Initial Problem

Start: start0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
Temp_Vars:
Locations: lbl101, lbl121, start, start0, stop
Transitions:
6:lbl101(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,2*Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_1+1<=Arg_3 && 2<=Arg_1 && Arg_1+2<=2*Arg_3 && Arg_3<=Arg_0 && Arg_5<=Arg_0 && Arg_0<=Arg_5
7:lbl101(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl121(Arg_0,Arg_1,Arg_2,Arg_3-1,Arg_4,Arg_5):|:Arg_3<=Arg_1 && 2<=Arg_1 && Arg_1+2<=2*Arg_3 && Arg_3<=Arg_0 && Arg_5<=Arg_0 && Arg_0<=Arg_5
5:lbl121(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,2,Arg_2,Arg_3,Arg_4,Arg_5):|:2<=Arg_3 && Arg_3+1<=Arg_0 && Arg_3+1<=Arg_1 && 1<=Arg_1 && 0<=1+Arg_3 && Arg_5<=Arg_0 && Arg_0<=Arg_5
4:lbl121(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl121(Arg_0,1,Arg_2,Arg_3-1,Arg_4,Arg_5):|:0<=Arg_3 && Arg_3<=1 && Arg_3+1<=Arg_0 && Arg_3+1<=Arg_1 && 1<=Arg_1 && 0<=1+Arg_3 && Arg_5<=Arg_0 && Arg_0<=Arg_5
3:lbl121(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:0<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 && Arg_3+1<=0 && 0<=1+Arg_3 && Arg_5<=Arg_0 && Arg_0<=Arg_5
2:start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,2,Arg_2,Arg_5,Arg_4,Arg_5):|:2<=Arg_0 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_3<=Arg_4 && Arg_4<=Arg_3 && Arg_5<=Arg_0 && Arg_0<=Arg_5
1:start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl121(Arg_0,1,Arg_2,Arg_5-1,Arg_4,Arg_5):|:0<=Arg_0 && Arg_0<=1 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_3<=Arg_4 && Arg_4<=Arg_3 && Arg_5<=Arg_0 && Arg_0<=Arg_5
0:start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> stop(Arg_0,Arg_1,Arg_2,Arg_5,Arg_4,Arg_5):|:Arg_0+1<=0 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_3<=Arg_4 && Arg_4<=Arg_3 && Arg_5<=Arg_0 && Arg_0<=Arg_5
8:start0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> start(Arg_0,Arg_2,Arg_2,Arg_4,Arg_4,Arg_0)

Preprocessing

Found invariant Arg_5<=Arg_0 && Arg_0<=Arg_5 && Arg_4<=Arg_3 && Arg_3<=Arg_4 && Arg_2<=Arg_1 && Arg_1<=Arg_2 for location start

Found invariant Arg_5<=Arg_0 && 2<=Arg_5 && 4<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 4<=Arg_1+Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_3<=Arg_0 && 2<=Arg_3 && 4<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 for location lbl101

Found invariant Arg_5<=Arg_0 && 0<=Arg_5 && 0<=1+Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 1<=Arg_1+Arg_5 && 0<=Arg_0+Arg_5 && Arg_0<=Arg_5 && 1+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 0<=1+Arg_3 && 0<=Arg_1+Arg_3 && 0<=1+Arg_0+Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 for location lbl121

Found invariant Arg_5<=Arg_0 && Arg_3<=Arg_5 && Arg_0<=Arg_5 && 1+Arg_3<=0 && Arg_3<=Arg_0 for location stop

Problem after Preprocessing

Start: start0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5
Temp_Vars:
Locations: lbl101, lbl121, start, start0, stop
Transitions:
6:lbl101(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,2*Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_0 && 2<=Arg_5 && 4<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 4<=Arg_1+Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_3<=Arg_0 && 2<=Arg_3 && 4<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1+1<=Arg_3 && 2<=Arg_1 && Arg_1+2<=2*Arg_3 && Arg_3<=Arg_0 && Arg_5<=Arg_0 && Arg_0<=Arg_5
7:lbl101(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl121(Arg_0,Arg_1,Arg_2,Arg_3-1,Arg_4,Arg_5):|:Arg_5<=Arg_0 && 2<=Arg_5 && 4<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 4<=Arg_1+Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_3<=Arg_0 && 2<=Arg_3 && 4<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_3<=Arg_1 && 2<=Arg_1 && Arg_1+2<=2*Arg_3 && Arg_3<=Arg_0 && Arg_5<=Arg_0 && Arg_0<=Arg_5
5:lbl121(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,2,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_0 && 0<=Arg_5 && 0<=1+Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 1<=Arg_1+Arg_5 && 0<=Arg_0+Arg_5 && Arg_0<=Arg_5 && 1+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 0<=1+Arg_3 && 0<=Arg_1+Arg_3 && 0<=1+Arg_0+Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 2<=Arg_3 && Arg_3+1<=Arg_0 && Arg_3+1<=Arg_1 && 1<=Arg_1 && 0<=1+Arg_3 && Arg_5<=Arg_0 && Arg_0<=Arg_5
4:lbl121(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl121(Arg_0,1,Arg_2,Arg_3-1,Arg_4,Arg_5):|:Arg_5<=Arg_0 && 0<=Arg_5 && 0<=1+Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 1<=Arg_1+Arg_5 && 0<=Arg_0+Arg_5 && Arg_0<=Arg_5 && 1+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 0<=1+Arg_3 && 0<=Arg_1+Arg_3 && 0<=1+Arg_0+Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_3 && Arg_3<=1 && Arg_3+1<=Arg_0 && Arg_3+1<=Arg_1 && 1<=Arg_1 && 0<=1+Arg_3 && Arg_5<=Arg_0 && Arg_0<=Arg_5
3:lbl121(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> stop(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_0 && 0<=Arg_5 && 0<=1+Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 1<=Arg_1+Arg_5 && 0<=Arg_0+Arg_5 && Arg_0<=Arg_5 && 1+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 0<=1+Arg_3 && 0<=Arg_1+Arg_3 && 0<=1+Arg_0+Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_0 && 0<=Arg_1 && 1<=Arg_1 && Arg_3+1<=0 && 0<=1+Arg_3 && Arg_5<=Arg_0 && Arg_0<=Arg_5
2:start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,2,Arg_2,Arg_5,Arg_4,Arg_5):|:Arg_5<=Arg_0 && Arg_0<=Arg_5 && Arg_4<=Arg_3 && Arg_3<=Arg_4 && Arg_2<=Arg_1 && Arg_1<=Arg_2 && 2<=Arg_0 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_3<=Arg_4 && Arg_4<=Arg_3 && Arg_5<=Arg_0 && Arg_0<=Arg_5
1:start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl121(Arg_0,1,Arg_2,Arg_5-1,Arg_4,Arg_5):|:Arg_5<=Arg_0 && Arg_0<=Arg_5 && Arg_4<=Arg_3 && Arg_3<=Arg_4 && Arg_2<=Arg_1 && Arg_1<=Arg_2 && 0<=Arg_0 && Arg_0<=1 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_3<=Arg_4 && Arg_4<=Arg_3 && Arg_5<=Arg_0 && Arg_0<=Arg_5
0:start(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> stop(Arg_0,Arg_1,Arg_2,Arg_5,Arg_4,Arg_5):|:Arg_5<=Arg_0 && Arg_0<=Arg_5 && Arg_4<=Arg_3 && Arg_3<=Arg_4 && Arg_2<=Arg_1 && Arg_1<=Arg_2 && Arg_0+1<=0 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_3<=Arg_4 && Arg_4<=Arg_3 && Arg_5<=Arg_0 && Arg_0<=Arg_5
8:start0(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> start(Arg_0,Arg_2,Arg_2,Arg_4,Arg_4,Arg_0)

MPRF for transition 7:lbl101(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl121(Arg_0,Arg_1,Arg_2,Arg_3-1,Arg_4,Arg_5):|:Arg_5<=Arg_0 && 2<=Arg_5 && 4<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 4<=Arg_1+Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_3<=Arg_0 && 2<=Arg_3 && 4<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_3<=Arg_1 && 2<=Arg_1 && Arg_1+2<=2*Arg_3 && Arg_3<=Arg_0 && Arg_5<=Arg_0 && Arg_0<=Arg_5 of depth 1:

new bound:

Arg_0+3 {O(n)}

MPRF:

lbl121 [Arg_3-1 ]
lbl101 [Arg_3-1 ]

MPRF for transition 4:lbl121(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl121(Arg_0,1,Arg_2,Arg_3-1,Arg_4,Arg_5):|:Arg_5<=Arg_0 && 0<=Arg_5 && 0<=1+Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 1<=Arg_1+Arg_5 && 0<=Arg_0+Arg_5 && Arg_0<=Arg_5 && 1+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 0<=1+Arg_3 && 0<=Arg_1+Arg_3 && 0<=1+Arg_0+Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 0<=Arg_3 && Arg_3<=1 && Arg_3+1<=Arg_0 && Arg_3+1<=Arg_1 && 1<=Arg_1 && 0<=1+Arg_3 && Arg_5<=Arg_0 && Arg_0<=Arg_5 of depth 1:

new bound:

Arg_0+2 {O(n)}

MPRF:

lbl121 [Arg_3+1 ]
lbl101 [Arg_3 ]

MPRF for transition 5:lbl121(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,2,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_0 && 0<=Arg_5 && 0<=1+Arg_3+Arg_5 && 1+Arg_3<=Arg_5 && 1<=Arg_1+Arg_5 && 0<=Arg_0+Arg_5 && Arg_0<=Arg_5 && 1+Arg_3<=Arg_1 && 1+Arg_3<=Arg_0 && 0<=1+Arg_3 && 0<=Arg_1+Arg_3 && 0<=1+Arg_0+Arg_3 && 1<=Arg_1 && 1<=Arg_0+Arg_1 && 0<=Arg_0 && 2<=Arg_3 && Arg_3+1<=Arg_0 && Arg_3+1<=Arg_1 && 1<=Arg_1 && 0<=1+Arg_3 && Arg_5<=Arg_0 && Arg_0<=Arg_5 of depth 1:

new bound:

Arg_0+4 {O(n)}

MPRF:

lbl121 [Arg_3-1 ]
lbl101 [Arg_3-2 ]

MPRF for transition 6:lbl101(Arg_0,Arg_1,Arg_2,Arg_3,Arg_4,Arg_5) -> lbl101(Arg_0,2*Arg_1,Arg_2,Arg_3,Arg_4,Arg_5):|:Arg_5<=Arg_0 && 2<=Arg_5 && 4<=Arg_3+Arg_5 && Arg_3<=Arg_5 && 4<=Arg_1+Arg_5 && 4<=Arg_0+Arg_5 && Arg_0<=Arg_5 && Arg_3<=Arg_0 && 2<=Arg_3 && 4<=Arg_1+Arg_3 && 4<=Arg_0+Arg_3 && 2<=Arg_1 && 4<=Arg_0+Arg_1 && 2<=Arg_0 && Arg_1+1<=Arg_3 && 2<=Arg_1 && Arg_1+2<=2*Arg_3 && Arg_3<=Arg_0 && Arg_5<=Arg_0 && Arg_0<=Arg_5 of depth 1:

new bound:

6*Arg_0*Arg_0+31*Arg_0+21 {O(n^2)}

MPRF:

lbl101 [Arg_0+2*Arg_3-Arg_1-2 ]
lbl121 [Arg_5 ]

All Bounds

Timebounds

Overall timebound:6*Arg_0*Arg_0+34*Arg_0+35 {O(n^2)}
6: lbl101->lbl101: 6*Arg_0*Arg_0+31*Arg_0+21 {O(n^2)}
7: lbl101->lbl121: Arg_0+3 {O(n)}
3: lbl121->stop: 1 {O(1)}
4: lbl121->lbl121: Arg_0+2 {O(n)}
5: lbl121->lbl101: Arg_0+4 {O(n)}
0: start->stop: 1 {O(1)}
1: start->lbl121: 1 {O(1)}
2: start->lbl101: 1 {O(1)}
8: start0->start: 1 {O(1)}

Costbounds

Overall costbound: 6*Arg_0*Arg_0+34*Arg_0+35 {O(n^2)}
6: lbl101->lbl101: 6*Arg_0*Arg_0+31*Arg_0+21 {O(n^2)}
7: lbl101->lbl121: Arg_0+3 {O(n)}
3: lbl121->stop: 1 {O(1)}
4: lbl121->lbl121: Arg_0+2 {O(n)}
5: lbl121->lbl101: Arg_0+4 {O(n)}
0: start->stop: 1 {O(1)}
1: start->lbl121: 1 {O(1)}
2: start->lbl101: 1 {O(1)}
8: start0->start: 1 {O(1)}

Sizebounds

6: lbl101->lbl101, Arg_0: 2*Arg_0 {O(n)}
6: lbl101->lbl101, Arg_1: 2^(6*Arg_0*Arg_0+31*Arg_0+21)*4 {O(EXP)}
6: lbl101->lbl101, Arg_2: 2*Arg_2 {O(n)}
6: lbl101->lbl101, Arg_3: 2*Arg_0 {O(n)}
6: lbl101->lbl101, Arg_4: 2*Arg_4 {O(n)}
6: lbl101->lbl101, Arg_5: 2*Arg_0 {O(n)}
7: lbl101->lbl121, Arg_0: 2*Arg_0 {O(n)}
7: lbl101->lbl121, Arg_1: 2^(6*Arg_0*Arg_0+31*Arg_0+21)*4+4 {O(EXP)}
7: lbl101->lbl121, Arg_2: 2*Arg_2 {O(n)}
7: lbl101->lbl121, Arg_3: 2*Arg_0 {O(n)}
7: lbl101->lbl121, Arg_4: 2*Arg_4 {O(n)}
7: lbl101->lbl121, Arg_5: 2*Arg_0 {O(n)}
3: lbl121->stop, Arg_0: 2*Arg_0+2 {O(n)}
3: lbl121->stop, Arg_1: 2 {O(1)}
3: lbl121->stop, Arg_2: 4*Arg_2 {O(n)}
3: lbl121->stop, Arg_3: 1 {O(1)}
3: lbl121->stop, Arg_4: 4*Arg_4 {O(n)}
3: lbl121->stop, Arg_5: 2*Arg_0+2 {O(n)}
4: lbl121->lbl121, Arg_0: 2*Arg_0+1 {O(n)}
4: lbl121->lbl121, Arg_1: 1 {O(1)}
4: lbl121->lbl121, Arg_2: 3*Arg_2 {O(n)}
4: lbl121->lbl121, Arg_3: 1 {O(1)}
4: lbl121->lbl121, Arg_4: 3*Arg_4 {O(n)}
4: lbl121->lbl121, Arg_5: 2*Arg_0+1 {O(n)}
5: lbl121->lbl101, Arg_0: 2*Arg_0 {O(n)}
5: lbl121->lbl101, Arg_1: 2 {O(1)}
5: lbl121->lbl101, Arg_2: 2*Arg_2 {O(n)}
5: lbl121->lbl101, Arg_3: 2*Arg_0 {O(n)}
5: lbl121->lbl101, Arg_4: 2*Arg_4 {O(n)}
5: lbl121->lbl101, Arg_5: 2*Arg_0 {O(n)}
0: start->stop, Arg_0: Arg_0 {O(n)}
0: start->stop, Arg_1: Arg_2 {O(n)}
0: start->stop, Arg_2: Arg_2 {O(n)}
0: start->stop, Arg_3: Arg_0 {O(n)}
0: start->stop, Arg_4: Arg_4 {O(n)}
0: start->stop, Arg_5: Arg_0 {O(n)}
1: start->lbl121, Arg_0: 1 {O(1)}
1: start->lbl121, Arg_1: 1 {O(1)}
1: start->lbl121, Arg_2: Arg_2 {O(n)}
1: start->lbl121, Arg_3: 1 {O(1)}
1: start->lbl121, Arg_4: Arg_4 {O(n)}
1: start->lbl121, Arg_5: 1 {O(1)}
2: start->lbl101, Arg_0: Arg_0 {O(n)}
2: start->lbl101, Arg_1: 2 {O(1)}
2: start->lbl101, Arg_2: Arg_2 {O(n)}
2: start->lbl101, Arg_3: Arg_0 {O(n)}
2: start->lbl101, Arg_4: Arg_4 {O(n)}
2: start->lbl101, Arg_5: Arg_0 {O(n)}
8: start0->start, Arg_0: Arg_0 {O(n)}
8: start0->start, Arg_1: Arg_2 {O(n)}
8: start0->start, Arg_2: Arg_2 {O(n)}
8: start0->start, Arg_3: Arg_4 {O(n)}
8: start0->start, Arg_4: Arg_4 {O(n)}
8: start0->start, Arg_5: Arg_0 {O(n)}