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 ]
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 54: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 56: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 58: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 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
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: inf {Infinity}
5: l3->l2: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
Costbounds
Overall costbound: inf {Infinity}
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: inf {Infinity}
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_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_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)}