Initial Problem

Start: start
Program_Vars: Arg_0
Temp_Vars:
Locations: a, start
Transitions:
2:a(Arg_0) -> a(Arg_0-1):|:1<=Arg_0
0:start(Arg_0) -> a(Arg_0):|:1<=Arg_0
1:start(Arg_0) -> a(100):|:Arg_0<=100 && 100<=Arg_0

Preprocessing

Found invariant 0<=Arg_0 for location a

Problem after Preprocessing

Start: start
Program_Vars: Arg_0
Temp_Vars:
Locations: a, start
Transitions:
2:a(Arg_0) -> a(Arg_0-1):|:0<=Arg_0 && 1<=Arg_0
0:start(Arg_0) -> a(Arg_0):|:1<=Arg_0
1:start(Arg_0) -> a(100):|:Arg_0<=100 && 100<=Arg_0

MPRF for transition 2:a(Arg_0) -> a(Arg_0-1):|:0<=Arg_0 && 1<=Arg_0 of depth 1:

new bound:

Arg_0+102 {O(n)}

MPRF:

a [Arg_0+1 ]

All Bounds

Timebounds

Overall timebound:Arg_0+104 {O(n)}
2: a->a: Arg_0+102 {O(n)}
0: start->a: 1 {O(1)}
1: start->a: 1 {O(1)}

Costbounds

Overall costbound: Arg_0+104 {O(n)}
2: a->a: Arg_0+102 {O(n)}
0: start->a: 1 {O(1)}
1: start->a: 1 {O(1)}

Sizebounds

2: a->a, Arg_0: Arg_0+100 {O(n)}
0: start->a, Arg_0: Arg_0 {O(n)}
1: start->a, Arg_0: 100 {O(1)}