Initial Problem

Start: start0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars: E
Locations: cut, lbl51, start, start0, stop
Transitions:
5:cut(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl51(E,Arg_1,Arg_0,Arg_3):|:Arg_0<=Arg_2+2 && Arg_0<=9 && 0<=Arg_2 && Arg_2+1<=Arg_0
3:lbl51(Arg_0,Arg_1,Arg_2,Arg_3) -> cut(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2+1<=Arg_0 && Arg_0<=Arg_2+2 && Arg_0<=9 && 0<=Arg_2 && Arg_2<=9
1:lbl51(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0<=Arg_2 && 0<=Arg_2 && Arg_2<=9
2:lbl51(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2+3<=Arg_0 && 0<=Arg_2 && Arg_2<=9
4:lbl51(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:10<=Arg_0 && Arg_2+1<=Arg_0 && Arg_0<=Arg_2+2 && 0<=Arg_2 && Arg_2<=9
0:start(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl51(E,Arg_1,0,Arg_3):|:Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && Arg_3<=Arg_2
6:start0(Arg_0,Arg_1,Arg_2,Arg_3) -> start(Arg_1,Arg_1,Arg_3,Arg_3)

Preprocessing

Found invariant Arg_3<=Arg_2 && Arg_2<=Arg_3 && Arg_1<=Arg_0 && Arg_0<=Arg_1 for location start

Found invariant Arg_2<=8 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=17 && 0<=Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=2+Arg_2 && Arg_0<=9 && 1<=Arg_0 for location cut

Found invariant Arg_2<=9 && 0<=Arg_2 for location stop

Found invariant Arg_2<=9 && 0<=Arg_2 for location lbl51

Problem after Preprocessing

Start: start0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars: E
Locations: cut, lbl51, start, start0, stop
Transitions:
5:cut(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl51(E,Arg_1,Arg_0,Arg_3):|:Arg_2<=8 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=17 && 0<=Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=2+Arg_2 && Arg_0<=9 && 1<=Arg_0 && Arg_0<=Arg_2+2 && Arg_0<=9 && 0<=Arg_2 && Arg_2+1<=Arg_0
3:lbl51(Arg_0,Arg_1,Arg_2,Arg_3) -> cut(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=9 && 0<=Arg_2 && Arg_2+1<=Arg_0 && Arg_0<=Arg_2+2 && Arg_0<=9 && 0<=Arg_2 && Arg_2<=9
1:lbl51(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=9 && 0<=Arg_2 && Arg_0<=Arg_2 && 0<=Arg_2 && Arg_2<=9
2:lbl51(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=9 && 0<=Arg_2 && Arg_2+3<=Arg_0 && 0<=Arg_2 && Arg_2<=9
4:lbl51(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=9 && 0<=Arg_2 && 10<=Arg_0 && Arg_2+1<=Arg_0 && Arg_0<=Arg_2+2 && 0<=Arg_2 && Arg_2<=9
0:start(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl51(E,Arg_1,0,Arg_3):|:Arg_3<=Arg_2 && Arg_2<=Arg_3 && Arg_1<=Arg_0 && Arg_0<=Arg_1 && Arg_0<=Arg_1 && Arg_1<=Arg_0 && Arg_2<=Arg_3 && Arg_3<=Arg_2
6:start0(Arg_0,Arg_1,Arg_2,Arg_3) -> start(Arg_1,Arg_1,Arg_3,Arg_3)

MPRF for transition 5:cut(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl51(E,Arg_1,Arg_0,Arg_3):|:Arg_2<=8 && 1+Arg_2<=Arg_0 && Arg_0+Arg_2<=17 && 0<=Arg_2 && 1<=Arg_0+Arg_2 && Arg_0<=2+Arg_2 && Arg_0<=9 && 1<=Arg_0 && Arg_0<=Arg_2+2 && Arg_0<=9 && 0<=Arg_2 && Arg_2+1<=Arg_0 of depth 1:

new bound:

9 {O(1)}

MPRF:

lbl51 [9-Arg_2 ]
cut [9-Arg_2 ]

MPRF for transition 3:lbl51(Arg_0,Arg_1,Arg_2,Arg_3) -> cut(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2<=9 && 0<=Arg_2 && Arg_2+1<=Arg_0 && Arg_0<=Arg_2+2 && Arg_0<=9 && 0<=Arg_2 && Arg_2<=9 of depth 1:

new bound:

10 {O(1)}

MPRF:

lbl51 [10-Arg_2 ]
cut [9-Arg_2 ]

All Bounds

Timebounds

Overall timebound:24 {O(1)}
5: cut->lbl51: 9 {O(1)}
1: lbl51->stop: 1 {O(1)}
2: lbl51->stop: 1 {O(1)}
3: lbl51->cut: 10 {O(1)}
4: lbl51->stop: 1 {O(1)}
0: start->lbl51: 1 {O(1)}
6: start0->start: 1 {O(1)}

Costbounds

Overall costbound: 24 {O(1)}
5: cut->lbl51: 9 {O(1)}
1: lbl51->stop: 1 {O(1)}
2: lbl51->stop: 1 {O(1)}
3: lbl51->cut: 10 {O(1)}
4: lbl51->stop: 1 {O(1)}
0: start->lbl51: 1 {O(1)}
6: start0->start: 1 {O(1)}

Sizebounds

5: cut->lbl51, Arg_1: Arg_1 {O(n)}
5: cut->lbl51, Arg_2: 9 {O(1)}
5: cut->lbl51, Arg_3: Arg_3 {O(n)}
1: lbl51->stop, Arg_1: 2*Arg_1 {O(n)}
1: lbl51->stop, Arg_2: 9 {O(1)}
1: lbl51->stop, Arg_3: 2*Arg_3 {O(n)}
2: lbl51->stop, Arg_1: 2*Arg_1 {O(n)}
2: lbl51->stop, Arg_2: 9 {O(1)}
2: lbl51->stop, Arg_3: 2*Arg_3 {O(n)}
3: lbl51->cut, Arg_0: 9 {O(1)}
3: lbl51->cut, Arg_1: Arg_1 {O(n)}
3: lbl51->cut, Arg_2: 8 {O(1)}
3: lbl51->cut, Arg_3: Arg_3 {O(n)}
4: lbl51->stop, Arg_0: 11 {O(1)}
4: lbl51->stop, Arg_1: Arg_1 {O(n)}
4: lbl51->stop, Arg_2: 9 {O(1)}
4: lbl51->stop, Arg_3: Arg_3 {O(n)}
0: start->lbl51, Arg_1: Arg_1 {O(n)}
0: start->lbl51, Arg_2: 0 {O(1)}
0: start->lbl51, Arg_3: Arg_3 {O(n)}
6: start0->start, Arg_0: Arg_1 {O(n)}
6: start0->start, Arg_1: Arg_1 {O(n)}
6: start0->start, Arg_2: Arg_3 {O(n)}
6: start0->start, Arg_3: Arg_3 {O(n)}