n_eval1___4(Arg_0-1,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && Arg_0<=Arg_2
6:n_eval2___2(Arg_0,Arg_1,Arg_2) -> n_eval1___5(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_2<=Arg_0
7:n_eval2___2(Arg_0,Arg_1,Arg_2) -> n_eval1___6(Arg_0,Arg_1+1,Arg_2):|:Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_2<=Arg_0
8:n_eval2___3(Arg_0,Arg_1,Arg_2) -> n_eval1___5(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_2<=Arg_0
9:n_eval2___3(Arg_0,Arg_1,Arg_2) -> n_eval1___6(Arg_0,Arg_1+1,Arg_2):|:1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_2<=Arg_0
10:n_eval2___7(Arg_0,Arg_1,Arg_2) -> n_eval1___4(Arg_0-1,Arg_1,Arg_2):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2
11:n_eval2___7(Arg_0,Arg_1,Arg_2) -> n_eval1___5(Arg_0,Arg_1,Arg_2+1):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_2<=Arg_0
12:n_eval2___7(Arg_0,Arg_1,Arg_2) -> n_eval1___6(Arg_0,Arg_1+1,Arg_2):|:1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_2<=Arg_0
13:n_start(Arg_0,Arg_1,Arg_2) -> n_eval1___8(Arg_0,Arg_1,Arg_2)

MPRF for transition 1:n_eval1___5(Arg_0,Arg_1,Arg_2) -> n_eval2___2(Arg_0,Arg_1,Arg_2):|:Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

2*Arg_0+2*Arg_2+2 {O(n)}

MPRF:

n_eval2___2 [Arg_0-Arg_2 ]
n_eval1___5 [Arg_0+1-Arg_2 ]
n_eval2___3 [Arg_0-Arg_2 ]
n_eval1___6 [Arg_0-Arg_2 ]

MPRF for transition 2:n_eval1___6(Arg_0,Arg_1,Arg_2) -> n_eval2___3(Arg_0,Arg_1,Arg_2):|:1+Arg_2<=Arg_0 && Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

2*Arg_0+2*Arg_1+2 {O(n)}

MPRF:

n_eval2___2 [Arg_0-Arg_1 ]
n_eval1___5 [Arg_0-Arg_1 ]
n_eval2___3 [Arg_0-Arg_1 ]
n_eval1___6 [Arg_0+1-Arg_1 ]

MPRF for transition 6:n_eval2___2(Arg_0,Arg_1,Arg_2) -> n_eval1___5(Arg_0,Arg_1,Arg_2+1):|:Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 of depth 1:

new bound:

2*Arg_0+2*Arg_2+2 {O(n)}

MPRF:

n_eval2___2 [Arg_0+1-Arg_2 ]
n_eval1___5 [Arg_0+1-Arg_2 ]
n_eval2___3 [Arg_0-Arg_2 ]
n_eval1___6 [Arg_0-Arg_2 ]

MPRF for transition 7:n_eval2___2(Arg_0,Arg_1,Arg_2) -> n_eval1___6(Arg_0,Arg_1+1,Arg_2):|:Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_1<=Arg_0 && Arg_2<=Arg_0 && 1+Arg_2<=Arg_0 of depth 1:

new bound:

2*Arg_0+2*Arg_1+1 {O(n)}

MPRF:

n_eval2___2 [Arg_0-Arg_1 ]
n_eval1___5 [Arg_0-Arg_1 ]
n_eval2___3 [Arg_0-Arg_1 ]
n_eval1___6 [Arg_0-Arg_1 ]

MPRF for transition 8:n_eval2___3(Arg_0,Arg_1,Arg_2) -> n_eval1___5(Arg_0,Arg_1,Arg_2+1):|:1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 of depth 1:

new bound:

2*Arg_0+2*Arg_2+1 {O(n)}

MPRF:

n_eval2___2 [Arg_0-Arg_2 ]
n_eval1___5 [Arg_0-Arg_2 ]
n_eval2___3 [Arg_0-Arg_2 ]
n_eval1___6 [Arg_0-Arg_2 ]

MPRF for transition 9:n_eval2___3(Arg_0,Arg_1,Arg_2) -> n_eval1___6(Arg_0,Arg_1+1,Arg_2):|:1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 && 1+Arg_1<=Arg_0 && 1+Arg_2<=Arg_0 of depth 1:

new bound:

2*Arg_0+2*Arg_1+1 {O(n)}

MPRF:

n_eval2___2 [Arg_0-Arg_1 ]
n_eval1___5 [Arg_0-Arg_1 ]
n_eval2___3 [Arg_0-Arg_1 ]
n_eval1___6 [Arg_0-Arg_1 ]

MPRF for transition 0:n_eval1___4(Arg_0,Arg_1,Arg_2) -> n_eval2___1(Arg_0,Arg_1,Arg_2):|:1+Arg_1<=Arg_2 && 1+Arg_0<=Arg_2 && Arg_1<=Arg_0 && Arg_0<=Arg_2 && 1+Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 of depth 1:

new bound:

7*Arg_0+7*Arg_1+7 {O(n)}

MPRF:

n_eval2___1 [Arg_0-Arg_1 ]
n_eval1___4 [Arg_0+1-Arg_1 ]

MPRF for transition 4:n_eval2___1(Arg_0,Arg_1,Arg_2) -> n_eval1___4(Arg_0-1,Arg_1,Arg_2):|:2+Arg_1<=Arg_2 && 1+Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && 1+Arg_0<=Arg_2 && 1+Arg_1<=Arg_0 && Arg_0<=Arg_2 of depth 1:

new bound:

7*Arg_0+7*Arg_1+5 {O(n)}

MPRF:

n_eval2___1 [Arg_0-Arg_1 ]
n_eval1___4 [Arg_0-Arg_1 ]

All Bounds

Timebounds

Overall timebound:20*Arg_1+26*Arg_0+6*Arg_2+27 {O(n)}
0: n_eval1___4->n_eval2___1: 7*Arg_0+7*Arg_1+7 {O(n)}
1: n_eval1___5->n_eval2___2: 2*Arg_0+2*Arg_2+2 {O(n)}
2: n_eval1___6->n_eval2___3: 2*Arg_0+2*Arg_1+2 {O(n)}
3: n_eval1___8->n_eval2___7: 1 {O(1)}
4: n_eval2___1->n_eval1___4: 7*Arg_0+7*Arg_1+5 {O(n)}
5: n_eval2___2->n_eval1___4: 1 {O(1)}
6: n_eval2___2->n_eval1___5: 2*Arg_0+2*Arg_2+2 {O(n)}
7: n_eval2___2->n_eval1___6: 2*Arg_0+2*Arg_1+1 {O(n)}
8: n_eval2___3->n_eval1___5: 2*Arg_0+2*Arg_2+1 {O(n)}
9: n_eval2___3->n_eval1___6: 2*Arg_0+2*Arg_1+1 {O(n)}
10: n_eval2___7->n_eval1___4: 1 {O(1)}
11: n_eval2___7->n_eval1___5: 1 {O(1)}
12: n_eval2___7->n_eval1___6: 1 {O(1)}
13: n_start->n_eval1___8: 1 {O(1)}

Costbounds

Overall costbound: 20*Arg_1+26*Arg_0+6*Arg_2+27 {O(n)}
0: n_eval1___4->n_eval2___1: 7*Arg_0+7*Arg_1+7 {O(n)}
1: n_eval1___5->n_eval2___2: 2*Arg_0+2*Arg_2+2 {O(n)}
2: n_eval1___6->n_eval2___3: 2*Arg_0+2*Arg_1+2 {O(n)}
3: n_eval1___8->n_eval2___7: 1 {O(1)}
4: n_eval2___1->n_eval1___4: 7*Arg_0+7*Arg_1+5 {O(n)}
5: n_eval2___2->n_eval1___4: 1 {O(1)}
6: n_eval2___2->n_eval1___5: 2*Arg_0+2*Arg_2+2 {O(n)}
7: n_eval2___2->n_eval1___6: 2*Arg_0+2*Arg_1+1 {O(n)}
8: n_eval2___3->n_eval1___5: 2*Arg_0+2*Arg_2+1 {O(n)}
9: n_eval2___3->n_eval1___6: 2*Arg_0+2*Arg_1+1 {O(n)}
10: n_eval2___7->n_eval1___4: 1 {O(1)}
11: n_eval2___7->n_eval1___5: 1 {O(1)}
12: n_eval2___7->n_eval1___6: 1 {O(1)}
13: n_start->n_eval1___8: 1 {O(1)}

Sizebounds

0: n_eval1___4->n_eval2___1, Arg_0: 10*Arg_0+7*Arg_1+7 {O(n)}
0: n_eval1___4->n_eval2___1, Arg_1: 4*Arg_0+7*Arg_1+3 {O(n)}
0: n_eval1___4->n_eval2___1, Arg_2: 4*Arg_0+7*Arg_2+4 {O(n)}
1: n_eval1___5->n_eval2___2, Arg_0: 2*Arg_0 {O(n)}
1: n_eval1___5->n_eval2___2, Arg_1: 4*Arg_0+6*Arg_1+3 {O(n)}
1: n_eval1___5->n_eval2___2, Arg_2: 4*Arg_0+6*Arg_2+4 {O(n)}
2: n_eval1___6->n_eval2___3, Arg_0: 2*Arg_0 {O(n)}
2: n_eval1___6->n_eval2___3, Arg_1: 4*Arg_0+6*Arg_1+3 {O(n)}
2: n_eval1___6->n_eval2___3, Arg_2: 4*Arg_0+6*Arg_2+4 {O(n)}
3: n_eval1___8->n_eval2___7, Arg_0: Arg_0 {O(n)}
3: n_eval1___8->n_eval2___7, Arg_1: Arg_1 {O(n)}
3: n_eval1___8->n_eval2___7, Arg_2: Arg_2 {O(n)}
4: n_eval2___1->n_eval1___4, Arg_0: 10*Arg_0+7*Arg_1+7 {O(n)}
4: n_eval2___1->n_eval1___4, Arg_1: 4*Arg_0+7*Arg_1+3 {O(n)}
4: n_eval2___1->n_eval1___4, Arg_2: 4*Arg_0+7*Arg_2+4 {O(n)}
5: n_eval2___2->n_eval1___4, Arg_0: 2*Arg_0+1 {O(n)}
5: n_eval2___2->n_eval1___4, Arg_1: 4*Arg_0+6*Arg_1+3 {O(n)}
5: n_eval2___2->n_eval1___4, Arg_2: 4*Arg_0+6*Arg_2+4 {O(n)}
6: n_eval2___2->n_eval1___5, Arg_0: 2*Arg_0 {O(n)}
6: n_eval2___2->n_eval1___5, Arg_1: 4*Arg_0+6*Arg_1+3 {O(n)}
6: n_eval2___2->n_eval1___5, Arg_2: 4*Arg_0+6*Arg_2+4 {O(n)}
7: n_eval2___2->n_eval1___6, Arg_0: 2*Arg_0 {O(n)}
7: n_eval2___2->n_eval1___6, Arg_1: 4*Arg_0+6*Arg_1+3 {O(n)}
7: n_eval2___2->n_eval1___6, Arg_2: 4*Arg_0+6*Arg_2+4 {O(n)}
8: n_eval2___3->n_eval1___5, Arg_0: 2*Arg_0 {O(n)}
8: n_eval2___3->n_eval1___5, Arg_1: 4*Arg_0+6*Arg_1+3 {O(n)}
8: n_eval2___3->n_eval1___5, Arg_2: 4*Arg_0+6*Arg_2+4 {O(n)}
9: n_eval2___3->n_eval1___6, Arg_0: 2*Arg_0 {O(n)}
9: n_eval2___3->n_eval1___6, Arg_1: 4*Arg_0+6*Arg_1+3 {O(n)}
9: n_eval2___3->n_eval1___6, Arg_2: 4*Arg_0+6*Arg_2+4 {O(n)}
10: n_eval2___7->n_eval1___4, Arg_0: Arg_0+1 {O(n)}
10: n_eval2___7->n_eval1___4, Arg_1: Arg_1 {O(n)}
10: n_eval2___7->n_eval1___4, Arg_2: Arg_2 {O(n)}
11: n_eval2___7->n_eval1___5, Arg_0: Arg_0 {O(n)}
11: n_eval2___7->n_eval1___5, Arg_1: Arg_1 {O(n)}
11: n_eval2___7->n_eval1___5, Arg_2: Arg_2+1 {O(n)}
12: n_eval2___7->n_eval1___6, Arg_0: Arg_0 {O(n)}
12: n_eval2___7->n_eval1___6, Arg_1: Arg_1+1 {O(n)}
12: n_eval2___7->n_eval1___6, Arg_2: Arg_2 {O(n)}
13: n_start->n_eval1___8, Arg_0: Arg_0 {O(n)}
13: n_start->n_eval1___8, Arg_1: Arg_1 {O(n)}
13: n_start->n_eval1___8, Arg_2: Arg_2 {O(n)}