Initial Problem

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

Preprocessing

Eliminate variables {Arg_0} that do not contribute to the problem

Found invariant Arg_1<=0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: Arg_1
Temp_Vars:
Locations: l0, l1, l2
Transitions:
7:l0(Arg_1) -> l1(Arg_1)
8:l1(Arg_1) -> l1(Arg_1-1):|:1<=Arg_1
9:l1(Arg_1) -> l2(Arg_1):|:Arg_1<=0

MPRF for transition 8:l1(Arg_1) -> l1(Arg_1-1):|:1<=Arg_1 of depth 1:

new bound:

Arg_1 {O(n)}

MPRF:

l1 [Arg_1 ]

All Bounds

Timebounds

Overall timebound:Arg_1+2 {O(n)}
7: l0->l1: 1 {O(1)}
8: l1->l1: Arg_1 {O(n)}
9: l1->l2: 1 {O(1)}

Costbounds

Overall costbound: Arg_1+2 {O(n)}
7: l0->l1: 1 {O(1)}
8: l1->l1: Arg_1 {O(n)}
9: l1->l2: 1 {O(1)}

Sizebounds

7: l0->l1, Arg_1: Arg_1 {O(n)}
8: l1->l1, Arg_1: Arg_1 {O(n)}
9: l1->l2, Arg_1: 2*Arg_1 {O(n)}