Initial Problem
Start: start0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: lbl81, lbl91, start, start0, stop
Transitions:
6:lbl81(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl81(Arg_0,Arg_1,Arg_2,1+Arg_3):|:Arg_3+3<=Arg_2 && Arg_0+1<=Arg_3 && 0<=Arg_0 && Arg_3+2<=Arg_2 && Arg_1<=Arg_2 && Arg_2<=Arg_1
7:lbl81(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl91(Arg_0,1+Arg_1,Arg_2,Arg_3):|:Arg_2+3<=Arg_3 && Arg_0+1<=Arg_3 && 0<=Arg_0 && Arg_3+2<=Arg_2 && Arg_1<=Arg_2 && Arg_2<=Arg_1
5:lbl81(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:3+Arg_0<=Arg_2 && 0<=Arg_0 && Arg_3+2<=Arg_2 && Arg_2<=Arg_3+2 && Arg_1<=Arg_2 && Arg_2<=Arg_1
9:lbl91(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl81(Arg_0,Arg_1,Arg_2,1+Arg_3):|:Arg_0+3<=Arg_1 && Arg_1+2<=Arg_0 && Arg_2+1<=Arg_1 && 0<=Arg_2 && Arg_3<=Arg_0 && Arg_0<=Arg_3
10:lbl91(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl91(Arg_0,1+Arg_1,Arg_2,Arg_3):|:Arg_1+3<=Arg_0 && Arg_1+2<=Arg_0 && Arg_2+1<=Arg_1 && 0<=Arg_2 && Arg_3<=Arg_0 && Arg_0<=Arg_3
8:lbl91(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:3+Arg_2<=Arg_0 && 0<=Arg_2 && Arg_1+2<=Arg_0 && Arg_0<=Arg_1+2 && Arg_3<=Arg_0 && Arg_0<=Arg_3
3:start(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl81(Arg_0,Arg_1,Arg_2,1+Arg_3):|:0<=Arg_0 && Arg_0+3<=Arg_2 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_3
4:start(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl91(Arg_0,1+Arg_1,Arg_2,Arg_3):|:Arg_2+3<=Arg_0 && 0<=Arg_2 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_3
0:start(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_0+1<=0 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_3
1:start(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_2+1<=0 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_3
2:start(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:0<=Arg_0 && Arg_2<=Arg_0+2 && 0<=Arg_2 && Arg_0<=Arg_2+2 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_3
11:start0(Arg_0,Arg_1,Arg_2,Arg_3) -> start(Arg_0,Arg_2,Arg_2,Arg_0)
Preprocessing
Cut unsatisfiable transition 7: lbl81->lbl91
Cut unsatisfiable transition 9: lbl91->lbl81
Found invariant 2+Arg_3<=Arg_2 && 2+Arg_3<=Arg_1 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 4<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && 3<=Arg_2 && 6<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 3+Arg_0<=Arg_2 && 3<=Arg_1 && 3<=Arg_0+Arg_1 && 3+Arg_0<=Arg_1 && 0<=Arg_0 for location lbl81
Found invariant Arg_3<=Arg_0 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_1<=Arg_2 for location start
Found invariant Arg_3<=Arg_0 && 3<=Arg_3 && 3<=Arg_2+Arg_3 && 3+Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && 2+Arg_1<=Arg_3 && 6<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && 3+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 2+Arg_1<=Arg_0 && 1<=Arg_1 && 4<=Arg_0+Arg_1 && 3<=Arg_0 for location lbl91
Found invariant Arg_0<=Arg_3 && Arg_2<=Arg_1 for location stop
Problem after Preprocessing
Start: start0
Program_Vars: Arg_0, Arg_1, Arg_2, Arg_3
Temp_Vars:
Locations: lbl81, lbl91, start, start0, stop
Transitions:
6:lbl81(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl81(Arg_0,Arg_1,Arg_2,1+Arg_3):|:2+Arg_3<=Arg_2 && 2+Arg_3<=Arg_1 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 4<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && 3<=Arg_2 && 6<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 3+Arg_0<=Arg_2 && 3<=Arg_1 && 3<=Arg_0+Arg_1 && 3+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_3+3<=Arg_2 && Arg_0+1<=Arg_3 && 0<=Arg_0 && Arg_3+2<=Arg_2 && Arg_1<=Arg_2 && Arg_2<=Arg_1
5:lbl81(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:2+Arg_3<=Arg_2 && 2+Arg_3<=Arg_1 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 4<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && 3<=Arg_2 && 6<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 3+Arg_0<=Arg_2 && 3<=Arg_1 && 3<=Arg_0+Arg_1 && 3+Arg_0<=Arg_1 && 0<=Arg_0 && 3+Arg_0<=Arg_2 && 0<=Arg_0 && Arg_3+2<=Arg_2 && Arg_2<=Arg_3+2 && Arg_1<=Arg_2 && Arg_2<=Arg_1
10:lbl91(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl91(Arg_0,1+Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 3<=Arg_3 && 3<=Arg_2+Arg_3 && 3+Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && 2+Arg_1<=Arg_3 && 6<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && 3+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 2+Arg_1<=Arg_0 && 1<=Arg_1 && 4<=Arg_0+Arg_1 && 3<=Arg_0 && Arg_1+3<=Arg_0 && Arg_1+2<=Arg_0 && Arg_2+1<=Arg_1 && 0<=Arg_2 && Arg_3<=Arg_0 && Arg_0<=Arg_3
8:lbl91(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 3<=Arg_3 && 3<=Arg_2+Arg_3 && 3+Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && 2+Arg_1<=Arg_3 && 6<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && 3+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 2+Arg_1<=Arg_0 && 1<=Arg_1 && 4<=Arg_0+Arg_1 && 3<=Arg_0 && 3+Arg_2<=Arg_0 && 0<=Arg_2 && Arg_1+2<=Arg_0 && Arg_0<=Arg_1+2 && Arg_3<=Arg_0 && Arg_0<=Arg_3
3:start(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl81(Arg_0,Arg_1,Arg_2,1+Arg_3):|:Arg_3<=Arg_0 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_1<=Arg_2 && 0<=Arg_0 && Arg_0+3<=Arg_2 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_3
4:start(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl91(Arg_0,1+Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_1<=Arg_2 && Arg_2+3<=Arg_0 && 0<=Arg_2 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_3
0:start(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_1<=Arg_2 && Arg_0+1<=0 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_3
1:start(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_1<=Arg_2 && Arg_2+1<=0 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_3
2:start(Arg_0,Arg_1,Arg_2,Arg_3) -> stop(Arg_0,Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && Arg_0<=Arg_3 && Arg_2<=Arg_1 && Arg_1<=Arg_2 && 0<=Arg_0 && Arg_2<=Arg_0+2 && 0<=Arg_2 && Arg_0<=Arg_2+2 && Arg_1<=Arg_2 && Arg_2<=Arg_1 && Arg_3<=Arg_0 && Arg_0<=Arg_3
11:start0(Arg_0,Arg_1,Arg_2,Arg_3) -> start(Arg_0,Arg_2,Arg_2,Arg_0)
MPRF for transition 10:lbl91(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl91(Arg_0,1+Arg_1,Arg_2,Arg_3):|:Arg_3<=Arg_0 && 3<=Arg_3 && 3<=Arg_2+Arg_3 && 3+Arg_2<=Arg_3 && 4<=Arg_1+Arg_3 && 2+Arg_1<=Arg_3 && 6<=Arg_0+Arg_3 && Arg_0<=Arg_3 && 1+Arg_2<=Arg_1 && 3+Arg_2<=Arg_0 && 0<=Arg_2 && 1<=Arg_1+Arg_2 && 3<=Arg_0+Arg_2 && 2+Arg_1<=Arg_0 && 1<=Arg_1 && 4<=Arg_0+Arg_1 && 3<=Arg_0 && Arg_1+3<=Arg_0 && Arg_1+2<=Arg_0 && Arg_2+1<=Arg_1 && 0<=Arg_2 && Arg_3<=Arg_0 && Arg_0<=Arg_3 of depth 1:
new bound:
Arg_0+Arg_2+1 {O(n)}
MPRF:
lbl91 [Arg_0-Arg_1 ]
MPRF for transition 6:lbl81(Arg_0,Arg_1,Arg_2,Arg_3) -> lbl81(Arg_0,Arg_1,Arg_2,1+Arg_3):|:2+Arg_3<=Arg_2 && 2+Arg_3<=Arg_1 && 1<=Arg_3 && 4<=Arg_2+Arg_3 && 4<=Arg_1+Arg_3 && 1<=Arg_0+Arg_3 && 1+Arg_0<=Arg_3 && Arg_2<=Arg_1 && 3<=Arg_2 && 6<=Arg_1+Arg_2 && Arg_1<=Arg_2 && 3<=Arg_0+Arg_2 && 3+Arg_0<=Arg_2 && 3<=Arg_1 && 3<=Arg_0+Arg_1 && 3+Arg_0<=Arg_1 && 0<=Arg_0 && Arg_3+3<=Arg_2 && Arg_0+1<=Arg_3 && 0<=Arg_0 && Arg_3+2<=Arg_2 && Arg_1<=Arg_2 && Arg_2<=Arg_1 of depth 1:
new bound:
Arg_0+Arg_2+1 {O(n)}
MPRF:
lbl81 [Arg_1-Arg_3 ]
All Bounds
Timebounds
Overall timebound:2*Arg_0+2*Arg_2+10 {O(n)}
5: lbl81->stop: 1 {O(1)}
6: lbl81->lbl81: Arg_0+Arg_2+1 {O(n)}
8: lbl91->stop: 1 {O(1)}
10: lbl91->lbl91: Arg_0+Arg_2+1 {O(n)}
0: start->stop: 1 {O(1)}
1: start->stop: 1 {O(1)}
2: start->stop: 1 {O(1)}
3: start->lbl81: 1 {O(1)}
4: start->lbl91: 1 {O(1)}
11: start0->start: 1 {O(1)}
Costbounds
Overall costbound: 2*Arg_0+2*Arg_2+10 {O(n)}
5: lbl81->stop: 1 {O(1)}
6: lbl81->lbl81: Arg_0+Arg_2+1 {O(n)}
8: lbl91->stop: 1 {O(1)}
10: lbl91->lbl91: Arg_0+Arg_2+1 {O(n)}
0: start->stop: 1 {O(1)}
1: start->stop: 1 {O(1)}
2: start->stop: 1 {O(1)}
3: start->lbl81: 1 {O(1)}
4: start->lbl91: 1 {O(1)}
11: start0->start: 1 {O(1)}
Sizebounds
5: lbl81->stop, Arg_0: 2*Arg_0 {O(n)}
5: lbl81->stop, Arg_1: 2*Arg_2 {O(n)}
5: lbl81->stop, Arg_2: 2*Arg_2 {O(n)}
5: lbl81->stop, Arg_3: 3*Arg_0+Arg_2+3 {O(n)}
6: lbl81->lbl81, Arg_0: Arg_0 {O(n)}
6: lbl81->lbl81, Arg_1: Arg_2 {O(n)}
6: lbl81->lbl81, Arg_2: Arg_2 {O(n)}
6: lbl81->lbl81, Arg_3: 2*Arg_0+Arg_2+2 {O(n)}
8: lbl91->stop, Arg_0: 2*Arg_0 {O(n)}
8: lbl91->stop, Arg_1: 3*Arg_2+Arg_0+3 {O(n)}
8: lbl91->stop, Arg_2: 2*Arg_2 {O(n)}
8: lbl91->stop, Arg_3: 2*Arg_0 {O(n)}
10: lbl91->lbl91, Arg_0: Arg_0 {O(n)}
10: lbl91->lbl91, Arg_1: 2*Arg_2+Arg_0+2 {O(n)}
10: lbl91->lbl91, Arg_2: Arg_2 {O(n)}
10: lbl91->lbl91, Arg_3: 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)}
1: start->stop, Arg_0: Arg_0 {O(n)}
1: start->stop, Arg_1: Arg_2 {O(n)}
1: start->stop, Arg_2: Arg_2 {O(n)}
1: start->stop, Arg_3: Arg_0 {O(n)}
2: start->stop, Arg_0: Arg_0 {O(n)}
2: start->stop, Arg_1: Arg_2 {O(n)}
2: start->stop, Arg_2: Arg_2 {O(n)}
2: start->stop, Arg_3: Arg_0 {O(n)}
3: start->lbl81, Arg_0: Arg_0 {O(n)}
3: start->lbl81, Arg_1: Arg_2 {O(n)}
3: start->lbl81, Arg_2: Arg_2 {O(n)}
3: start->lbl81, Arg_3: Arg_0+1 {O(n)}
4: start->lbl91, Arg_0: Arg_0 {O(n)}
4: start->lbl91, Arg_1: Arg_2+1 {O(n)}
4: start->lbl91, Arg_2: Arg_2 {O(n)}
4: start->lbl91, Arg_3: Arg_0 {O(n)}
11: start0->start, Arg_0: Arg_0 {O(n)}
11: start0->start, Arg_1: Arg_2 {O(n)}
11: start0->start, Arg_2: Arg_2 {O(n)}
11: start0->start, Arg_3: Arg_0 {O(n)}