Initial Problem

Start: n_l0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: n_l0, n_l1___6, n_l1___7, n_l2___1, n_l2___5, n_l3___2, n_l3___3, n_l3___4
Transitions:
0:n_l0(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___7(Arg_0,Arg_1,Arg_2,Arg_3)
1:n_l1___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___6(Arg_0,Arg_1,Arg_2+Arg_3,Arg_3-1):|:0<=Arg_3 && 1<=Arg_3
2:n_l1___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___5(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && Arg_3<1
3:n_l1___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___6(Arg_0,Arg_1,Arg_2+Arg_3,Arg_3-1):|:1<=Arg_3
4:n_l1___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___5(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<1
5:n_l2___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___4(Arg_2,Arg_2,Arg_2,Arg_3):|:Arg_0<=0 && 1<=Arg_2
6:n_l2___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___4(Arg_2,Arg_2,Arg_2,Arg_3):|:1<=Arg_2
7:n_l3___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___1(Arg_0,Arg_1,Arg_2-1,Arg_3):|:2+Arg_1<=Arg_0 && Arg_0<=0
8:n_l3___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___2(Arg_0+Arg_1,Arg_1-1,Arg_2,Arg_3):|:2+Arg_1<=Arg_0 && 1<=Arg_0
9:n_l3___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___2(Arg_0+Arg_1,Arg_1-1,Arg_2,Arg_3):|:1<=Arg_0 && 1<=Arg_0 && 2+Arg_1<=Arg_0 && 1<=Arg_0
10:n_l3___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___3(Arg_0+Arg_1,Arg_1-1,Arg_2,Arg_3):|:1<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0

Preprocessing

Found invariant 0<=Arg_3 for location n_l1___6

Found invariant Arg_3<=0 && 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 for location n_l3___4

Found invariant Arg_3<=0 for location n_l2___5

Found invariant Arg_3<=0 && 1+Arg_3<=Arg_2 && Arg_3<=Arg_1 && 2+Arg_3<=Arg_0 && Arg_2<=1+Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 for location n_l3___3

Found invariant Arg_3<=0 && Arg_3<=Arg_2 && 2+Arg_1+Arg_3<=0 && Arg_0+Arg_3<=0 && 0<=Arg_2 && 2+Arg_1<=Arg_2 && Arg_0<=Arg_2 && 2+Arg_1<=0 && 2+Arg_1<=Arg_0 && 2+Arg_0+Arg_1<=0 && Arg_0<=0 for location n_l2___1

Found invariant Arg_3<=0 && 1+Arg_3<=Arg_2 && 1<=Arg_2 && 2+Arg_1<=Arg_2 && 2+Arg_1<=Arg_0 for location n_l3___2

Problem after Preprocessing

Start: n_l0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: n_l0, n_l1___6, n_l1___7, n_l2___1, n_l2___5, n_l3___2, n_l3___3, n_l3___4
Transitions:
0:n_l0(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___7(Arg_0,Arg_1,Arg_2,Arg_3)
1:n_l1___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___6(Arg_0,Arg_1,Arg_2+Arg_3,Arg_3-1):|:0<=Arg_3 && 0<=Arg_3 && 1<=Arg_3
2:n_l1___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___5(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_3 && 0<=Arg_3 && Arg_3<1
3:n_l1___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___6(Arg_0,Arg_1,Arg_2+Arg_3,Arg_3-1):|:1<=Arg_3
4:n_l1___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___5(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<1
5:n_l2___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___4(Arg_2,Arg_2,Arg_2,Arg_3):|:Arg_3<=0 && Arg_3<=Arg_2 && 2+Arg_1+Arg_3<=0 && Arg_0+Arg_3<=0 && 0<=Arg_2 && 2+Arg_1<=Arg_2 && Arg_0<=Arg_2 && 2+Arg_1<=0 && 2+Arg_1<=Arg_0 && 2+Arg_0+Arg_1<=0 && Arg_0<=0 && Arg_0<=0 && 1<=Arg_2
6:n_l2___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___4(Arg_2,Arg_2,Arg_2,Arg_3):|:Arg_3<=0 && 1<=Arg_2
7:n_l3___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___1(Arg_0,Arg_1,Arg_2-1,Arg_3):|:Arg_3<=0 && 1+Arg_3<=Arg_2 && 1<=Arg_2 && 2+Arg_1<=Arg_2 && 2+Arg_1<=Arg_0 && 2+Arg_1<=Arg_0 && Arg_0<=0
8:n_l3___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___2(Arg_0+Arg_1,Arg_1-1,Arg_2,Arg_3):|:Arg_3<=0 && 1+Arg_3<=Arg_2 && 1<=Arg_2 && 2+Arg_1<=Arg_2 && 2+Arg_1<=Arg_0 && 2+Arg_1<=Arg_0 && 1<=Arg_0
9:n_l3___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___2(Arg_0+Arg_1,Arg_1-1,Arg_2,Arg_3):|:Arg_3<=0 && 1+Arg_3<=Arg_2 && Arg_3<=Arg_1 && 2+Arg_3<=Arg_0 && Arg_2<=1+Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 2+Arg_1<=Arg_0 && 1<=Arg_0
10:n_l3___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___3(Arg_0+Arg_1,Arg_1-1,Arg_2,Arg_3):|:Arg_3<=0 && 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0

MPRF for transition 1:n_l1___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___6(Arg_0,Arg_1,Arg_2+Arg_3,Arg_3-1):|:0<=Arg_3 && 0<=Arg_3 && 1<=Arg_3 of depth 1:

new bound:

Arg_3+1 {O(n)}

MPRF:

n_l1___6 [Arg_3+1 ]

MPRF for transition 5:n_l2___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___4(Arg_2,Arg_2,Arg_2,Arg_3):|:Arg_3<=0 && Arg_3<=Arg_2 && 2+Arg_1+Arg_3<=0 && Arg_0+Arg_3<=0 && 0<=Arg_2 && 2+Arg_1<=Arg_2 && Arg_0<=Arg_2 && 2+Arg_1<=0 && 2+Arg_1<=Arg_0 && 2+Arg_0+Arg_1<=0 && Arg_0<=0 && Arg_0<=0 && 1<=Arg_2 of depth 1:

new bound:

2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}

MPRF:

n_l2___1 [Arg_2+1 ]
n_l3___2 [Arg_2 ]
n_l3___4 [Arg_1 ]
n_l3___3 [Arg_2 ]

MPRF for transition 7:n_l3___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___1(Arg_0,Arg_1,Arg_2-1,Arg_3):|:Arg_3<=0 && 1+Arg_3<=Arg_2 && 1<=Arg_2 && 2+Arg_1<=Arg_2 && 2+Arg_1<=Arg_0 && 2+Arg_1<=Arg_0 && Arg_0<=0 of depth 1:

new bound:

2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}

MPRF:

n_l2___1 [Arg_2 ]
n_l3___2 [Arg_2 ]
n_l3___4 [Arg_0 ]
n_l3___3 [Arg_2 ]

MPRF for transition 9:n_l3___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___2(Arg_0+Arg_1,Arg_1-1,Arg_2,Arg_3):|:Arg_3<=0 && 1+Arg_3<=Arg_2 && Arg_3<=Arg_1 && 2+Arg_3<=Arg_0 && Arg_2<=1+Arg_1 && 1+Arg_2<=Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 2+Arg_1<=Arg_0 && 0<=Arg_1 && 2<=Arg_0+Arg_1 && 2<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 2+Arg_1<=Arg_0 && 1<=Arg_0 of depth 1:

new bound:

2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}

MPRF:

n_l2___1 [Arg_2 ]
n_l3___2 [Arg_2-1 ]
n_l3___4 [Arg_1 ]
n_l3___3 [Arg_1+1 ]

MPRF for transition 10:n_l3___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___3(Arg_0+Arg_1,Arg_1-1,Arg_2,Arg_3):|:Arg_3<=0 && 1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && Arg_2<=Arg_1 && Arg_2<=Arg_0 && 1<=Arg_2 && 2<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_1 && 2<=Arg_0+Arg_1 && Arg_0<=Arg_1 && 1<=Arg_0 && 1<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 of depth 1:

new bound:

2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}

MPRF:

n_l2___1 [Arg_2 ]
n_l3___2 [Arg_2-1 ]
n_l3___4 [Arg_0 ]
n_l3___3 [Arg_2-1 ]

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: n_l0->n_l1___7: 1 {O(1)}
1: n_l1___6->n_l1___6: Arg_3+1 {O(n)}
2: n_l1___6->n_l2___5: 1 {O(1)}
3: n_l1___7->n_l1___6: 1 {O(1)}
4: n_l1___7->n_l2___5: 1 {O(1)}
5: n_l2___1->n_l3___4: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}
6: n_l2___5->n_l3___4: 1 {O(1)}
7: n_l3___2->n_l2___1: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}
8: n_l3___2->n_l3___2: inf {Infinity}
9: n_l3___3->n_l3___2: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}
10: n_l3___4->n_l3___3: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}

Costbounds

Overall costbound: inf {Infinity}
0: n_l0->n_l1___7: 1 {O(1)}
1: n_l1___6->n_l1___6: Arg_3+1 {O(n)}
2: n_l1___6->n_l2___5: 1 {O(1)}
3: n_l1___7->n_l1___6: 1 {O(1)}
4: n_l1___7->n_l2___5: 1 {O(1)}
5: n_l2___1->n_l3___4: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}
6: n_l2___5->n_l3___4: 1 {O(1)}
7: n_l3___2->n_l2___1: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}
8: n_l3___2->n_l3___2: inf {Infinity}
9: n_l3___3->n_l3___2: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}
10: n_l3___4->n_l3___3: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}

Sizebounds

0: n_l0->n_l1___7, Arg_0: Arg_0 {O(n)}
0: n_l0->n_l1___7, Arg_1: Arg_1 {O(n)}
0: n_l0->n_l1___7, Arg_2: Arg_2 {O(n)}
0: n_l0->n_l1___7, Arg_3: Arg_3 {O(n)}
1: n_l1___6->n_l1___6, Arg_0: Arg_0 {O(n)}
1: n_l1___6->n_l1___6, Arg_1: Arg_1 {O(n)}
1: n_l1___6->n_l1___6, Arg_2: 2*Arg_3*Arg_3+5*Arg_3+Arg_2 {O(n^2)}
1: n_l1___6->n_l1___6, Arg_3: Arg_3 {O(n)}
2: n_l1___6->n_l2___5, Arg_0: 2*Arg_0 {O(n)}
2: n_l1___6->n_l2___5, Arg_1: 2*Arg_1 {O(n)}
2: n_l1___6->n_l2___5, Arg_2: 2*Arg_3*Arg_3+2*Arg_2+6*Arg_3 {O(n^2)}
2: n_l1___6->n_l2___5, Arg_3: 0 {O(1)}
3: n_l1___7->n_l1___6, Arg_0: Arg_0 {O(n)}
3: n_l1___7->n_l1___6, Arg_1: Arg_1 {O(n)}
3: n_l1___7->n_l1___6, Arg_2: Arg_2+Arg_3 {O(n)}
3: n_l1___7->n_l1___6, Arg_3: Arg_3 {O(n)}
4: n_l1___7->n_l2___5, Arg_0: Arg_0 {O(n)}
4: n_l1___7->n_l2___5, Arg_1: Arg_1 {O(n)}
4: n_l1___7->n_l2___5, Arg_2: Arg_2 {O(n)}
4: n_l1___7->n_l2___5, Arg_3: Arg_3 {O(n)}
5: n_l2___1->n_l3___4, Arg_0: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}
5: n_l2___1->n_l3___4, Arg_1: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}
5: n_l2___1->n_l3___4, Arg_2: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}
5: n_l2___1->n_l3___4, Arg_3: Arg_3 {O(n)}
6: n_l2___5->n_l3___4, Arg_0: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}
6: n_l2___5->n_l3___4, Arg_1: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}
6: n_l2___5->n_l3___4, Arg_2: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}
6: n_l2___5->n_l3___4, Arg_3: Arg_3 {O(n)}
7: n_l3___2->n_l2___1, Arg_2: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}
7: n_l3___2->n_l2___1, Arg_3: Arg_3 {O(n)}
8: n_l3___2->n_l3___2, Arg_2: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}
8: n_l3___2->n_l3___2, Arg_3: Arg_3 {O(n)}
9: n_l3___3->n_l3___2, Arg_0: 16*Arg_3*Arg_3+24*Arg_2+48*Arg_3 {O(n^2)}
9: n_l3___3->n_l3___2, Arg_1: 4*Arg_3*Arg_3+12*Arg_3+6*Arg_2+1 {O(n^2)}
9: n_l3___3->n_l3___2, Arg_2: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}
9: n_l3___3->n_l3___2, Arg_3: Arg_3 {O(n)}
10: n_l3___4->n_l3___3, Arg_0: 8*Arg_3*Arg_3+12*Arg_2+24*Arg_3 {O(n^2)}
10: n_l3___4->n_l3___3, Arg_1: 4*Arg_3*Arg_3+12*Arg_3+6*Arg_2 {O(n^2)}
10: n_l3___4->n_l3___3, Arg_2: 2*Arg_3*Arg_3+3*Arg_2+6*Arg_3 {O(n^2)}
10: n_l3___4->n_l3___3, Arg_3: Arg_3 {O(n)}