Initial Problem

Start: n_start
Program_Vars: Arg_0
Temp_Vars:
Locations: n_a___1, n_a___2, n_a___3, n_start
Transitions:
0:n_a___1(Arg_0) -> n_a___1(Arg_0-1):|:0<=Arg_0 && 1<=Arg_0
1:n_a___2(Arg_0) -> n_a___3(Arg_0-1):|:1<=Arg_0 && 1<=Arg_0 && Arg_0<=100 && 100<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0
2:n_a___3(Arg_0) -> n_a___1(Arg_0-1):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0
3:n_start(Arg_0) -> n_a___2(100):|:Arg_0<=100 && 100<=Arg_0
4:n_start(Arg_0) -> n_a___3(Arg_0):|:1<=Arg_0

Preprocessing

Found invariant 0<=Arg_0 for location n_a___1

Found invariant Arg_0<=100 && 100<=Arg_0 for location n_a___2

Found invariant 1<=Arg_0 for location n_a___3

Problem after Preprocessing

Start: n_start
Program_Vars: Arg_0
Temp_Vars:
Locations: n_a___1, n_a___2, n_a___3, n_start
Transitions:
0:n_a___1(Arg_0) -> n_a___1(Arg_0-1):|:0<=Arg_0 && 0<=Arg_0 && 1<=Arg_0
1:n_a___2(Arg_0) -> n_a___3(Arg_0-1):|:Arg_0<=100 && 100<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && Arg_0<=100 && 100<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0
2:n_a___3(Arg_0) -> n_a___1(Arg_0-1):|:1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 1<=Arg_0 && 0<=Arg_0 && 1<=Arg_0
3:n_start(Arg_0) -> n_a___2(100):|:Arg_0<=100 && 100<=Arg_0
4:n_start(Arg_0) -> n_a___3(Arg_0):|:1<=Arg_0

MPRF for transition 0:n_a___1(Arg_0) -> n_a___1(Arg_0-1):|:0<=Arg_0 && 0<=Arg_0 && 1<=Arg_0 of depth 1:

new bound:

Arg_0+100 {O(n)}

MPRF:

n_a___1 [Arg_0+1 ]

All Bounds

Timebounds

Overall timebound:Arg_0+104 {O(n)}
0: n_a___1->n_a___1: Arg_0+100 {O(n)}
1: n_a___2->n_a___3: 1 {O(1)}
2: n_a___3->n_a___1: 1 {O(1)}
3: n_start->n_a___2: 1 {O(1)}
4: n_start->n_a___3: 1 {O(1)}

Costbounds

Overall costbound: Arg_0+104 {O(n)}
0: n_a___1->n_a___1: Arg_0+100 {O(n)}
1: n_a___2->n_a___3: 1 {O(1)}
2: n_a___3->n_a___1: 1 {O(1)}
3: n_start->n_a___2: 1 {O(1)}
4: n_start->n_a___3: 1 {O(1)}

Sizebounds

0: n_a___1->n_a___1, Arg_0: Arg_0+99 {O(n)}
1: n_a___2->n_a___3, Arg_0: 99 {O(1)}
2: n_a___3->n_a___1, Arg_0: Arg_0+99 {O(n)}
3: n_start->n_a___2, Arg_0: 100 {O(1)}
4: n_start->n_a___3, Arg_0: Arg_0 {O(n)}