Initial Problem

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

Preprocessing

Found invariant Arg_3<=0 for location l2

Found invariant Arg_3<=0 && 1+Arg_3<=Arg_2 && 1<=Arg_2 && Arg_1<=Arg_2 && Arg_1<=Arg_0 for location l3

Problem after Preprocessing

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

MPRF for transition 1:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_0,Arg_1,Arg_2+Arg_3,Arg_3-1):|:0<Arg_3 of depth 1:

new bound:

Arg_3 {O(n)}

MPRF:

l1 [Arg_3 ]

MPRF for transition 3:l2(Arg_0,Arg_1,Arg_2,Arg_3) -> l3(Arg_2,Arg_2,Arg_2,Arg_3):|:Arg_3<=0 && 0<Arg_2 of depth 1:

new bound:

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

MPRF:

l3 [Arg_2-1 ]
l2 [Arg_2 ]

MPRF for transition 5:l3(Arg_0,Arg_1,Arg_2,Arg_3) -> l2(Arg_0,Arg_1,Arg_2-1,Arg_3):|:Arg_3<=0 && 1+Arg_3<=Arg_2 && 1<=Arg_2 && Arg_1<=Arg_2 && Arg_1<=Arg_0 && Arg_0<=0 of depth 1:

new bound:

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

MPRF:

l3 [Arg_2 ]
l2 [Arg_2 ]

MPRF for transition 4:l3(Arg_0,Arg_1,Arg_2,Arg_3) -> l3(Arg_0+Arg_1,Arg_1-1,Arg_2,Arg_3):|:Arg_3<=0 && 1+Arg_3<=Arg_2 && 1<=Arg_2 && Arg_1<=Arg_2 && Arg_1<=Arg_0 && 0<Arg_0 of depth 2:

new bound:

64*Arg_3*Arg_3*Arg_3*Arg_3+128*Arg_2*Arg_3*Arg_3+128*Arg_3*Arg_3*Arg_3+128*Arg_2*Arg_3+146*Arg_3*Arg_3+64*Arg_2*Arg_2+82*Arg_2+82*Arg_3+25 {O(n^4)}

MPRF:

l2 [Arg_2+3 ; Arg_2 ]
l3 [Arg_1+3 ; Arg_0+2*Arg_2-2*Arg_1 ]

Analysing control-flow refined program

Found invariant Arg_3<=0 for location l2

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___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 && 1+Arg_1<=Arg_2 && 2+Arg_1<=Arg_0 for location n_l3___2

MPRF for transition 55:n_l2___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___3(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_3<=0 && Arg_3<=0 && 0<=Arg_2 && Arg_3<=0 && Arg_1<=Arg_0 && Arg_0<=0 && 0<Arg_2 && Arg_3<=0 of depth 1:

new bound:

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

MPRF:

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

MPRF for transition 57: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 && 1+Arg_1<=Arg_2 && 2+Arg_1<=Arg_0 && Arg_1<=Arg_0 && Arg_3<=0 && 1<=Arg_2 && Arg_1<=Arg_2 && 1<=Arg_2 && Arg_3<=0 && Arg_1<=Arg_0 && Arg_0<=0 of depth 1:

new bound:

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

MPRF:

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

MPRF for transition 59: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 && 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 && Arg_1<=Arg_0 && Arg_3<=0 && Arg_1<=Arg_2 && 0<Arg_0 && Arg_1<=Arg_0 && 1<=Arg_2 && 0<Arg_0 && Arg_3<=0 && Arg_1<=Arg_2 of depth 1:

new bound:

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

MPRF:

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

MPRF for transition 58: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 && 1+Arg_1<=Arg_2 && 2+Arg_1<=Arg_0 && Arg_1<=Arg_0 && Arg_3<=0 && 1<=Arg_2 && Arg_1<=Arg_2 && Arg_1<=Arg_0 && 1<=Arg_2 && 0<Arg_0 && Arg_3<=0 && Arg_1<=Arg_2 of depth 2:

new bound:

224*Arg_3*Arg_3*Arg_3*Arg_3+448*Arg_2*Arg_3*Arg_3+448*Arg_3*Arg_3*Arg_3+224*Arg_2*Arg_2+338*Arg_3*Arg_3+448*Arg_2*Arg_3+114*Arg_2+114*Arg_3+1 {O(n^4)}

MPRF:

n_l2___1 [3*Arg_2 ; 4*Arg_2 ]
n_l3___3 [3*Arg_1 ; Arg_0+Arg_1+2*Arg_2 ]
n_l3___2 [Arg_1+3 ; Arg_0+2*Arg_2-2*Arg_1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:64*Arg_3*Arg_3*Arg_3*Arg_3+128*Arg_2*Arg_3*Arg_3+128*Arg_3*Arg_3*Arg_3+128*Arg_2*Arg_3+150*Arg_3*Arg_3+64*Arg_2*Arg_2+86*Arg_2+87*Arg_3+27 {O(n^4)}
0: l0->l1: 1 {O(1)}
1: l1->l1: Arg_3 {O(n)}
2: l1->l2: 1 {O(1)}
3: l2->l3: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
4: l3->l3: 64*Arg_3*Arg_3*Arg_3*Arg_3+128*Arg_2*Arg_3*Arg_3+128*Arg_3*Arg_3*Arg_3+128*Arg_2*Arg_3+146*Arg_3*Arg_3+64*Arg_2*Arg_2+82*Arg_2+82*Arg_3+25 {O(n^4)}
5: l3->l2: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}

Costbounds

Overall costbound: 64*Arg_3*Arg_3*Arg_3*Arg_3+128*Arg_2*Arg_3*Arg_3+128*Arg_3*Arg_3*Arg_3+128*Arg_2*Arg_3+150*Arg_3*Arg_3+64*Arg_2*Arg_2+86*Arg_2+87*Arg_3+27 {O(n^4)}
0: l0->l1: 1 {O(1)}
1: l1->l1: Arg_3 {O(n)}
2: l1->l2: 1 {O(1)}
3: l2->l3: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
4: l3->l3: 64*Arg_3*Arg_3*Arg_3*Arg_3+128*Arg_2*Arg_3*Arg_3+128*Arg_3*Arg_3*Arg_3+128*Arg_2*Arg_3+146*Arg_3*Arg_3+64*Arg_2*Arg_2+82*Arg_2+82*Arg_3+25 {O(n^4)}
5: l3->l2: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}

Sizebounds

0: l0->l1, Arg_0: Arg_0 {O(n)}
0: l0->l1, Arg_1: Arg_1 {O(n)}
0: l0->l1, Arg_2: Arg_2 {O(n)}
0: l0->l1, Arg_3: Arg_3 {O(n)}
1: l1->l1, Arg_0: Arg_0 {O(n)}
1: l1->l1, Arg_1: Arg_1 {O(n)}
1: l1->l1, Arg_2: 2*Arg_3*Arg_3+2*Arg_3+Arg_2 {O(n^2)}
1: l1->l1, Arg_3: Arg_3 {O(n)}
2: l1->l2, Arg_0: 2*Arg_0 {O(n)}
2: l1->l2, Arg_1: 2*Arg_1 {O(n)}
2: l1->l2, Arg_2: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
2: l1->l2, Arg_3: 2*Arg_3 {O(n)}
3: l2->l3, Arg_0: 4*Arg_3*Arg_3+4*Arg_2+4*Arg_3 {O(n^2)}
3: l2->l3, Arg_1: 4*Arg_3*Arg_3+4*Arg_2+4*Arg_3 {O(n^2)}
3: l2->l3, Arg_2: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
3: l2->l3, Arg_3: 2*Arg_3 {O(n)}
4: l3->l3, Arg_0: 4096*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3+16384*Arg_2*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3+16384*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3+24576*Arg_2*Arg_2*Arg_3*Arg_3*Arg_3*Arg_3+35584*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3+49152*Arg_2*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3+16384*Arg_2*Arg_2*Arg_2*Arg_3*Arg_3+49152*Arg_2*Arg_2*Arg_3*Arg_3*Arg_3+49408*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3+82176*Arg_2*Arg_3*Arg_3*Arg_3*Arg_3+16384*Arg_2*Arg_2*Arg_2*Arg_3+4096*Arg_2*Arg_2*Arg_2*Arg_2+47764*Arg_3*Arg_3*Arg_3*Arg_3+57600*Arg_2*Arg_2*Arg_3*Arg_3+82432*Arg_2*Arg_3*Arg_3*Arg_3+11008*Arg_2*Arg_2*Arg_2+32296*Arg_3*Arg_3*Arg_3+33024*Arg_2*Arg_2*Arg_3+54312*Arg_2*Arg_3*Arg_3+10644*Arg_2*Arg_2+15038*Arg_3*Arg_3+21288*Arg_2*Arg_3+4394*Arg_2+4394*Arg_3+650 {O(n^8)}
4: l3->l3, Arg_1: 64*Arg_3*Arg_3*Arg_3*Arg_3+128*Arg_2*Arg_3*Arg_3+128*Arg_3*Arg_3*Arg_3+128*Arg_2*Arg_3+150*Arg_3*Arg_3+64*Arg_2*Arg_2+86*Arg_2+86*Arg_3+25 {O(n^4)}
4: l3->l3, Arg_2: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
4: l3->l3, Arg_3: 2*Arg_3 {O(n)}
5: l3->l2, Arg_0: 4096*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3+16384*Arg_2*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3+16384*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3+24576*Arg_2*Arg_2*Arg_3*Arg_3*Arg_3*Arg_3+35584*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3+49152*Arg_2*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3+16384*Arg_2*Arg_2*Arg_2*Arg_3*Arg_3+49152*Arg_2*Arg_2*Arg_3*Arg_3*Arg_3+49408*Arg_3*Arg_3*Arg_3*Arg_3*Arg_3+82176*Arg_2*Arg_3*Arg_3*Arg_3*Arg_3+16384*Arg_2*Arg_2*Arg_2*Arg_3+4096*Arg_2*Arg_2*Arg_2*Arg_2+47764*Arg_3*Arg_3*Arg_3*Arg_3+57600*Arg_2*Arg_2*Arg_3*Arg_3+82432*Arg_2*Arg_3*Arg_3*Arg_3+11008*Arg_2*Arg_2*Arg_2+32296*Arg_3*Arg_3*Arg_3+33024*Arg_2*Arg_2*Arg_3+54312*Arg_2*Arg_3*Arg_3+10644*Arg_2*Arg_2+15038*Arg_3*Arg_3+21288*Arg_2*Arg_3+4394*Arg_2+4394*Arg_3+650 {O(n^8)}
5: l3->l2, Arg_1: 64*Arg_3*Arg_3*Arg_3*Arg_3+128*Arg_2*Arg_3*Arg_3+128*Arg_3*Arg_3*Arg_3+128*Arg_2*Arg_3+150*Arg_3*Arg_3+64*Arg_2*Arg_2+86*Arg_2+86*Arg_3+25 {O(n^4)}
5: l3->l2, Arg_2: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
5: l3->l2, Arg_3: 2*Arg_3 {O(n)}