Initial Problem
Start: n_l0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: n_l0, n_l1___5, n_l2___1, n_l2___4, n_l3___2, n_l3___3
Transitions:
0:n_l0(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___5(Arg_0,Arg_1,Arg_2,Arg_3)
1:n_l1___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___5(Arg_0,Arg_1,Arg_2+Arg_3,Arg_3-1):|:0<Arg_3
2:n_l1___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___4(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=0
3:n_l2___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___3(Arg_2,Arg_2,Arg_2,Arg_3):|:Arg_0<=0 && 0<Arg_2
4:n_l2___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___3(Arg_2,Arg_2,Arg_2,Arg_3):|:Arg_3<=0 && 0<Arg_2
5:n_l3___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___1(Arg_0,Arg_1,Arg_2-1,Arg_3):|:Arg_0<=0
6: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):|:0<Arg_0
7: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):|:0<Arg_0 && 0<Arg_0
Preprocessing
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
Found invariant Arg_3<=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___5, n_l2___1, n_l2___4, n_l3___2, n_l3___3
Transitions:
0:n_l0(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___5(Arg_0,Arg_1,Arg_2,Arg_3)
1:n_l1___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___5(Arg_0,Arg_1,Arg_2+Arg_3,Arg_3-1):|:0<Arg_3
2:n_l1___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___4(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=0
3: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_0<=0 && 0<Arg_2
4:n_l2___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l3___3(Arg_2,Arg_2,Arg_2,Arg_3):|:Arg_3<=0 && Arg_3<=0 && 0<Arg_2
5: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_0<=0
6: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 && 0<Arg_0
7: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 && 0<Arg_0 && 0<Arg_0
MPRF for transition 1:n_l1___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___5(Arg_0,Arg_1,Arg_2+Arg_3,Arg_3-1):|:0<Arg_3 of depth 1:
new bound:
Arg_3 {O(n)}
MPRF:
n_l1___5 [Arg_3 ]
MPRF for transition 3: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_0<=0 && 0<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+1 ]
n_l3___3 [Arg_2 ]
n_l3___2 [Arg_2 ]
MPRF for transition 5: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_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_1 ]
n_l3___2 [Arg_2 ]
MPRF for transition 7: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 && 0<Arg_0 && 0<Arg_0 of depth 1:
new bound:
4*Arg_3*Arg_3+4*Arg_2+4*Arg_3+1 {O(n^2)}
MPRF:
n_l2___1 [2*Arg_2-1 ]
n_l3___3 [2*Arg_0-1 ]
n_l3___2 [2*Arg_2-3 ]
All Bounds
Timebounds
Overall timebound:inf {Infinity}
0: n_l0->n_l1___5: 1 {O(1)}
1: n_l1___5->n_l1___5: Arg_3 {O(n)}
2: n_l1___5->n_l2___4: 1 {O(1)}
3: n_l2___1->n_l3___3: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
4: n_l2___4->n_l3___3: 1 {O(1)}
5: n_l3___2->n_l2___1: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
6: n_l3___2->n_l3___2: inf {Infinity}
7: n_l3___3->n_l3___2: 4*Arg_3*Arg_3+4*Arg_2+4*Arg_3+1 {O(n^2)}
Costbounds
Overall costbound: inf {Infinity}
0: n_l0->n_l1___5: 1 {O(1)}
1: n_l1___5->n_l1___5: Arg_3 {O(n)}
2: n_l1___5->n_l2___4: 1 {O(1)}
3: n_l2___1->n_l3___3: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
4: n_l2___4->n_l3___3: 1 {O(1)}
5: n_l3___2->n_l2___1: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
6: n_l3___2->n_l3___2: inf {Infinity}
7: n_l3___3->n_l3___2: 4*Arg_3*Arg_3+4*Arg_2+4*Arg_3+1 {O(n^2)}
Sizebounds
0: n_l0->n_l1___5, Arg_0: Arg_0 {O(n)}
0: n_l0->n_l1___5, Arg_1: Arg_1 {O(n)}
0: n_l0->n_l1___5, Arg_2: Arg_2 {O(n)}
0: n_l0->n_l1___5, Arg_3: Arg_3 {O(n)}
1: n_l1___5->n_l1___5, Arg_0: Arg_0 {O(n)}
1: n_l1___5->n_l1___5, Arg_1: Arg_1 {O(n)}
1: n_l1___5->n_l1___5, Arg_2: 2*Arg_3*Arg_3+2*Arg_3+Arg_2 {O(n^2)}
1: n_l1___5->n_l1___5, Arg_3: Arg_3 {O(n)}
2: n_l1___5->n_l2___4, Arg_0: 2*Arg_0 {O(n)}
2: n_l1___5->n_l2___4, Arg_1: 2*Arg_1 {O(n)}
2: n_l1___5->n_l2___4, Arg_2: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
2: n_l1___5->n_l2___4, Arg_3: 2*Arg_3 {O(n)}
3: n_l2___1->n_l3___3, Arg_0: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
3: n_l2___1->n_l3___3, Arg_1: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
3: n_l2___1->n_l3___3, Arg_2: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
3: n_l2___1->n_l3___3, Arg_3: 2*Arg_3 {O(n)}
4: n_l2___4->n_l3___3, Arg_0: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
4: n_l2___4->n_l3___3, Arg_1: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
4: n_l2___4->n_l3___3, Arg_2: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
4: n_l2___4->n_l3___3, Arg_3: 2*Arg_3 {O(n)}
5: n_l3___2->n_l2___1, Arg_2: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
5: n_l3___2->n_l2___1, Arg_3: 2*Arg_3 {O(n)}
6: n_l3___2->n_l3___2, Arg_2: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
6: n_l3___2->n_l3___2, Arg_3: 2*Arg_3 {O(n)}
7: n_l3___3->n_l3___2, Arg_0: 8*Arg_3*Arg_3+8*Arg_2+8*Arg_3 {O(n^2)}
7: n_l3___3->n_l3___2, Arg_1: 4*Arg_3*Arg_3+4*Arg_2+4*Arg_3 {O(n^2)}
7: n_l3___3->n_l3___2, Arg_2: 2*Arg_3*Arg_3+2*Arg_2+2*Arg_3 {O(n^2)}
7: n_l3___3->n_l3___2, Arg_3: 2*Arg_3 {O(n)}