Initial Problem

Start: start
Program_Vars: Arg_0
Temp_Vars: B
Locations: a, start
Transitions:
3:a(Arg_0) -> a(B):|:2<=2*B && Arg_0<=2*B && 2*B<=Arg_0
4:a(Arg_0) -> a(B):|:1<=2*B && Arg_0<=2*B+1 && 2*B+1<=Arg_0
0:start(Arg_0) -> a(Arg_0):|:1<=Arg_0
1:start(Arg_0) -> a(Arg_0):|:2<=Arg_0
2:start(Arg_0) -> a(Arg_0):|:4<=Arg_0

Preprocessing

Found invariant 1<=Arg_0 for location a

Problem after Preprocessing

Start: start
Program_Vars: Arg_0
Temp_Vars: B
Locations: a, start
Transitions:
3:a(Arg_0) -> a(B):|:1<=Arg_0 && 2<=2*B && Arg_0<=2*B && 2*B<=Arg_0
4:a(Arg_0) -> a(B):|:1<=Arg_0 && 1<=2*B && Arg_0<=2*B+1 && 2*B+1<=Arg_0
0:start(Arg_0) -> a(Arg_0):|:1<=Arg_0
1:start(Arg_0) -> a(Arg_0):|:2<=Arg_0
2:start(Arg_0) -> a(Arg_0):|:4<=Arg_0

MPRF for transition 3:a(Arg_0) -> a(B):|:1<=Arg_0 && 2<=2*B && Arg_0<=2*B && 2*B<=Arg_0 of depth 1:

new bound:

6*Arg_0 {O(n)}

MPRF:

a [2*Arg_0 ]

MPRF for transition 4:a(Arg_0) -> a(B):|:1<=Arg_0 && 1<=2*B && Arg_0<=2*B+1 && 2*B+1<=Arg_0 of depth 1:

new bound:

6*Arg_0+3 {O(n)}

MPRF:

a [2*Arg_0-1 ]

All Bounds

Timebounds

Overall timebound:12*Arg_0+6 {O(n)}
3: a->a: 6*Arg_0 {O(n)}
4: a->a: 6*Arg_0+3 {O(n)}
0: start->a: 1 {O(1)}
1: start->a: 1 {O(1)}
2: start->a: 1 {O(1)}

Costbounds

Overall costbound: 12*Arg_0+6 {O(n)}
3: a->a: 6*Arg_0 {O(n)}
4: a->a: 6*Arg_0+3 {O(n)}
0: start->a: 1 {O(1)}
1: start->a: 1 {O(1)}
2: start->a: 1 {O(1)}

Sizebounds

3: a->a, Arg_0: 6*Arg_0 {O(n)}
4: a->a, Arg_0: 6*Arg_0 {O(n)}
0: start->a, Arg_0: Arg_0 {O(n)}
1: start->a, Arg_0: Arg_0 {O(n)}
2: start->a, Arg_0: Arg_0 {O(n)}