Initial Problem
Start: n_l0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: n_l0, n_l1___1, n_l1___2, n_l1___5, n_l1___6, n_l2___3, n_l2___4
Transitions:
0:n_l0(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___6(Arg_0,Arg_1,Arg_2,Arg_3)
1:n_l1___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___5(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:1<=Arg_0 && 1<=Arg_0 && Arg_1<=Arg_0+Arg_2 && 1<=Arg_0
2:n_l1___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___1(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:1<=Arg_0 && 1<=Arg_0 && Arg_1<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && Arg_0<=Arg_3 && Arg_3<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0
3:n_l1___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___5(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:Arg_1<=Arg_0+Arg_2 && 1<=Arg_0
4:n_l1___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___3(Arg_0,Arg_1,Arg_2,Arg_3-1):|:Arg_1<=Arg_0+Arg_2 && Arg_0<=0
5:n_l1___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___5(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:1<=Arg_0
6:n_l1___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___4(Arg_0,Arg_1,Arg_2,Arg_3-1):|:Arg_0<=0
7:n_l2___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___2(Arg_3,Arg_3,Arg_3,Arg_3):|:Arg_0<=0 && Arg_1<=Arg_0+Arg_2 && 1<=Arg_3
8:n_l2___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___2(Arg_3,Arg_3,Arg_3,Arg_3):|:Arg_0<=0 && 1<=Arg_3
Preprocessing
Found invariant Arg_3<=Arg_2 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 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_l1___2
Found invariant Arg_0<=0 for location n_l2___3
Found invariant Arg_3<=1+Arg_2 && 1+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 2+Arg_2<=Arg_1 && 2+Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location n_l1___1
Found invariant Arg_0<=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___1, n_l1___2, n_l1___5, n_l1___6, n_l2___3, n_l2___4
Transitions:
0:n_l0(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___6(Arg_0,Arg_1,Arg_2,Arg_3)
1:n_l1___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___5(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:Arg_3<=1+Arg_2 && 1+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 2+Arg_2<=Arg_1 && 2+Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=Arg_0+Arg_2 && 1<=Arg_0
2:n_l1___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___1(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 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 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && Arg_0<=Arg_3 && Arg_3<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0
3:n_l1___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___5(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:Arg_1<=Arg_0+Arg_2 && 1<=Arg_0
4:n_l1___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___3(Arg_0,Arg_1,Arg_2,Arg_3-1):|:Arg_1<=Arg_0+Arg_2 && Arg_0<=0
5:n_l1___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___5(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:1<=Arg_0
6:n_l1___6(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___4(Arg_0,Arg_1,Arg_2,Arg_3-1):|:Arg_0<=0
7:n_l2___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___2(Arg_3,Arg_3,Arg_3,Arg_3):|:Arg_0<=0 && Arg_0<=0 && Arg_1<=Arg_0+Arg_2 && 1<=Arg_3
8:n_l2___4(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___2(Arg_3,Arg_3,Arg_3,Arg_3):|:Arg_0<=0 && Arg_0<=0 && 1<=Arg_3
MPRF for transition 1:n_l1___1(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___5(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:Arg_3<=1+Arg_2 && 1+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 1<=Arg_3 && 1<=Arg_2+Arg_3 && 1+Arg_2<=Arg_3 && 3<=Arg_1+Arg_3 && 3<=Arg_0+Arg_3 && 2+Arg_2<=Arg_1 && 2+Arg_2<=Arg_0 && 0<=Arg_2 && 2<=Arg_1+Arg_2 && 2<=Arg_0+Arg_2 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=Arg_0+Arg_2 && 1<=Arg_0 of depth 1:
new bound:
2*Arg_3+2 {O(n)}
MPRF:
n_l1___1 [Arg_2+1 ]
n_l1___5 [Arg_3-1 ]
n_l2___3 [Arg_3 ]
n_l1___2 [Arg_0 ]
MPRF for transition 2:n_l1___2(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___1(Arg_0+Arg_1,Arg_1+Arg_2,Arg_2-1,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=Arg_1 && Arg_3<=Arg_0 && 1<=Arg_3 && 2<=Arg_2+Arg_3 && Arg_2<=Arg_3 && 2<=Arg_1+Arg_3 && Arg_1<=Arg_3 && 2<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 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 && 1<=Arg_0 && 1<=Arg_0 && Arg_1<=Arg_0+Arg_2 && Arg_0<=Arg_2 && Arg_2<=Arg_0 && Arg_0<=Arg_3 && Arg_3<=Arg_0 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 of depth 1:
new bound:
2*Arg_3+2 {O(n)}
MPRF:
n_l1___1 [Arg_3-1 ]
n_l1___5 [Arg_3-1 ]
n_l2___3 [Arg_3 ]
n_l1___2 [Arg_3 ]
MPRF for transition 7:n_l2___3(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l1___2(Arg_3,Arg_3,Arg_3,Arg_3):|:Arg_0<=0 && Arg_0<=0 && Arg_1<=Arg_0+Arg_2 && 1<=Arg_3 of depth 1:
new bound:
2*Arg_3+3 {O(n)}
MPRF:
n_l1___1 [Arg_2 ]
n_l1___5 [Arg_3-1 ]
n_l2___3 [Arg_3 ]
n_l1___2 [Arg_0-1 ]
MPRF for transition 4:n_l1___5(Arg_0,Arg_1,Arg_2,Arg_3) -> n_l2___3(Arg_0,Arg_1,Arg_2,Arg_3-1):|:Arg_1<=Arg_0+Arg_2 && Arg_0<=0 of depth 1:
new bound:
2*Arg_3+5 {O(n)}
MPRF:
n_l1___2 [1 ]
n_l1___1 [1 ]
n_l1___5 [1 ]
n_l2___3 [0 ]
All Bounds
Timebounds
Overall timebound:inf {Infinity}
0: n_l0->n_l1___6: 1 {O(1)}
1: n_l1___1->n_l1___5: 2*Arg_3+2 {O(n)}
2: n_l1___2->n_l1___1: 2*Arg_3+2 {O(n)}
3: n_l1___5->n_l1___5: inf {Infinity}
4: n_l1___5->n_l2___3: 2*Arg_3+5 {O(n)}
5: n_l1___6->n_l1___5: 1 {O(1)}
6: n_l1___6->n_l2___4: 1 {O(1)}
7: n_l2___3->n_l1___2: 2*Arg_3+3 {O(n)}
8: n_l2___4->n_l1___2: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
0: n_l0->n_l1___6: 1 {O(1)}
1: n_l1___1->n_l1___5: 2*Arg_3+2 {O(n)}
2: n_l1___2->n_l1___1: 2*Arg_3+2 {O(n)}
3: n_l1___5->n_l1___5: inf {Infinity}
4: n_l1___5->n_l2___3: 2*Arg_3+5 {O(n)}
5: n_l1___6->n_l1___5: 1 {O(1)}
6: n_l1___6->n_l2___4: 1 {O(1)}
7: n_l2___3->n_l1___2: 2*Arg_3+3 {O(n)}
8: n_l2___4->n_l1___2: 1 {O(1)}
Sizebounds
0: n_l0->n_l1___6, Arg_0: Arg_0 {O(n)}
0: n_l0->n_l1___6, Arg_1: Arg_1 {O(n)}
0: n_l0->n_l1___6, Arg_2: Arg_2 {O(n)}
0: n_l0->n_l1___6, Arg_3: Arg_3 {O(n)}
1: n_l1___1->n_l1___5, Arg_0: 24*Arg_3+28 {O(n)}
1: n_l1___1->n_l1___5, Arg_1: 24*Arg_3+28 {O(n)}
1: n_l1___1->n_l1___5, Arg_2: 6*Arg_3+8 {O(n)}
1: n_l1___1->n_l1___5, Arg_3: 5*Arg_3+6 {O(n)}
2: n_l1___2->n_l1___1, Arg_0: 12*Arg_3+14 {O(n)}
2: n_l1___2->n_l1___1, Arg_1: 12*Arg_3+14 {O(n)}
2: n_l1___2->n_l1___1, Arg_2: 6*Arg_3+7 {O(n)}
2: n_l1___2->n_l1___1, Arg_3: 5*Arg_3+6 {O(n)}
3: n_l1___5->n_l1___5, Arg_3: 5*Arg_3+6 {O(n)}
4: n_l1___5->n_l2___3, Arg_3: 5*Arg_3+6 {O(n)}
5: n_l1___6->n_l1___5, Arg_0: Arg_0+Arg_1 {O(n)}
5: n_l1___6->n_l1___5, Arg_1: Arg_1+Arg_2 {O(n)}
5: n_l1___6->n_l1___5, Arg_2: Arg_2+1 {O(n)}
5: n_l1___6->n_l1___5, Arg_3: Arg_3 {O(n)}
6: n_l1___6->n_l2___4, Arg_0: Arg_0 {O(n)}
6: n_l1___6->n_l2___4, Arg_1: Arg_1 {O(n)}
6: n_l1___6->n_l2___4, Arg_2: Arg_2 {O(n)}
6: n_l1___6->n_l2___4, Arg_3: Arg_3+1 {O(n)}
7: n_l2___3->n_l1___2, Arg_0: 5*Arg_3+6 {O(n)}
7: n_l2___3->n_l1___2, Arg_1: 5*Arg_3+6 {O(n)}
7: n_l2___3->n_l1___2, Arg_2: 5*Arg_3+6 {O(n)}
7: n_l2___3->n_l1___2, Arg_3: 5*Arg_3+6 {O(n)}
8: n_l2___4->n_l1___2, Arg_0: Arg_3+1 {O(n)}
8: n_l2___4->n_l1___2, Arg_1: Arg_3+1 {O(n)}
8: n_l2___4->n_l1___2, Arg_2: Arg_3+1 {O(n)}
8: n_l2___4->n_l1___2, Arg_3: Arg_3+1 {O(n)}