Initial Problem

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

Preprocessing

Found invariant Arg_0<=0 for location l2

Problem after Preprocessing

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

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

new bound:

Arg_0 {O(n)}

MPRF:

l1 [Arg_0 ]

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

new bound:

2*Arg_0*Arg_0+2*Arg_0+2*Arg_1 {O(n^2)}

MPRF:

l2 [Arg_1 ]

All Bounds

Timebounds

Overall timebound:2*Arg_0*Arg_0+2*Arg_1+3*Arg_0+2 {O(n^2)}
0: l0->l1: 1 {O(1)}
1: l1->l1: Arg_0 {O(n)}
2: l1->l2: 1 {O(1)}
3: l2->l2: 2*Arg_0*Arg_0+2*Arg_0+2*Arg_1 {O(n^2)}

Costbounds

Overall costbound: 2*Arg_0*Arg_0+2*Arg_1+3*Arg_0+2 {O(n^2)}
0: l0->l1: 1 {O(1)}
1: l1->l1: Arg_0 {O(n)}
2: l1->l2: 1 {O(1)}
3: l2->l2: 2*Arg_0*Arg_0+2*Arg_0+2*Arg_1 {O(n^2)}

Sizebounds

0: l0->l1, Arg_0: Arg_0 {O(n)}
0: l0->l1, Arg_1: Arg_1 {O(n)}
1: l1->l1, Arg_0: Arg_0 {O(n)}
1: l1->l1, Arg_1: 2*Arg_0*Arg_0+2*Arg_0+Arg_1 {O(n^2)}
2: l1->l2, Arg_0: 2*Arg_0 {O(n)}
2: l1->l2, Arg_1: 2*Arg_0*Arg_0+2*Arg_0+2*Arg_1 {O(n^2)}
3: l2->l2, Arg_0: 2*Arg_0 {O(n)}
3: l2->l2, Arg_1: 2*Arg_0*Arg_0+2*Arg_0+2*Arg_1 {O(n^2)}