Initial Problem

Start: l0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
0:l0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> l1(Arg_4,Arg_5,Arg_6,Arg_3,Arg_4,Arg_5,Arg_6)
1:l1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> l1(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3,Arg_4,Arg_5,Arg_6):|:1<=Arg_0
2:l1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> l2(Arg_0,Arg_1,Arg_2,Arg_3-1,Arg_4,Arg_5,Arg_6):|:Arg_0<=0
3:l2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> l1(Arg_4,Arg_5,Arg_6,Arg_3,Arg_4,Arg_5,Arg_6):|:1<=Arg_3
4:l2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> l3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_3<=0

Preprocessing

Found invariant Arg_2<=Arg_6 && Arg_0<=0 for location l2

Found invariant Arg_2<=Arg_6 for location l1

Found invariant Arg_2<=Arg_6 && Arg_3<=0 && Arg_0+Arg_3<=0 && Arg_0<=0 for location l3

Problem after Preprocessing

Start: l0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
0:l0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> l1(Arg_4,Arg_5,Arg_6,Arg_3,Arg_4,Arg_5,Arg_6)
1:l1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> l1(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_2<=Arg_6 && 1<=Arg_0
2:l1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> l2(Arg_0,Arg_1,Arg_2,Arg_3-1,Arg_4,Arg_5,Arg_6):|:Arg_2<=Arg_6 && Arg_0<=0
3:l2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> l1(Arg_4,Arg_5,Arg_6,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_2<=Arg_6 && Arg_0<=0 && 1<=Arg_3
4:l2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> l3(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_2<=Arg_6 && Arg_0<=0 && Arg_3<=0

MPRF for transition 3:l2(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> l1(Arg_4,Arg_5,Arg_6,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_2<=Arg_6 && Arg_0<=0 && 1<=Arg_3 of depth 1:

new bound:

Arg_3+1 {O(n)}

MPRF:

l2 [Arg_3 ]
l1 [Arg_3-1 ]

MPRF for transition 2:l1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> l2(Arg_0,Arg_1,Arg_2,Arg_3-1,Arg_4,Arg_5,Arg_6):|:Arg_2<=Arg_6 && Arg_0<=0 of depth 1:

new bound:

Arg_3+2 {O(n)}

MPRF:

l1 [1 ]
l2 [0 ]

Analysing control-flow refined program

Found invariant Arg_2<=Arg_6 && Arg_0<=Arg_4 && Arg_0<=0 for location l2

Found invariant Arg_6<=Arg_2 && Arg_2<=Arg_6 && Arg_5<=Arg_1 && Arg_1<=Arg_5 && Arg_4<=Arg_0 && Arg_0<=Arg_4 for location l1

Found invariant Arg_2<=Arg_6 && Arg_0<=Arg_4 && Arg_3<=0 && Arg_0+Arg_3<=0 && Arg_0<=0 for location l3

Found invariant 1+Arg_2<=Arg_6 && 1<=Arg_4 for location n_l1___1

knowledge_propagation leads to new time bound Arg_3+2 {O(n)} for transition 39:l1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> n_l1___1(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_6<=Arg_2 && Arg_2<=Arg_6 && Arg_5<=Arg_1 && Arg_1<=Arg_5 && Arg_4<=Arg_0 && Arg_0<=Arg_4 && Arg_2<=Arg_6 && Arg_1<=Arg_5 && Arg_5<=Arg_1 && Arg_2<=Arg_6 && Arg_6<=Arg_2 && Arg_0<=Arg_4 && Arg_4<=Arg_0 && Arg_2<=Arg_6 && Arg_6<=Arg_2 && Arg_0<=Arg_4 && Arg_4<=Arg_0 && Arg_1<=Arg_5 && Arg_5<=Arg_1 && 1<=Arg_3 && 1<=Arg_0 && Arg_2<=Arg_6

knowledge_propagation leads to new time bound Arg_3+2 {O(n)} for transition 40:l1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> n_l1___1(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3,Arg_4,Arg_5,Arg_6):|:Arg_6<=Arg_2 && Arg_2<=Arg_6 && Arg_5<=Arg_1 && Arg_1<=Arg_5 && Arg_4<=Arg_0 && Arg_0<=Arg_4 && Arg_2<=Arg_6 && Arg_1<=Arg_5 && Arg_5<=Arg_1 && Arg_2<=Arg_6 && Arg_6<=Arg_2 && Arg_0<=Arg_4 && Arg_4<=Arg_0 && 1<=Arg_0 && Arg_2<=Arg_6

MPRF for transition 43:n_l1___1(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5,Arg_6) -> l2(Arg_0,Arg_1,Arg_2,Arg_3-1,Arg_4,Arg_5,Arg_6):|:1+Arg_2<=Arg_6 && 1<=Arg_4 && Arg_2<=Arg_6 && Arg_0<=0 of depth 1:

new bound:

9*Arg_3*Arg_4+11*Arg_4+Arg_3+2 {O(n^2)}

MPRF:

l1 [Arg_4+1-Arg_0 ]
n_l1___1 [1 ]
l2 [2*Arg_2+1-2*Arg_6 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
0: l0->l1: 1 {O(1)}
1: l1->l1: inf {Infinity}
2: l1->l2: Arg_3+2 {O(n)}
3: l2->l1: Arg_3+1 {O(n)}
4: l2->l3: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
0: l0->l1: 1 {O(1)}
1: l1->l1: inf {Infinity}
2: l1->l2: Arg_3+2 {O(n)}
3: l2->l1: Arg_3+1 {O(n)}
4: l2->l3: 1 {O(1)}

Sizebounds

0: l0->l1, Arg_0: Arg_4 {O(n)}
0: l0->l1, Arg_1: Arg_5 {O(n)}
0: l0->l1, Arg_2: Arg_6 {O(n)}
0: l0->l1, Arg_3: Arg_3 {O(n)}
0: l0->l1, Arg_4: Arg_4 {O(n)}
0: l0->l1, Arg_5: Arg_5 {O(n)}
0: l0->l1, Arg_6: Arg_6 {O(n)}
1: l1->l1, Arg_3: 3*Arg_3+2 {O(n)}
1: l1->l1, Arg_4: 2*Arg_4 {O(n)}
1: l1->l1, Arg_5: 2*Arg_5 {O(n)}
1: l1->l1, Arg_6: 2*Arg_6 {O(n)}
2: l1->l2, Arg_3: 3*Arg_3+2 {O(n)}
2: l1->l2, Arg_4: 2*Arg_4 {O(n)}
2: l1->l2, Arg_5: 2*Arg_5 {O(n)}
2: l1->l2, Arg_6: 2*Arg_6 {O(n)}
3: l2->l1, Arg_0: 2*Arg_4 {O(n)}
3: l2->l1, Arg_1: 2*Arg_5 {O(n)}
3: l2->l1, Arg_2: 2*Arg_6 {O(n)}
3: l2->l1, Arg_3: 3*Arg_3+2 {O(n)}
3: l2->l1, Arg_4: 2*Arg_4 {O(n)}
3: l2->l1, Arg_5: 2*Arg_5 {O(n)}
3: l2->l1, Arg_6: 2*Arg_6 {O(n)}
4: l2->l3, Arg_3: 3*Arg_3+2 {O(n)}
4: l2->l3, Arg_4: 2*Arg_4 {O(n)}
4: l2->l3, Arg_5: 2*Arg_5 {O(n)}
4: l2->l3, Arg_6: 2*Arg_6 {O(n)}