Initial Problem

Start: evalaaron2start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: D
Locations: evalaaron2bb3in, evalaaron2bb4in, evalaaron2bb5in, evalaaron2bb6in, evalaaron2entryin, evalaaron2returnin, evalaaron2start, evalaaron2stop
Transitions:
6:evalaaron2bb3in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb4in(Arg_0,Arg_1,Arg_2):|:D+1<=0
7:evalaaron2bb3in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb4in(Arg_0,Arg_1,Arg_2):|:1<=D
8:evalaaron2bb3in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb5in(Arg_0,Arg_1,Arg_2)
9:evalaaron2bb4in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb6in(Arg_0,Arg_1,Arg_2-Arg_0-1)
10:evalaaron2bb5in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb6in(Arg_0,Arg_1+Arg_0+1,Arg_2)
5:evalaaron2bb6in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb3in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0
3:evalaaron2bb6in(Arg_0,Arg_1,Arg_2) -> evalaaron2returnin(Arg_0,Arg_1,Arg_2):|:Arg_2+1<=Arg_1
4:evalaaron2bb6in(Arg_0,Arg_1,Arg_2) -> evalaaron2returnin(Arg_0,Arg_1,Arg_2):|:Arg_0+1<=0
1:evalaaron2entryin(Arg_0,Arg_1,Arg_2) -> evalaaron2bb6in(Arg_0,Arg_2,Arg_1):|:0<=Arg_0
2:evalaaron2entryin(Arg_0,Arg_1,Arg_2) -> evalaaron2returnin(Arg_0,Arg_1,Arg_2):|:Arg_0+1<=0
11:evalaaron2returnin(Arg_0,Arg_1,Arg_2) -> evalaaron2stop(Arg_0,Arg_1,Arg_2)
0:evalaaron2start(Arg_0,Arg_1,Arg_2) -> evalaaron2entryin(Arg_0,Arg_1,Arg_2)

Preprocessing

Found invariant Arg_1<=Arg_2 && 0<=Arg_0 for location evalaaron2bb5in

Found invariant Arg_1<=Arg_2 && 0<=Arg_0 for location evalaaron2bb4in

Found invariant Arg_1<=Arg_2 && 0<=Arg_0 for location evalaaron2bb3in

Found invariant 0<=Arg_0 for location evalaaron2bb6in

Cut unsatisfiable transition 4: evalaaron2bb6in->evalaaron2returnin

Problem after Preprocessing

Start: evalaaron2start
Program_Vars: Arg_0, Arg_1, Arg_2
Temp_Vars: D
Locations: evalaaron2bb3in, evalaaron2bb4in, evalaaron2bb5in, evalaaron2bb6in, evalaaron2entryin, evalaaron2returnin, evalaaron2start, evalaaron2stop
Transitions:
6:evalaaron2bb3in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb4in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0 && D+1<=0
7:evalaaron2bb3in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb4in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0 && 1<=D
8:evalaaron2bb3in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb5in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0
9:evalaaron2bb4in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb6in(Arg_0,Arg_1,Arg_2-Arg_0-1):|:Arg_1<=Arg_2 && 0<=Arg_0
10:evalaaron2bb5in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb6in(Arg_0,Arg_1+Arg_0+1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0
5:evalaaron2bb6in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb3in(Arg_0,Arg_1,Arg_2):|:0<=Arg_0 && Arg_1<=Arg_2 && 0<=Arg_0
3:evalaaron2bb6in(Arg_0,Arg_1,Arg_2) -> evalaaron2returnin(Arg_0,Arg_1,Arg_2):|:0<=Arg_0 && Arg_2+1<=Arg_1
1:evalaaron2entryin(Arg_0,Arg_1,Arg_2) -> evalaaron2bb6in(Arg_0,Arg_2,Arg_1):|:0<=Arg_0
2:evalaaron2entryin(Arg_0,Arg_1,Arg_2) -> evalaaron2returnin(Arg_0,Arg_1,Arg_2):|:Arg_0+1<=0
11:evalaaron2returnin(Arg_0,Arg_1,Arg_2) -> evalaaron2stop(Arg_0,Arg_1,Arg_2)
0:evalaaron2start(Arg_0,Arg_1,Arg_2) -> evalaaron2entryin(Arg_0,Arg_1,Arg_2)

MPRF for transition 6:evalaaron2bb3in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb4in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0 && D+1<=0 of depth 1:

new bound:

Arg_1+Arg_2+1 {O(n)}

MPRF:

evalaaron2bb4in [Arg_2-Arg_1 ]
evalaaron2bb5in [Arg_2-Arg_1 ]
evalaaron2bb6in [Arg_2+1-Arg_1 ]
evalaaron2bb3in [Arg_2+1-Arg_1 ]

MPRF for transition 7:evalaaron2bb3in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb4in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0 && 1<=D of depth 1:

new bound:

Arg_1+Arg_2+1 {O(n)}

MPRF:

evalaaron2bb4in [Arg_2-Arg_1 ]
evalaaron2bb5in [Arg_2-Arg_1 ]
evalaaron2bb6in [Arg_2+1-Arg_1 ]
evalaaron2bb3in [Arg_2+1-Arg_1 ]

MPRF for transition 8:evalaaron2bb3in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb5in(Arg_0,Arg_1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0 of depth 1:

new bound:

Arg_1+Arg_2+1 {O(n)}

MPRF:

evalaaron2bb4in [Arg_2-Arg_1 ]
evalaaron2bb5in [Arg_2-Arg_1 ]
evalaaron2bb6in [Arg_2+1-Arg_1 ]
evalaaron2bb3in [Arg_2+1-Arg_1 ]

MPRF for transition 9:evalaaron2bb4in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb6in(Arg_0,Arg_1,Arg_2-Arg_0-1):|:Arg_1<=Arg_2 && 0<=Arg_0 of depth 1:

new bound:

Arg_1+Arg_2+1 {O(n)}

MPRF:

evalaaron2bb4in [Arg_2+1-Arg_1 ]
evalaaron2bb5in [Arg_2-Arg_1 ]
evalaaron2bb6in [Arg_2+1-Arg_1 ]
evalaaron2bb3in [Arg_2+1-Arg_1 ]

MPRF for transition 10:evalaaron2bb5in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb6in(Arg_0,Arg_1+Arg_0+1,Arg_2):|:Arg_1<=Arg_2 && 0<=Arg_0 of depth 1:

new bound:

Arg_1+Arg_2+1 {O(n)}

MPRF:

evalaaron2bb4in [Arg_2-Arg_1 ]
evalaaron2bb5in [Arg_2+1-Arg_1 ]
evalaaron2bb6in [Arg_2+1-Arg_1 ]
evalaaron2bb3in [Arg_2+1-Arg_1 ]

MPRF for transition 5:evalaaron2bb6in(Arg_0,Arg_1,Arg_2) -> evalaaron2bb3in(Arg_0,Arg_1,Arg_2):|:0<=Arg_0 && Arg_1<=Arg_2 && 0<=Arg_0 of depth 1:

new bound:

Arg_1+Arg_2+1 {O(n)}

MPRF:

evalaaron2bb4in [Arg_2-Arg_1 ]
evalaaron2bb5in [Arg_2-Arg_1 ]
evalaaron2bb6in [Arg_2+1-Arg_1 ]
evalaaron2bb3in [Arg_2-Arg_1 ]

All Bounds

Timebounds

Overall timebound:6*Arg_1+6*Arg_2+11 {O(n)}
6: evalaaron2bb3in->evalaaron2bb4in: Arg_1+Arg_2+1 {O(n)}
7: evalaaron2bb3in->evalaaron2bb4in: Arg_1+Arg_2+1 {O(n)}
8: evalaaron2bb3in->evalaaron2bb5in: Arg_1+Arg_2+1 {O(n)}
9: evalaaron2bb4in->evalaaron2bb6in: Arg_1+Arg_2+1 {O(n)}
10: evalaaron2bb5in->evalaaron2bb6in: Arg_1+Arg_2+1 {O(n)}
3: evalaaron2bb6in->evalaaron2returnin: 1 {O(1)}
5: evalaaron2bb6in->evalaaron2bb3in: Arg_1+Arg_2+1 {O(n)}
1: evalaaron2entryin->evalaaron2bb6in: 1 {O(1)}
2: evalaaron2entryin->evalaaron2returnin: 1 {O(1)}
11: evalaaron2returnin->evalaaron2stop: 1 {O(1)}
0: evalaaron2start->evalaaron2entryin: 1 {O(1)}

Costbounds

Overall costbound: 6*Arg_1+6*Arg_2+11 {O(n)}
6: evalaaron2bb3in->evalaaron2bb4in: Arg_1+Arg_2+1 {O(n)}
7: evalaaron2bb3in->evalaaron2bb4in: Arg_1+Arg_2+1 {O(n)}
8: evalaaron2bb3in->evalaaron2bb5in: Arg_1+Arg_2+1 {O(n)}
9: evalaaron2bb4in->evalaaron2bb6in: Arg_1+Arg_2+1 {O(n)}
10: evalaaron2bb5in->evalaaron2bb6in: Arg_1+Arg_2+1 {O(n)}
3: evalaaron2bb6in->evalaaron2returnin: 1 {O(1)}
5: evalaaron2bb6in->evalaaron2bb3in: Arg_1+Arg_2+1 {O(n)}
1: evalaaron2entryin->evalaaron2bb6in: 1 {O(1)}
2: evalaaron2entryin->evalaaron2returnin: 1 {O(1)}
11: evalaaron2returnin->evalaaron2stop: 1 {O(1)}
0: evalaaron2start->evalaaron2entryin: 1 {O(1)}

Sizebounds

6: evalaaron2bb3in->evalaaron2bb4in, Arg_0: Arg_0 {O(n)}
6: evalaaron2bb3in->evalaaron2bb4in, Arg_1: Arg_0*Arg_1+Arg_0*Arg_2+2*Arg_0+2*Arg_2+Arg_1+1 {O(n^2)}
6: evalaaron2bb3in->evalaaron2bb4in, Arg_2: 2*Arg_0*Arg_1+2*Arg_0*Arg_2+2*Arg_1+4*Arg_0+Arg_2+1 {O(n^2)}
7: evalaaron2bb3in->evalaaron2bb4in, Arg_0: Arg_0 {O(n)}
7: evalaaron2bb3in->evalaaron2bb4in, Arg_1: Arg_0*Arg_1+Arg_0*Arg_2+2*Arg_0+2*Arg_2+Arg_1+1 {O(n^2)}
7: evalaaron2bb3in->evalaaron2bb4in, Arg_2: 2*Arg_0*Arg_1+2*Arg_0*Arg_2+2*Arg_1+4*Arg_0+Arg_2+1 {O(n^2)}
8: evalaaron2bb3in->evalaaron2bb5in, Arg_0: Arg_0 {O(n)}
8: evalaaron2bb3in->evalaaron2bb5in, Arg_1: Arg_0*Arg_1+Arg_0*Arg_2+2*Arg_0+2*Arg_2+Arg_1+1 {O(n^2)}
8: evalaaron2bb3in->evalaaron2bb5in, Arg_2: 2*Arg_0*Arg_1+2*Arg_0*Arg_2+2*Arg_1+4*Arg_0+Arg_2+1 {O(n^2)}
9: evalaaron2bb4in->evalaaron2bb6in, Arg_0: Arg_0 {O(n)}
9: evalaaron2bb4in->evalaaron2bb6in, Arg_1: Arg_0*Arg_1+Arg_0*Arg_2+2*Arg_0+2*Arg_2+Arg_1+1 {O(n^2)}
9: evalaaron2bb4in->evalaaron2bb6in, Arg_2: 2*Arg_0*Arg_1+2*Arg_0*Arg_2+2*Arg_1+4*Arg_0+Arg_2+1 {O(n^2)}
10: evalaaron2bb5in->evalaaron2bb6in, Arg_0: Arg_0 {O(n)}
10: evalaaron2bb5in->evalaaron2bb6in, Arg_1: Arg_0*Arg_1+Arg_0*Arg_2+2*Arg_0+2*Arg_2+Arg_1+1 {O(n^2)}
10: evalaaron2bb5in->evalaaron2bb6in, Arg_2: 2*Arg_0*Arg_1+2*Arg_0*Arg_2+2*Arg_1+4*Arg_0+Arg_2+1 {O(n^2)}
3: evalaaron2bb6in->evalaaron2returnin, Arg_0: 3*Arg_0 {O(n)}
3: evalaaron2bb6in->evalaaron2returnin, Arg_1: 2*Arg_0*Arg_1+2*Arg_0*Arg_2+2*Arg_1+4*Arg_0+5*Arg_2+2 {O(n^2)}
3: evalaaron2bb6in->evalaaron2returnin, Arg_2: 4*Arg_0*Arg_1+4*Arg_0*Arg_2+2*Arg_2+5*Arg_1+8*Arg_0+2 {O(n^2)}
5: evalaaron2bb6in->evalaaron2bb3in, Arg_0: Arg_0 {O(n)}
5: evalaaron2bb6in->evalaaron2bb3in, Arg_1: Arg_0*Arg_1+Arg_0*Arg_2+2*Arg_0+2*Arg_2+Arg_1+1 {O(n^2)}
5: evalaaron2bb6in->evalaaron2bb3in, Arg_2: 2*Arg_0*Arg_1+2*Arg_0*Arg_2+2*Arg_1+4*Arg_0+Arg_2+1 {O(n^2)}
1: evalaaron2entryin->evalaaron2bb6in, Arg_0: Arg_0 {O(n)}
1: evalaaron2entryin->evalaaron2bb6in, Arg_1: Arg_2 {O(n)}
1: evalaaron2entryin->evalaaron2bb6in, Arg_2: Arg_1 {O(n)}
2: evalaaron2entryin->evalaaron2returnin, Arg_0: Arg_0 {O(n)}
2: evalaaron2entryin->evalaaron2returnin, Arg_1: Arg_1 {O(n)}
2: evalaaron2entryin->evalaaron2returnin, Arg_2: Arg_2 {O(n)}
11: evalaaron2returnin->evalaaron2stop, Arg_0: 4*Arg_0 {O(n)}
11: evalaaron2returnin->evalaaron2stop, Arg_1: 2*Arg_0*Arg_1+2*Arg_0*Arg_2+3*Arg_1+4*Arg_0+5*Arg_2+2 {O(n^2)}
11: evalaaron2returnin->evalaaron2stop, Arg_2: 4*Arg_0*Arg_1+4*Arg_0*Arg_2+3*Arg_2+5*Arg_1+8*Arg_0+2 {O(n^2)}
0: evalaaron2start->evalaaron2entryin, Arg_0: Arg_0 {O(n)}
0: evalaaron2start->evalaaron2entryin, Arg_1: Arg_1 {O(n)}
0: evalaaron2start->evalaaron2entryin, Arg_2: Arg_2 {O(n)}