A problem in the Theory of Computation

1
AUTOMATA EQUAL NUMBER OF goods, bads AND uglies
2
AUTOMATA EQUAL NUMBER OF feasts, famines and
messes
3
AUTOMATA EQUAL NUMBER OF boom days, bust
days and messy days
4
AUTOMATA EQUAL NUMBER OF sunny days, rainy
days and messy days
5
AUTOMATA EQUAL NUMBER OF Rules 1..n of rule
book Tigger follows rules 1..n Pooh follows rules
1..n Kanga follows rules 1.n Roo follows rules
1..n All follow an equal number of rules
6
AUTOMATA Related number of Strings consisting
of as and bs and cs
7
AUTOMATA EQUAL NUMBER OF Rules 1..n of rule
book Tigger follows i rules in 1..n Pooh follows
j rules in 1..n Kanga follows k rules in 1.n Roo
follows l rules in 1..n All i,j,k and l are
related
8
A period in ones life is a sequence of days
9
We model the sequences as consisting of good
days, followed by an equal number of bad days,
which are then followed by an equal number of
ugly days
10
The set of all such sequences or periods in one
life is what we call a language L
11
L consists of strings over the alphabet good,
bad, ugly
12
A LINEAR BOUNDED AUTOMATA(LBA)
13
A LBA IS A RESTRICTED TURING MACHINE(TM)
14
A LBA CANNOT LEAVE ITS INPUT IT THUS USES O(n)
SPACE
15
The formal language consisdered is Lgoodn badn
uglynngt1
16
THE LBA FOR
Lgoodn badn uglynngt1
17
THE LBA FOR
Lgoodn badn uglynngt1
TRANSITION DIAGRAM
18
S
start
19
Base
,R
S
start
20
goodX,R
Base
Upper
,R
S
start
21
goodX,R
Base
Upper
,R
S
YY,R
goodgood,R
start
22
goodX,R
badY,R
Base
Upper
Middle
,R
S
YY,R
goodgood,R
start
23
goodX,R
badY,R
Base
Upper
Middle
,R
S
YY,R
goodgood,R
ZZ,R
badbad,R
start
24
goodX,R
badY,R
Base
Upper
Middle
,R
uglyZ,L
S
YY,R
goodgood,R
ZZ,R
badbad,R
start
Lower
25
goodX,R
badY,R
Base
Upper
Middle
,R
uglyZ,L
S
YY,R
goodgood,R
ZZ,R
badbad,R
start
Lower
badbad,L
ZZ,L
YY,L
goodgood,L
26
goodX,R
badY,R
Base
Upper
Middle
,R
uglyZ,L
S
YY,R
goodgood,R
ZZ,R
badbad,R
XX,R
start
Lower
badbad,L
ZZ,L
YY,L
goodgood,L
27
goodX,R
badY,R
Base
Upper
Middle
,R
uglyZ,L
S
YY,R
YY,R
goodgood,R
ZZ,R
badbad,R
XX,R
Check
start
Lower
badbad,L
ZZ,L
YY,L
goodgood,L
28
goodX,R
badY,R
Base
Upper
Middle
,R
uglyZ,L
S
YY,R
YY,R
goodgood,R
ZZ,R
badbad,R
XX,R
Check
start
Lower
badbad,L
yy,R
ZZ,R
ZZ,L
YY,L
goodgood,L
29
goodX,R
badY,R
Base
Upper
Middle
,R
uglyZ,L
S
YY,R
YY,R
goodgood,R
ZZ,R
badbad,R
XX,R
Check
start
Lower
badbad,L
,R
yy,R
ZZ,R
ZZ,L
YY,L
goodgood,L
THE LINEAR BOUNDED AUTOMATA(LBA)
Success
30
goodX,R
badY,R
Base
Upper
Middle
,R
uglyZ,L
S
YY,R
YY,R
goodgood,R
ZZ,R
badbad,R
XX,R
Check
start
Lower
badbad,L
,R
yy,R
ZZ,R
ZZ,L
YY,L
goodgood,L
Success
31
THE LBA FOR
Lgoodn badn uglynngt1
TRANSITION TABLE
32
d good bad ugly X Y Z
S START?
Base
Upper
Middle
Lower
Check
Success
33
d good bad ugly X Y Z
S START? Base,,R
Base
Upper
Middle
Lower
Check
Success
34
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R
Upper
Middle
Lower
Check
Success
35
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R
Upper Upper,good,R Upper,Y,R
Middle
Lower
Check
Success
36
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle
Lower
Check
Success
37
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Middle,Z,R
Lower
Check
Success
38
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower
Check
Success
39
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Lower,Y,L Lower,Z,L
Check
Success
40
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check
Success
41
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check
Success
42
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R
Success
43
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
44
SIMULATION OF THE LBA ON THE INPUT goodgoodgoodba
dbadbaduglyuglyugly
45
The LBA
good good good bad bad bad ugly ugly ugly
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
46
S?
good good good bad bad bad ugly ugly ugly
S
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
47
S?Basegood
good good good bad bad bad ugly ugly ugly
Base
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
48
S?Basegood?XUpper
X good good bad bad bad ugly ugly ugly
Upper
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
49
S?Basegood?XUpper?XgoodUpper
X good good bad bad bad ugly ugly ugly
Upper
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
50
S?Basegood?XUpper?XgoodUpper?XgoodgoodUpp
er
X good good bad bad bad ugly ugly ugly
Upper
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
51
S?Basegood?XUpper?XgoodUpper?XgoodgoodUpp
er? XgoodgoodYMiddle
X good good Y bad bad ugly ugly ugly
Middle
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
52
S?Basegood?XUpper?XgoodUpper?XgoodgoodUpp
er? XgoodgoodYMiddle?XgoodgoodYbadMiddle
X good good Y bad bad ugly ugly ugly
Middle
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
53
S?Basegood?XUpper?XgoodUpper?XgoodgoodUpp
er? XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle
X good good Y bad bad ugly ugly ugly
Middle
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
54
S?Basegood?XUpper?XgoodUpper?XgoodgoodUpp
er? XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
X good good Y bad bad Z ugly ugly
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
55
S?Basegood?XUpper?XgoodUpper?XgoodgoodUpp
er? XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?
X good good Y bad bad Z ugly ugly
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
56
S?Basegood?XUpper?XgoodUpper?XgoodgoodUpp
er? XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?

X good good Y bad bad Z ugly ugly
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
57
S?Basegood?XUpper?XgoodUpper?XgoodgoodUpp
er? XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?
X good good Y bad bad Z ugly ugly
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
58
S?Basegood?XUpper?XgoodUpper?XgoodgoodUpp
er? XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ??XLowergoodgoodYbadbad
Z?
X good good Y bad bad Z ugly ugly
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
59
S?Basegood?XUpper?XgoodUpper?XgoodgoodUpp
er? XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
??LowerXgoodgoodYbadbadZ?
X good good Y bad bad Z ugly ugly
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
60
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?
X good good Y bad bad Z ugly ugly
Base
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
61
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?
X X good Y bad bad Z ugly ugly
Upper
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
62
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?
X X good Y bad bad Z ugly ugly
Upper
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
63
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?
X X good Y bad bad Z ugly ugly
Upper
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
64
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ?
X X good Y Y bad Z ugly ugly
Middle
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
65
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle ?XgoodgoodYbadMiddle?Xg
oodaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
XgoodLowergoodYbadbadZ ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ?
XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgoo
dYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYba
dMiddleZ?
X X good Y Y bad Z ugly ugly
Middle
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
66
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ??XXgoodYYbadZMiddleugly?
X X good Y Y bad Z ugly ugly
Middle
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
67
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly
X X good Y Y bad Z Z ugly
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
68
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
X X good Y Y bad Z Z ugly
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
69
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly?
X X good Y Y bad Z Z ugly
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
70
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?
X X good Y Y bad Z Z ugly
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
71
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?
X X good Y Y bad Z Z ugly
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
72
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y?
X X good Y Y bad Z Z ugly
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
73
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly?
X X good Y Y bad Z Z ugly
Base
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
74
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?
X X X Y Y bad Z Z ugly
Upper
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
75
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
??XXXYUpperYbadZZugly?
X X X Y Y bad Z Z ugly
Upper
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
76
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?
X X X Y Y bad Z Z ugly
Upper
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
77
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?
X X X Y Y bad Z Z ugly
Upper
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
78
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXY
YYMiddleZZugly?
X X X Y Y Y Z Z ugly
Middle
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
79
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXY
YYMiddleZZugly??XXXYYYZMiddleZugly?
X X X Y Y Y Z Z ugly
Middle
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
80
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXY
YYMiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?
X X X Y Y Y Z Z ugly
Middle
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
81
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXY
YYMiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?XXXYYYZLowerZZ?
X X X Y Y Y Z Z Z
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
82
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXY
YYMiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?XXXYYYZLowerZZ?XXXYYYLowe
rZZZ?
X X X Y Y Y Z Z Z
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
83
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXY
YYMiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?XXXYYYZLowerZZ?XXXYYYLowe
rZZZ?XXXYYLowerYZZZ?
X X X Y Y Y Z Z Z
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
84
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXY
YYMiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?XXXYYYZLowerZZ?XXXYYYLowe
rZZZ?XXXYYLowerYZZZ?XXXYLowerYYZZZ?
X X X Y Y Y Z Z Z
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
85
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXY
YYMiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?XXXYYYZLowerZZ?XXXYYYLowe
rZZZ?XXXYYLowerYZZZ?XXXYLowerYYZZZ?XXXLowerYY
YZZZ?
X X X Y Y Y Z Z Z
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
86
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXY
YYMiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?XXXYYYZLowerZZ?XXXYYYLowe
rZZZ?XXXYYLowerYZZZ?XXXYLowerYYZZZ?XXXLowerYY
YZZZ ?XXLowerXYYYZZZ?
X X X Y Y Y Z Z Z
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
87
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXY
YYMiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?XXXYYYZLowerZZ?XXXYYYLowe
rZZZ?XXXYYLowerYZZZ?XXXYLowerYYZZZ?XXXLowerYY
YZZZ ?XXLowerXYYYZZZ?
X X X Y Y Y Z Z Z
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
88
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXY
YYMiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?XXXYYYZLowerZZ?XXXYYYLowe
rZZZ?XXXYYLowerYZZZ?XXXYLowerYYZZZ?XXXLowerYY
YZZZ ?XXLowerXYYYZZZ
X X X Y Y Y Z Z Z
Lower
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
89
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXY
YYMiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?XXXYYYZLowerZZ?XXXYYYLowe
rZZZ?XXXYYLowerYZZZ?XXXYLowerYYZZZ?XXXLowerYY
YZZZ ?XXLowerXYYYZZZ??XXXq0YYYZZZ?
X X X Y Y Y Z Z Z
Base
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
90
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXY
YYMiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?XXXYYYZLowerZZ?XXXYYYLowe
rZZZ?XXXYYLowerYZZZ?XXXYLowerYYZZZ?XXXLowerYY
YZZZ ?XXLowerXYYYZZZ?XXXq0YYYZZZ??XXXYCheckY
YZZZ?
X X X Y Y Y Z Z Z
Check
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
91
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXY
YYMiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?XXXYYYZLowerZZ?XXXYYYLowe
rZZZ?XXXYYLowerYZZZ?XXXYLowerYYZZZ?XXXLowerYY
YZZZ ?XXLowerXYYYZZZ?XXXq0YYYZZZ?XXXYCheckYY
ZZZ?XXXYYCheckYZZZ?
X X X Y Y Y Z Z Z
Check
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
92
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXY
YYMiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?XXXYYYZLowerZZ?XXXYYYLowe
rZZZ?XXXYYLowerYZZZ?XXXYLowerYYZZZ?XXXLowerYY
YZZZ ?XXLowerXYYYZZZ?XXXq0YYYZZZ?XXXYCheckYY
ZZZ?XXXYYCheckYZZZ?XXXYYYCheckZZZ?
X X X Y Y Y Z Z Z
Check
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
93
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly? ?XXXUpperYYbadZZugly
?XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXY
YYMiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?XXXYYYZLowerZZ?XXXYYYLowe
rZZZ?XXXYYLowerYZZZ?XXXYLowerYYZZZ?XXXLowerYY
YZZZ ?XXLowerXYYYZZZ?XXXq0YYYZZZ?XXXYCheckYY
ZZZ?XXXYYCheckYZZZ?XXXYYYCheckZZZ?XXXYYYZChe
ckZZ?
X X X Y Y Y Z Z Z
Check
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
94
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly?XXXUpperYYbadZZugly?
XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXYYY
MiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?XXXYYYZLowerZZ?XXXYYYLowe
rZZZ?XXXYYLowerYZZZ?XXXYLowerYYZZZ?XXXLowerYY
YZZZ ?XXLowerXYYYZZZ?XXXq0YYYZZZ?XXXYCheckYY
ZZZ?XXXYYCheckYZZZ?XXXYYYCheckZZZ?XXXYYYZChe
ckZZ? ?XXXYYYZZCheckZ?
X X X Y Y Y Z Z Z
Check
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
95
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly?XXXUpperYYbadZZugly?
XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXYYY
MiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?XXXYYYZLowerZZ?XXXYYYLowe
rZZZ?XXXYYLowerYZZZ?XXXYLowerYYZZZ?XXXLowerYY
YZZZ ?XXLowerXYYYZZZ?XXXq0YYYZZZ?XXXYCheckYY
ZZZ?XXXYYCheckYZZZ?XXXYYYCheckZZZ?XXXYYYZChe
ckZZ? ?XXXYYYZZCheckZ??XXXYYYZZZCheck?
X X X Y Y Y Z Z Z
Check
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
96
S ?Basegood?XUpper?XgoodUpper?XgoodgoodUp
per?XgoodgoodYMiddle?XgoodgoodYbadMiddle?Xgo
odaYbadbadMiddle? XgoodgoodYbadLowerbadZ?
XgoodgoodYLowerbadbadZ?XgoodgoodLowerYbadbadZ?
?XgoodLowergoodYbadbadZ?XLowergoodgoodYbadbadZ
?LowerXgoodgoodYbadbadZ? ?Xq0goodgoodYbadbadZ
?XXUppergoodYbadbadZ?XXgoodUpperYbadbadZ?XXgo
odYUpperbadbadZ?XXgoodYYMiddlebadZ? ?XXgoodYYb
adMiddleZ?XXgoodYYbadZMiddleugly
?XXgoodYYbadLowerZZugly?XXgoodYYLowerbadZZugly
?XXgoodYLowerYbadZZugly? ?XXgoodLowerYYbadZZugl
y?XXLowergoodYYbadZZugly?XLowerXgoodYYbadZZugl
y? ?XXq0goodYYbadZZugly?XXXUpperYYbadZZugly?
XXXYUpperYbadZZugly?XXXYYUpperbadZZugly?XXXYYY
MiddleZZugly?XXXYYYZMiddleZugly?
?XXXYYYZZMiddleugly?XXXYYYZLowerZZ?XXXYYYLowe
rZZZ?XXXYYLowerYZZZ?XXXYLowerYYZZZ?XXXLowerYY
YZZZ ?XXLowerXYYYZZZ?XXXq0YYYZZZ?XXXYCheckYY
ZZZ?XXXYYCheckYZZZ?XXXYYYCheckZZZ?XXXYYYZChe
ckZZ? ?XXXYYYZZCheckZ?XXXYYYZZZCheck?XXXYYYZ
ZZ4Success?HALT AND ACCEPT
X X X Y Y Y Z Z Z
Success
d good bad ugly X Y Z
S START? Base,,R
Base Upper,X,R Check,Y,R
Upper Upper,good,R Middle,Y,R Upper,Y,R
Middle Middle,bad,R Lower,Z,L Middle,Z,R
Lower Lower,good,L Lower,bad,L Base,X,R Lower,Y,L Lower,Z,L
Check Check,Y,R Check,Z,R Success,,S
Success - - - - - - - -
97
END