Initial Problem

Start: evaleasy1start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: evaleasy1bb1in, evaleasy1bb2in, evaleasy1bb3in, evaleasy1bbin, evaleasy1entryin, evaleasy1returnin, evaleasy1start, evaleasy1stop
Transitions:
7:evaleasy1bb1in(Arg_0,Arg_1) -> evaleasy1bb3in(Arg_0+1,Arg_1)
8:evaleasy1bb2in(Arg_0,Arg_1) -> evaleasy1bb3in(Arg_0+2,Arg_1)
2:evaleasy1bb3in(Arg_0,Arg_1) -> evaleasy1bbin(Arg_0,Arg_1):|:Arg_0<=39
3:evaleasy1bb3in(Arg_0,Arg_1) -> evaleasy1returnin(Arg_0,Arg_1):|:40<=Arg_0
4:evaleasy1bbin(Arg_0,Arg_1) -> evaleasy1bb1in(Arg_0,Arg_1):|:Arg_1<=0 && 0<=Arg_1
5:evaleasy1bbin(Arg_0,Arg_1) -> evaleasy1bb2in(Arg_0,Arg_1):|:Arg_1+1<=0
6:evaleasy1bbin(Arg_0,Arg_1) -> evaleasy1bb2in(Arg_0,Arg_1):|:1<=Arg_1
1:evaleasy1entryin(Arg_0,Arg_1) -> evaleasy1bb3in(0,Arg_1)
9:evaleasy1returnin(Arg_0,Arg_1) -> evaleasy1stop(Arg_0,Arg_1)
0:evaleasy1start(Arg_0,Arg_1) -> evaleasy1entryin(Arg_0,Arg_1)

Preprocessing

Found invariant 40<=Arg_0 for location evaleasy1returnin

Found invariant Arg_0<=39 && 0<=Arg_0 for location evaleasy1bbin

Found invariant 0<=Arg_0 for location evaleasy1bb2in

Found invariant 0<=Arg_0 for location evaleasy1bb3in

Found invariant 40<=Arg_0 for location evaleasy1stop

Found invariant Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0 for location evaleasy1bb1in

Problem after Preprocessing

Start: evaleasy1start
Program_Vars: Arg_0, Arg_1
Temp_Vars:
Locations: evaleasy1bb1in, evaleasy1bb2in, evaleasy1bb3in, evaleasy1bbin, evaleasy1entryin, evaleasy1returnin, evaleasy1start, evaleasy1stop
Transitions:
7:evaleasy1bb1in(Arg_0,Arg_1) -> evaleasy1bb3in(Arg_0+1,Arg_1):|:Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0
8:evaleasy1bb2in(Arg_0,Arg_1) -> evaleasy1bb3in(Arg_0+2,Arg_1):|:0<=Arg_0
2:evaleasy1bb3in(Arg_0,Arg_1) -> evaleasy1bbin(Arg_0,Arg_1):|:0<=Arg_0 && Arg_0<=39
3:evaleasy1bb3in(Arg_0,Arg_1) -> evaleasy1returnin(Arg_0,Arg_1):|:0<=Arg_0 && 40<=Arg_0
4:evaleasy1bbin(Arg_0,Arg_1) -> evaleasy1bb1in(Arg_0,Arg_1):|:Arg_0<=39 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1
5:evaleasy1bbin(Arg_0,Arg_1) -> evaleasy1bb2in(Arg_0,Arg_1):|:Arg_0<=39 && 0<=Arg_0 && Arg_1+1<=0
6:evaleasy1bbin(Arg_0,Arg_1) -> evaleasy1bb2in(Arg_0,Arg_1):|:Arg_0<=39 && 0<=Arg_0 && 1<=Arg_1
1:evaleasy1entryin(Arg_0,Arg_1) -> evaleasy1bb3in(0,Arg_1)
9:evaleasy1returnin(Arg_0,Arg_1) -> evaleasy1stop(Arg_0,Arg_1):|:40<=Arg_0
0:evaleasy1start(Arg_0,Arg_1) -> evaleasy1entryin(Arg_0,Arg_1)

MPRF for transition 2:evaleasy1bb3in(Arg_0,Arg_1) -> evaleasy1bbin(Arg_0,Arg_1):|:0<=Arg_0 && Arg_0<=39 of depth 1:

new bound:

40 {O(1)}

MPRF:

evaleasy1bb3in [40-Arg_0 ]
evaleasy1bb1in [39-Arg_0 ]
evaleasy1bbin [39-Arg_0 ]
evaleasy1bb2in [38-Arg_0 ]

MPRF for transition 4:evaleasy1bbin(Arg_0,Arg_1) -> evaleasy1bb1in(Arg_0,Arg_1):|:Arg_0<=39 && 0<=Arg_0 && Arg_1<=0 && 0<=Arg_1 of depth 1:

new bound:

40 {O(1)}

MPRF:

evaleasy1bb3in [40-Arg_0 ]
evaleasy1bb1in [39-Arg_0 ]
evaleasy1bbin [40-Arg_0 ]
evaleasy1bb2in [38-Arg_0 ]

MPRF for transition 5:evaleasy1bbin(Arg_0,Arg_1) -> evaleasy1bb2in(Arg_0,Arg_1):|:Arg_0<=39 && 0<=Arg_0 && Arg_1+1<=0 of depth 1:

new bound:

40 {O(1)}

MPRF:

evaleasy1bb3in [40-Arg_0 ]
evaleasy1bb1in [39-Arg_0 ]
evaleasy1bbin [40-Arg_0 ]
evaleasy1bb2in [38-Arg_0 ]

MPRF for transition 6:evaleasy1bbin(Arg_0,Arg_1) -> evaleasy1bb2in(Arg_0,Arg_1):|:Arg_0<=39 && 0<=Arg_0 && 1<=Arg_1 of depth 1:

new bound:

40 {O(1)}

MPRF:

evaleasy1bb3in [40-Arg_0 ]
evaleasy1bb1in [39-Arg_0 ]
evaleasy1bbin [40-Arg_0 ]
evaleasy1bb2in [38-Arg_0 ]

knowledge_propagation leads to new time bound 40 {O(1)} for transition 7:evaleasy1bb1in(Arg_0,Arg_1) -> evaleasy1bb3in(Arg_0+1,Arg_1):|:Arg_1<=0 && Arg_1<=Arg_0 && 0<=Arg_1 && 0<=Arg_0+Arg_1 && 0<=Arg_0

knowledge_propagation leads to new time bound 80 {O(1)} for transition 8:evaleasy1bb2in(Arg_0,Arg_1) -> evaleasy1bb3in(Arg_0+2,Arg_1):|:0<=Arg_0

All Bounds

Timebounds

Overall timebound:284 {O(1)}
7: evaleasy1bb1in->evaleasy1bb3in: 40 {O(1)}
8: evaleasy1bb2in->evaleasy1bb3in: 80 {O(1)}
2: evaleasy1bb3in->evaleasy1bbin: 40 {O(1)}
3: evaleasy1bb3in->evaleasy1returnin: 1 {O(1)}
4: evaleasy1bbin->evaleasy1bb1in: 40 {O(1)}
5: evaleasy1bbin->evaleasy1bb2in: 40 {O(1)}
6: evaleasy1bbin->evaleasy1bb2in: 40 {O(1)}
1: evaleasy1entryin->evaleasy1bb3in: 1 {O(1)}
9: evaleasy1returnin->evaleasy1stop: 1 {O(1)}
0: evaleasy1start->evaleasy1entryin: 1 {O(1)}

Costbounds

Overall costbound: 284 {O(1)}
7: evaleasy1bb1in->evaleasy1bb3in: 40 {O(1)}
8: evaleasy1bb2in->evaleasy1bb3in: 80 {O(1)}
2: evaleasy1bb3in->evaleasy1bbin: 40 {O(1)}
3: evaleasy1bb3in->evaleasy1returnin: 1 {O(1)}
4: evaleasy1bbin->evaleasy1bb1in: 40 {O(1)}
5: evaleasy1bbin->evaleasy1bb2in: 40 {O(1)}
6: evaleasy1bbin->evaleasy1bb2in: 40 {O(1)}
1: evaleasy1entryin->evaleasy1bb3in: 1 {O(1)}
9: evaleasy1returnin->evaleasy1stop: 1 {O(1)}
0: evaleasy1start->evaleasy1entryin: 1 {O(1)}

Sizebounds

7: evaleasy1bb1in->evaleasy1bb3in, Arg_0: 40 {O(1)}
7: evaleasy1bb1in->evaleasy1bb3in, Arg_1: 0 {O(1)}
8: evaleasy1bb2in->evaleasy1bb3in, Arg_0: 82 {O(1)}
8: evaleasy1bb2in->evaleasy1bb3in, Arg_1: Arg_1 {O(n)}
2: evaleasy1bb3in->evaleasy1bbin, Arg_0: 39 {O(1)}
2: evaleasy1bb3in->evaleasy1bbin, Arg_1: Arg_1 {O(n)}
3: evaleasy1bb3in->evaleasy1returnin, Arg_0: 122 {O(1)}
3: evaleasy1bb3in->evaleasy1returnin, Arg_1: Arg_1 {O(n)}
4: evaleasy1bbin->evaleasy1bb1in, Arg_0: 39 {O(1)}
4: evaleasy1bbin->evaleasy1bb1in, Arg_1: 0 {O(1)}
5: evaleasy1bbin->evaleasy1bb2in, Arg_0: 39 {O(1)}
5: evaleasy1bbin->evaleasy1bb2in, Arg_1: Arg_1 {O(n)}
6: evaleasy1bbin->evaleasy1bb2in, Arg_0: 39 {O(1)}
6: evaleasy1bbin->evaleasy1bb2in, Arg_1: Arg_1 {O(n)}
1: evaleasy1entryin->evaleasy1bb3in, Arg_0: 0 {O(1)}
1: evaleasy1entryin->evaleasy1bb3in, Arg_1: Arg_1 {O(n)}
9: evaleasy1returnin->evaleasy1stop, Arg_0: 122 {O(1)}
9: evaleasy1returnin->evaleasy1stop, Arg_1: Arg_1 {O(n)}
0: evaleasy1start->evaleasy1entryin, Arg_0: Arg_0 {O(n)}
0: evaleasy1start->evaleasy1entryin, Arg_1: Arg_1 {O(n)}