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___4, n_l2___5, n_l3___2, n_l3___3
Transitions:
0:n_l0(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___7(0,Arg_1,Arg_2,Arg_3)
1:n_l1___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___6(Arg_0+1,Arg_1-1,Arg_2,Arg_3):|:1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1
2:n_l1___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___4(Arg_0,Arg_1,Arg_0,Arg_3):|:1<=Arg_0 && 0<=Arg_1 && Arg_1<=0
3:n_l1___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___6(Arg_0+1,Arg_1-1,Arg_2,Arg_3):|:Arg_0<=0 && 0<=Arg_0 && 1<=Arg_1
4:n_l1___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___5(Arg_0,Arg_1,Arg_0,Arg_3):|:Arg_0<=0 && 0<=Arg_0 && Arg_1<=0
5:n_l2___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___3(Arg_0,Arg_1,Arg_2,Arg_2):|:0<=Arg_2 && Arg_3<=0 && 1<=Arg_2
6:n_l2___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___3(Arg_0,Arg_1,Arg_2,Arg_2):|:1<=Arg_2 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && Arg_1<=0 && 1<=Arg_2 && 1<=Arg_2
7:n_l2___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___3(Arg_0,Arg_1,Arg_2,Arg_2):|:Arg_0<=Arg_2 && Arg_2<=Arg_0 && Arg_1<=0 && 1<=Arg_2
8:n_l3___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___1(Arg_0,Arg_1,Arg_2-1,Arg_3):|:1<=Arg_2 && 1<=Arg_2 && 0<=Arg_3 && 1<=Arg_2 && Arg_3<=0
9:n_l3___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___2(Arg_0,Arg_1,Arg_2,Arg_3-1):|:1<=Arg_2 && 1<=Arg_2 && 0<=Arg_3 && 1<=Arg_2 && 1<=Arg_3
10:n_l3___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___2(Arg_0,Arg_1,Arg_2,Arg_3-1):|:1<=Arg_2 && 1<=Arg_3 && Arg_2<=Arg_3 && Arg_3<=Arg_2 && 1<=Arg_2 && 1<=Arg_2 && 1<=Arg_3 && 1<=Arg_2 && 0<=Arg_3 && 1<=Arg_2 && 1<=Arg_3

Preprocessing

Cut unsatisfiable transition 7: n_l2___5->n_l3___3

Found invariant 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_l1___6

Found invariant Arg_2<=0 && Arg_1+Arg_2<=0 && Arg_2<=Arg_0 && Arg_0+Arg_2<=0 && 0<=Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && Arg_1<=Arg_0 && Arg_0+Arg_1<=0 && Arg_0<=0 && 0<=Arg_0 for location n_l2___5

Found invariant Arg_0<=0 && 0<=Arg_0 for location n_l1___7

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

Found invariant Arg_3<=0 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && Arg_1+Arg_3<=0 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_l2___1

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

Found invariant Arg_2<=Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 for location n_l2___4

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___4, n_l2___5, n_l3___2, n_l3___3
Transitions:
0:n_l0(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___7(0,Arg_1,Arg_2,Arg_3)
1:n_l1___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___6(Arg_0+1,Arg_1-1,Arg_2,Arg_3):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && 1<=Arg_1
2:n_l1___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___4(Arg_0,Arg_1,Arg_0,Arg_3):|:0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_1 && Arg_1<=0
3:n_l1___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___6(Arg_0+1,Arg_1-1,Arg_2,Arg_3):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && 1<=Arg_1
4:n_l1___7(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___5(Arg_0,Arg_1,Arg_0,Arg_3):|:Arg_0<=0 && 0<=Arg_0 && Arg_0<=0 && 0<=Arg_0 && Arg_1<=0
5:n_l2___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___3(Arg_0,Arg_1,Arg_2,Arg_2):|:Arg_3<=0 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && Arg_1+Arg_3<=0 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_2 && Arg_3<=0 && 1<=Arg_2
6:n_l2___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___3(Arg_0,Arg_1,Arg_2,Arg_2):|:Arg_2<=Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_2 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && Arg_1<=0 && 1<=Arg_2 && 1<=Arg_2
8:n_l3___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___1(Arg_0,Arg_1,Arg_2-1,Arg_3):|:1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_2 && 1<=Arg_2 && 0<=Arg_3 && 1<=Arg_2 && Arg_3<=0
9:n_l3___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___2(Arg_0,Arg_1,Arg_2,Arg_3-1):|:1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_2 && 1<=Arg_2 && 0<=Arg_3 && 1<=Arg_2 && 1<=Arg_3
10:n_l3___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___2(Arg_0,Arg_1,Arg_2,Arg_3-1):|:Arg_3<=Arg_2 && Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_2 && 1<=Arg_3 && Arg_2<=Arg_3 && Arg_3<=Arg_2 && 1<=Arg_2 && 1<=Arg_2 && 1<=Arg_3 && 1<=Arg_2 && 0<=Arg_3 && 1<=Arg_2 && 1<=Arg_3

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

new bound:

2*Arg_1+1 {O(n)}

MPRF:

n_l1___6 [Arg_0+2*Arg_1 ]

MPRF for transition 5:n_l2___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___3(Arg_0,Arg_1,Arg_2,Arg_2):|:Arg_3<=0 && Arg_3<=Arg_2 && Arg_3<=Arg_1 && Arg_1+Arg_3<=0 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 0<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_2<=Arg_0 && 0<=Arg_2 && 0<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 1<=Arg_0+Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 0<=Arg_2 && Arg_3<=0 && 1<=Arg_2 of depth 1:

new bound:

2*Arg_1+3 {O(n)}

MPRF:

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

MPRF for transition 8:n_l3___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___1(Arg_0,Arg_1,Arg_2-1,Arg_3):|:1+Arg_3<=Arg_2 && 1+Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && 0<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_2 && 1<=Arg_2 && 0<=Arg_3 && 1<=Arg_2 && Arg_3<=0 of depth 1:

new bound:

2*Arg_1+3 {O(n)}

MPRF:

n_l2___1 [Arg_2 ]
n_l3___3 [Arg_2 ]
n_l3___2 [Arg_2 ]

MPRF for transition 10:n_l3___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___2(Arg_0,Arg_1,Arg_2,Arg_3-1):|:Arg_3<=Arg_2 && Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 1<=Arg_1+Arg_3 && 1+Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 1<=Arg_2 && 1<=Arg_1+Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 0<=Arg_1 && 1<=Arg_0+Arg_1 && 1<=Arg_0 && 1<=Arg_2 && 1<=Arg_3 && Arg_2<=Arg_3 && Arg_3<=Arg_2 && 1<=Arg_2 && 1<=Arg_2 && 1<=Arg_3 && 1<=Arg_2 && 0<=Arg_3 && 1<=Arg_2 && 1<=Arg_3 of depth 1:

new bound:

2*Arg_1+4 {O(n)}

MPRF:

n_l2___1 [Arg_2+1 ]
n_l3___3 [Arg_3+1 ]
n_l3___2 [Arg_2 ]

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

new bound:

8*Arg_1*Arg_1+30*Arg_1+28 {O(n^2)}

MPRF:

n_l3___3 [0 ]
n_l2___1 [0 ]
n_l3___2 [Arg_3+1 ]

All Bounds

Timebounds

Overall timebound:8*Arg_1*Arg_1+38*Arg_1+44 {O(n^2)}
0: n_l0->n_l1___7: 1 {O(1)}
1: n_l1___6->n_l1___6: 2*Arg_1+1 {O(n)}
2: n_l1___6->n_l2___4: 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___3: 2*Arg_1+3 {O(n)}
6: n_l2___4->n_l3___3: 1 {O(1)}
8: n_l3___2->n_l2___1: 2*Arg_1+3 {O(n)}
9: n_l3___2->n_l3___2: 8*Arg_1*Arg_1+30*Arg_1+28 {O(n^2)}
10: n_l3___3->n_l3___2: 2*Arg_1+4 {O(n)}

Costbounds

Overall costbound: 8*Arg_1*Arg_1+38*Arg_1+44 {O(n^2)}
0: n_l0->n_l1___7: 1 {O(1)}
1: n_l1___6->n_l1___6: 2*Arg_1+1 {O(n)}
2: n_l1___6->n_l2___4: 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___3: 2*Arg_1+3 {O(n)}
6: n_l2___4->n_l3___3: 1 {O(1)}
8: n_l3___2->n_l2___1: 2*Arg_1+3 {O(n)}
9: n_l3___2->n_l3___2: 8*Arg_1*Arg_1+30*Arg_1+28 {O(n^2)}
10: n_l3___3->n_l3___2: 2*Arg_1+4 {O(n)}

Sizebounds

0: n_l0->n_l1___7, Arg_0: 0 {O(1)}
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: 2*Arg_1+2 {O(n)}
1: n_l1___6->n_l1___6, Arg_1: Arg_1 {O(n)}
1: n_l1___6->n_l1___6, Arg_2: Arg_2 {O(n)}
1: n_l1___6->n_l1___6, Arg_3: Arg_3 {O(n)}
2: n_l1___6->n_l2___4, Arg_0: 2*Arg_1+3 {O(n)}
2: n_l1___6->n_l2___4, Arg_1: 0 {O(1)}
2: n_l1___6->n_l2___4, Arg_2: 2*Arg_1+3 {O(n)}
2: n_l1___6->n_l2___4, Arg_3: 2*Arg_3 {O(n)}
3: n_l1___7->n_l1___6, Arg_0: 1 {O(1)}
3: n_l1___7->n_l1___6, Arg_1: Arg_1 {O(n)}
3: n_l1___7->n_l1___6, Arg_2: Arg_2 {O(n)}
3: n_l1___7->n_l1___6, Arg_3: Arg_3 {O(n)}
4: n_l1___7->n_l2___5, Arg_0: 0 {O(1)}
4: n_l1___7->n_l2___5, Arg_1: Arg_1 {O(n)}
4: n_l1___7->n_l2___5, Arg_2: 0 {O(1)}
4: n_l1___7->n_l2___5, Arg_3: Arg_3 {O(n)}
5: n_l2___1->n_l3___3, Arg_0: 2*Arg_1+3 {O(n)}
5: n_l2___1->n_l3___3, Arg_1: 0 {O(1)}
5: n_l2___1->n_l3___3, Arg_2: 2*Arg_1+3 {O(n)}
5: n_l2___1->n_l3___3, Arg_3: 2*Arg_1+3 {O(n)}
6: n_l2___4->n_l3___3, Arg_0: 2*Arg_1+3 {O(n)}
6: n_l2___4->n_l3___3, Arg_1: 0 {O(1)}
6: n_l2___4->n_l3___3, Arg_2: 2*Arg_1+3 {O(n)}
6: n_l2___4->n_l3___3, Arg_3: 2*Arg_1+3 {O(n)}
8: n_l3___2->n_l2___1, Arg_0: 2*Arg_1+3 {O(n)}
8: n_l3___2->n_l2___1, Arg_1: 0 {O(1)}
8: n_l3___2->n_l2___1, Arg_2: 2*Arg_1+3 {O(n)}
8: n_l3___2->n_l2___1, Arg_3: 0 {O(1)}
9: n_l3___2->n_l3___2, Arg_0: 2*Arg_1+3 {O(n)}
9: n_l3___2->n_l3___2, Arg_1: 0 {O(1)}
9: n_l3___2->n_l3___2, Arg_2: 2*Arg_1+3 {O(n)}
9: n_l3___2->n_l3___2, Arg_3: 4*Arg_1+6 {O(n)}
10: n_l3___3->n_l3___2, Arg_0: 2*Arg_1+3 {O(n)}
10: n_l3___3->n_l3___2, Arg_1: 0 {O(1)}
10: n_l3___3->n_l3___2, Arg_2: 2*Arg_1+3 {O(n)}
10: n_l3___3->n_l3___2, Arg_3: 4*Arg_1+6 {O(n)}