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(0,Arg_1,Arg_2,Arg_3)
1:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_0+1,Arg_1-1,Arg_2,Arg_3):|:1<=Arg_1
2:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l2(Arg_0,Arg_1,Arg_0,Arg_3):|:Arg_1<=0
3:l2(Arg_0,Arg_1,Arg_2,Arg_3) -> l3(Arg_0,Arg_1,Arg_2,Arg_2):|:1<=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_2
4:l3(Arg_0,Arg_1,Arg_2,Arg_3) -> l3(Arg_0,Arg_1,Arg_2,Arg_3-1):|:1<=Arg_3 && 1<=Arg_2
Preprocessing
Found invariant Arg_2<=Arg_0 && 0<=Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_0 for location l2
Found invariant 0<=Arg_0 for location l1
Found invariant Arg_3<=Arg_2 && Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 1<=Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 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(0,Arg_1,Arg_2,Arg_3)
1:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_0+1,Arg_1-1,Arg_2,Arg_3):|:0<=Arg_0 && 1<=Arg_1
2:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l2(Arg_0,Arg_1,Arg_0,Arg_3):|:0<=Arg_0 && Arg_1<=0
3:l2(Arg_0,Arg_1,Arg_2,Arg_3) -> l3(Arg_0,Arg_1,Arg_2,Arg_2):|:Arg_2<=Arg_0 && 0<=Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_0 && 1<=Arg_2
5:l3(Arg_0,Arg_1,Arg_2,Arg_3) -> l2(Arg_0,Arg_1,Arg_2-1,Arg_3):|:Arg_3<=Arg_2 && Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 1<=Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 1<=Arg_0 && Arg_3<=0 && 1<=Arg_2
4:l3(Arg_0,Arg_1,Arg_2,Arg_3) -> l3(Arg_0,Arg_1,Arg_2,Arg_3-1):|:Arg_3<=Arg_2 && Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 1<=Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_3 && 1<=Arg_2
MPRF for transition 1:l1(Arg_0,Arg_1,Arg_2,Arg_3) -> l1(Arg_0+1,Arg_1-1,Arg_2,Arg_3):|:0<=Arg_0 && 1<=Arg_1 of depth 1:
new bound:
Arg_1 {O(n)}
MPRF:
l1 [Arg_1 ]
MPRF for transition 3:l2(Arg_0,Arg_1,Arg_2,Arg_3) -> l3(Arg_0,Arg_1,Arg_2,Arg_2):|:Arg_2<=Arg_0 && 0<=Arg_2 && Arg_1<=Arg_2 && 0<=Arg_0+Arg_2 && Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_0 && 1<=Arg_2 of depth 1:
new bound:
Arg_1+1 {O(n)}
MPRF:
l3 [Arg_2 ]
l2 [Arg_2+1 ]
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<=Arg_2 && Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 1<=Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 1<=Arg_0 && Arg_3<=0 && 1<=Arg_2 of depth 1:
new bound:
Arg_1 {O(n)}
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_2,Arg_3-1):|:Arg_3<=Arg_2 && Arg_3<=Arg_0 && 0<=Arg_3 && 1<=Arg_2+Arg_3 && Arg_1<=Arg_3 && 1<=Arg_0+Arg_3 && Arg_2<=Arg_0 && 1<=Arg_2 && 1+Arg_1<=Arg_2 && 2<=Arg_0+Arg_2 && Arg_1<=0 && 1+Arg_1<=Arg_0 && 1<=Arg_0 && 1<=Arg_3 && 1<=Arg_2 of depth 1:
new bound:
Arg_1*Arg_1+2*Arg_1+1 {O(n^2)}
MPRF:
l2 [Arg_2+1 ]
l3 [Arg_3+1 ]
All Bounds
Timebounds
Overall timebound:Arg_1*Arg_1+5*Arg_1+4 {O(n^2)}
0: l0->l1: 1 {O(1)}
1: l1->l1: Arg_1 {O(n)}
2: l1->l2: 1 {O(1)}
3: l2->l3: Arg_1+1 {O(n)}
4: l3->l3: Arg_1*Arg_1+2*Arg_1+1 {O(n^2)}
5: l3->l2: Arg_1 {O(n)}
Costbounds
Overall costbound: Arg_1*Arg_1+5*Arg_1+4 {O(n^2)}
0: l0->l1: 1 {O(1)}
1: l1->l1: Arg_1 {O(n)}
2: l1->l2: 1 {O(1)}
3: l2->l3: Arg_1+1 {O(n)}
4: l3->l3: Arg_1*Arg_1+2*Arg_1+1 {O(n^2)}
5: l3->l2: Arg_1 {O(n)}
Sizebounds
0: l0->l1, Arg_0: 0 {O(1)}
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_1 {O(n)}
1: l1->l1, Arg_1: Arg_1 {O(n)}
1: l1->l1, Arg_2: Arg_2 {O(n)}
1: l1->l1, Arg_3: Arg_3 {O(n)}
2: l1->l2, Arg_0: Arg_1 {O(n)}
2: l1->l2, Arg_1: 2*Arg_1 {O(n)}
2: l1->l2, Arg_2: Arg_1 {O(n)}
2: l1->l2, Arg_3: 2*Arg_3 {O(n)}
3: l2->l3, Arg_0: Arg_1 {O(n)}
3: l2->l3, Arg_1: 2*Arg_1 {O(n)}
3: l2->l3, Arg_2: Arg_1 {O(n)}
3: l2->l3, Arg_3: 2*Arg_1 {O(n)}
4: l3->l3, Arg_0: Arg_1 {O(n)}
4: l3->l3, Arg_1: 2*Arg_1 {O(n)}
4: l3->l3, Arg_2: Arg_1 {O(n)}
4: l3->l3, Arg_3: 2*Arg_1 {O(n)}
5: l3->l2, Arg_0: Arg_1 {O(n)}
5: l3->l2, Arg_1: 2*Arg_1 {O(n)}
5: l3->l2, Arg_2: Arg_1 {O(n)}
5: l3->l2, Arg_3: 0 {O(1)}