A Cook's Tour of E!uational Axio8atiAations for Prefix Iteration. Luca Aceto* Wan
Fokkinky Anna Ing щolfsd щottir*. 1 Introduction. Equationally based proof ...
"!$#% &'( *)+( ,.-/1032#546 07 ( 8:9=@?%;>A,BDCFE G=IH/JKCILML1N Hswtuxw,+
q, svu ,P\o>prqsu{w6yrqtzxz{| }rq6\
vww,v|ZsMqty }IKprv"svw^w6v|sv6u¡ ^qsu{w6yrFuxyq:
p
zx|"v|y>sq, svu ¢qD|,Fqtyrw,£svrm}rq6u"wt¤qt¥u{w6eqtsvu6u¡ Iqsu{w6ysvww6zx"zxu{¦6,F, rx1§F¨©«ª¡¬D\®¯m
w, svr+s
w6vsvuqtzIIw,uxy6s¢wt(>ux w,e
zx svq¥uxw,qsu{°\qsu{w6yrKw,M}^rqDu{w6p
qtzr\o>p
u{q,z{yr \ q,svprv7svr:yr 7wtFu{±Ivy6sPy
w,svuxw,yrsux w,P
w v u{ymsvvzxu{ssvzx u:Zsu{zxz1¦y
w:y~w6y~s
svw6
uwt(±I\*su{6w,e
zx s q¥uxw,qsu{°\qsu{w6yr7wtMs
y
w,svuxw,yr¢w,sux:Zspruxu{y³ª ¶D®Mw6¢u¡sqsu{6
w \vv ÌÍy´sv
u Zspr|61¤evrqtzxzP
vy>sq w6y>svu{}
p
svuxw,yswsv
uz{uxy
ewt7v\\qt}|u{y6À svux6qtsvuxy
%q%ux,yru¡ ^qty>s+qt6ey>sw,Ksv
y
w,svuxw,yrwtK\o6pru{qtzxy^ eqtyrrvw,+vw6¾ª ¶® w,3©kuxz{y
Î K}^q,vuxÏ:Ï¢µkÐX
y^ w6svv\msvwq63ÑÏ:Ï¢µ
Ò:ª{¬Ó®I ¥svyr\:u¡s]
¥ u{svqsu{w6y1³§K
¥³u{svqtsvuxw,y/ªÕÔ®:uxeqDq,vuqsu{w6yRw,yRsv
w,u{6u{y^qtz7}
u{y^qt|6uxw,y³w,svr Özxyr~Zsqtmw,Iqsvuxw,yR×ØÙ¾ª{¬,¬*®¯Pw,}sqtuxy
}|v\Zsvu*su{yrsv
~ rZseqt,p
ey>s sw}I qtyqsw,euq6*su{w6y1Mqty^|uxz
uxe
zxu¡sqsvux,}IrqDuxw,p
svrqtsqty´}^\o>prqsu{w6yrqtzxz{| rq,q6*svvux°\}|\qtyrKwtI ry
u{svw,zxz{\*su{w6yrux¤srqs¢u¡s:w7y
w,s7uxy,w6z{6q^qtqte svu
w \v7 ^y
u¡À ÷ ê*ð6íDÛó éDÜ7øDæZÝéDâëî·ÞZäÕê*ߢâé>ç àRðó áxÜ7ræZìâââç ã çXî äÕî·äåâë:õÕÝ:õ æZÿé æîIã·ã í\æêâìDò6ç·ìtñVå¯ê*èkê*ç ë:î äÕæéìDøíߤû î·æZÿ"ê*çIë:î ùèDìDåZæ íäÕæî·Mé\æZåçíDæ*ëà>ðúw,X7wt(¢
Ór Ô qty^]Órx¬\6Ò*PÂ(wmw6p
¤euxyrFs
u7v
w7
w s
qtyrq,z{|vux¤wt(sv
w6z{zx svuxw,y~w,(qtzxu]uyÀ svu{svux w,svr]eq,y>svu w6yrvuxv\uxysv
u rq,^qtzxv\q,|}Iw,e
u ] prz¡s,y´uxy svr
v\yr ew,¤,v|vuxrz{u{svqtsvux,e}^rqDu{w6p
Fzxu{¦6sv
w>sv^qsq,y´}I ¥
v prvu{yrrv
¥~u{svqsu{w6y1 ¢
rq,^]uw,6q,y
u{° q,ew6z{zxw¨:²sv~q}
u{ v>ux.wt"sv
}rq,vuxkyrwtsvuxw,y^ w,
w ¤sv
w,|y
\%uxy~s
veq,u{y^7wt(sv
rq,^зµ s^6Ò*7"rv\y6s7svr zqty
6prqt6ÑÏ:Ï¢µ´:u¡s³
¥u¡sqsvuxw,yqty^´u{szxq,}^z{zxsq,yru{svuxw,yv|sv vqty>sux Ð µ*s\,Ê6Ò Kµ stÓuK6wtssvwq",p
u\sw,p
Pw,Iw6p
K w6e
z{svy
s wt svrux¢7w,¦V
qtyrqeux p^vvu{w6y%w, w6y
,w6u{yrmvq,зµ s 6Ò* f l «lc fKl ÌÍys
ux7v*su{w6y¤+
v\y>sKsv
}rq,vu:y
wtsu{w6yrPw,
w \vg 6mb i l f- ml(dm ©g ¬ 6dm g¢¡i m¢k i mdm g 6m ll b - k i k(m igj
b °z ¯ ¤ g 6m ¤
ll X dbL5m g dmdd y ti m ¦±
i b £g 5bed4k f kRm i bll¨ fX m f d©k(mb f l l g m i 'b Zftg b tZ¬ ft ¡ bll¨m ®t R m i l f5 ml }
w6²N³H;]q,yr´µ }¶ ···"}¸£~ uXv-w Ø I¤:u{sv ºz ¹ ¤ u{±´s
¥uZs"Zsqsv\ » s ··· s ¸ y¢½ y¢Á vprsvrqts µ » z y¼ ¶ z¿ µ ¤ÌÍyksvrqts+q,v,r¤qD|sv^qs ´ uqkÇLÂÃÆ ¼ Ðw, zxyrtsv ²MÒ¤wt svrZsqsv ¾ K¾¾
w6¸6ÀJqe¶ z Zsq sv¸ ~ ¤ o peq6r7 ^y
ÅÄ ÆÇ5Æ ÈÆ v-É ÊÐ Ì Ò µ Ë x }~ uXv-w {ÅÍ ¤ Ä z y ¤ ·
J # 3c1 ,7+ "B.(,"/0) .R/9¡ ) , B )¨ Mq,}^z{zxmsq,yru{svuxw,yv|ZsK\vvux}^7s
w,Iqsu{w6yrqtz}I^qD>uxw,prPwtV
vw\suxyw,qsvuxw,yÚw6y sv
7qD|
w\ w6e
psv6q³7qtz{sv w, y
wtsu{w6yrwt}I^qD>uxw,prq,z:o>p
uxDq,z{yr w,~q,
wD¥uxqsu{w6y rqD6 }IyZsprux uxy s
zxu{svqsp
w,y/
vwsvrw,|,¨ v|Zsqsuxu{y,\Zsu{>qsu{w6y wt svrv]y
wtsu{w6yrurv\y6suxy/ª ¶®·p
u{qtÀ zxyr¢w,¤zqt}Izxzx~svqtyrvu¡su{w6yv|Zs7w,~}|]u{y^ zxpruxw,yMPÌÍy~s
ux:svp^|,
7rq,z{z uxy>6svux6qtsveq%vu{6y
u{ ^q,y6s"qt,ey6swt¤sv
yrwtsvuxw,y^w,¤\o6pru{qtzxy^ qtyr
w,+w, ª ¶®¯K¢
v¤y
w
vw~svwrv\y6s7w,sv
qt¦6w, w6e
z{svy
=5? @BADC AFE@HGJIeGVM![ AL^B SLPRCALEZ@ =6P(T \[JAF^B SLP(C ALEZ@VP(@8T' ALYAL^B SLPRCALEZ@ _ ` b ¨fXihi ml ftg b t X d g©ftg mdbed f vuxp
zqsu{w6y b § 6m m m i+ ¶ > fX } bed f l f5 mlª
b ¶ z y ¤¶ g 6m ag 6m i m¡bed fhgji!fX db g b X z y ¤ d g fXg ¤¶ ¤ ` b ¨fXi i ml fXg b X t d g©ftg mdbed f q,
|]uxp
zqsu{w6y b §ºb g bed f db 'Rl ftg b t b g g Rmk i k(m igj g fXg 6m m m i+ ¶ ft } bed f l f5 mln
b ¶ ¦ y g Rm ¦ y `}
uuxp
zqsu{w6y bed f d hm gFi bL¡db Rl fXg b X b § 6m m bed bedb 'Rl b d g¢fXg md °fX ¤fti m }
uvu{euxzxq, i b gjg m "! mi l fXg md g 6m h$ # m m tig g Rm i ml ftg b t%! bll m i ¤ m m ii mg g¢i f d¢}
f°u uxprzxqtsvuxfXw,g ykXVo>p
g ux>fXÀg qtzxy^ - '& m i b g m )(*,+ ¤.j- i md©k¨ "(*0/1+ ¤32 b § g 6m i m bed f db 'Rl fXg b X4©- i md©k] f£i m f db Rl fXg b X526 b g 7 ¤ Ñ7uxvuxp
zqsu{w6y~o>p
uxqtzxyrª¡¬ 8D®1vzxqtsv\3sZ7weZsqsv\7u{ykqzxq,}^z{zx~svqtyrvu{svuxw,y%v|ZsrvÀ uvzx|:ry sv
|³rqD,s
vq,e~}
qtyrru{y
Zsvp^*svprv6³µu{mp
zxqtsvuxw,yÐXv,3, rx+ª¡¬ 8D®Ò qty^kv\q,|~vuxp
zqsu{w6yRª Ó® vzxqt¥~s
ux+v\o>p
u{ey6s:sw]u{±Ivy6s"6v¤Â¢
w6z{zxw:uxy
y
w,svuxw,y1V:
uu+}rq6\w,y´q],vuxw,ywt3
w6qtsv\ksvq,^u+uxyrp^ }||6 sqty
w,sv
¢qD|wtPqt}rsvq, svuxy
w,sv
p
zxzM}rq,yr
uxy
svpr svp
wt^s
zqsu{w6y u"q]
w6w,+sqswt3q,yqt}
u{svqt| zqt}Izxz{\~~OsNQPq,yrvu¡sP u{w6yv|Zs"Xu¡s:¦,vyrzV:u{(*Fzxz1W }Iyrwtsv\}>|"Y W Ê F
&(/47
ld
f
bId f "dsvuxy
]s
ezxq,y
,p^qt,mwt¤Ñ¢q6ueÏ:Ï¢µ Ðryr w,vsv´wt²syqt}
}
uqs svwÑÏ:Ï¢µ
Ò7:u{svk
¥u¡sqsu{w6y´ªÕÔ\®¯svw6, s
::u{svku{s¢w6^qtsvuxw,yrq,z1eq,y>svu
$
143)4.R
¤q,vp
e3qy
w6yÀ¯esZ|qtzx
rqt}I s rÈ1w,rqsvw6euxKq6*su{w6yr\:u{svsZ|
uq,z,z{y>ssst ¢
ezqty
6prqt6m ÐXÑÏ:Ï¢µ Ø Ð rÈÒÒwt7Ñ7q6uÏ:Ï¢µ:u{sv
¥u{svqtsvuxw,yu,ux,y}|svr w,zxzxw:u{y
Ñ +R,qteqtÄ × ÄªÄ¥µ { K { · × { "× !@× { Ø × · :+^qtzxzrprv+ × shÙ sA'R s sAU svwqty
6¢w,¤Â ÐXÑÏ:Ï¢µ Ø #Ð rÈÒvÒ*y>sq¥F¤ vrqtzxP z1qtzx¢qD|7q,vp
esrqs:s
w,Iqsw, · }
uxyr
:svw,y
67svrq,$y !m :"vrqtzxzVprvsvrv|}Iw,& z %svwZsqtyr]w,¢|y>sq6*suxo>prq,z{u{sZ|ewt1seP¢
" ¥
uxw,y ×'ª !Ù"®1:u{zxz1}I prv~svw]y
wtss
Xq, s:svrqtsÙ uq,y%w6svuxw,yrq,z1prq,yrF B , V=q =6r+13^N^UJ+J+V)P(G_W)Lt(+s [*-13q;/8uS, `v.0a]w3b#/2xW>'x+D313/8[/51c13474d/6D3IW>@/8/8V71:GtGeD39;/4=M 6yf]@47?Aghz{>@4=RYVd1:\|O/}Q BCR >'>@A?Ai)ZkEF.h6]D2>A/?AG0IY.0/4dD~15B \)H /FIKVXJ+G06V=J+>AImD3D3LN>Aj>AG0/5MAi76$O8Z0P)D3Q >AIWRS.k.04=47/D2G066TD3j8.BCV)/FG0>AD3ImIm.UDcl]4=GhGhIWDcV7D34=AV=)1o9YkD3V).0Z/p4=1:Gk?@[476T13G0/8
ki7\]ZkY>AV74=~i)Z0G/Ib Û :
D3D3Z0.k>'4dD3D>A\|j5/47?'lhGTR7D3V).0G0/ ?'lD3/8D313/8AD3?@/K?0Im>ADcAV)GIRkj89~@R0/) iARM 7Q A 1s }^~q
uxsvuxy
,pruxv
³v|}Iw,zKyrwtsmw,y>sq,u{y
\u{y ~vrqtzxzKprv .svwsq,yr w,sv
q,*su{w6yk^w6vek}|q
w:q,+u¡s+Iw,vsu¡s+vprZp
zMsvveuxyrqsu{w6y17¢r e sqÀ¯Dq,vuqt}rz{F% :uxzxzPq,y
,ew,+s
]v so + V>e¢rw,Iqsvuxw,y^qtzPqty>svu"w6 svr zxq,y
,prq,, ÐXÑÏ:Ï¢µ Ø Ð ÒÒ7u:,ux,y~}|]s
Nzxq,}^z{zx~svqty^u{svuxw,yk|sv  ÐXÑÏ:Ï¢µ0 Ø Ð vÒÒ N V ] N V :
v¤sv
¤svqty^u{svuxw,ymvzxqtsvuxw,yr qtKsvr7zxq6Zsuxy
´sv
kp
zxu{y Â(q,}
zx¬6RÌÍy>svp
u{svux,z{|6¤qsvqtyrvu{svuxw,y × ÙÈ\qtyrmsrqsesvr v|sv$
vy>s}|]svrsvv × qtykIvw,s
mq6*svuxw,y$I
s
}|%,w6z{uxy
eu{y>sw Ùe y@s
kwts
rq,yrF7× ÙÈe\qtyrmsv^qs~× qty@sveu{y^qsvkuxe\uqsvz{| :u¡s vpr Xs
v\q,¢:u{zxz1uxe\uxqtsvz{|%v\qtzxu{°+srqs\
u{ysrqs+q,v,rÙ%M F
J&(B.(,"/0) 1 79 )0.(, ]*
«
rÈ >:
rÈ
«
«
rÈ
rÈ s
rÈ
« 5s
z
{
~
rÈ
«
rÈ
z
z
z¯
× × × × ×¡@! Ù¢ × Ø ×¤ Ø × ·
K z¯
z
Ù¢z Ù ¤ ×£! Ù z Ù ¤ z ¤ × z × ¤ ¢ z
Ø ¢ × z × ¤ Â qt}
zx¬ÅÄPÂ(q,yru{svuxw, y ¥:p
zx z
¤
Ó
: u{svsvr3qt}Iw,P ry
u{svuxw,yrs
Kzqty
6prqt6PÂ ÐXÑÏ:Ï¢ µ Ø Ð rÈvÒvÒVuxy
u{sMq,z{ztsv
Kyrwtsvuxw,y^ wtF\o6pru{qtzxy^ +q,yr
vw,3w,Prvw \vvP
ry
\uxy~µ s>
¢r:w,zxz{w:uxy
vp
z{s u:Zsqtyr
q,1 WXE4EYADCALEZ@ 9 ILK = Xi L ~N R P s P sT S sA'R sAU ÅV g 6m i ml fXg b X d (*FW|ft 6Y W|fXi m k i mdm i m R m ( k m ¡ d b R m d b m µ Ø #Ð rÈÒvÒ ]Rmd f hm lnd ti bedb ' g i!ftg©ti °g ÅZftg i  ÐXÑÏ:Ï¢ l ftg b t mIH Rb f lªm m =5? @BADC AFE@9 IeG J6m dm g
u{qsu{6 × bed g Rm£lªm f d g dm g Xg©f b b - × g ftg bed l dm Åm ig Rm gji!fX db g b tai ml fXg b X d ̯suq,v|%svw%vsvrqtss
mv s"wt3vuxqsvux,\w, rs7
w,y]uxyª \®Fw,¢}
uvu{mp
zxqtsvuxw,yÀ¯}rq6\o>p
ux>À qtzxy^ ¢w6¢}rq6uÏ:Ï¢µ]:u{svk
¥u¡sqsu{w6y1:u{zxzV ryrkq,
zxuxqsvuxw,yuxy%s
qtuxyr wt svr rqtIÐ *Zs
w>w,(w,svuuxy svrz{uxy
\qtvÀ su{eDÁ}
qtyr
uxy
,À su{e v^\*svp
ux p^vv%u{yµ\*s\^Õ
!
K !!/ Ðo!Ò
Ð !
Ò&!
µ
µ
!! Ð~
Ø Ø6 Ð~ÒS ! Ø Ò
µ
µ
µ
·
µ
ØØ
 qt}
zxRÄK¢
q¥uxw,$v|Zs B = × ÚÙ IH × Ù Ù × &
×
Ù IH IH IH :× Ù × ª ! ,® ]Ù ª ! ,® IH
£EC PRCALEZ@ 8ILK b § g 6mb m ftg b t XifX|f! b ±d d g m #"h0m> i b g m$"&% &' ' bedk i!tf- lnm i! g Rm f! b db " 6db ->g 6m i Rlnmd b m ftg b tZf l l bL ` m ftg b t µ bll m 6dm f d f d tig fX Xig 6mk f b i¡ b m ftg b t d (' fX )' Rm m m i 0m i b g m fX b m ftg b t2" g 6m Xi K *' K F 0m m ft g fXg b ¡g Rm¡K dR fX f kÅk(m fXi d t g 6mlªm g fX dbL5m " g 6mb m fXg b X g 6m b gf l¥d f k5kRm fti d Xag 6m i b g fX hdbL5m µ +.- 95m ¨Xg md g fXg , fX fti mm f l6 XRl ¡f dd b fXg b b gjfX ' g¢fXg b b gj L b m ª ` 0 n ` 2 $ 1 % º µ "$/ g ftg rÈ 0m Xihf llªm g b t2" b m fXg b X d X m i g 6m'db ÅZfXg i m
×
Ù
IH
× :Ù IH %× Ù = ? Â ÐXÑÏ:Ï¢µ0 Ø Ð vÒvÒ "- 52 IH i b g m+×43 'Ú 576 Ù d d `80Xn`21t:9;%~×qtyr u3q" ry
u{svu{y^ ¥s:#Ð ¥q,z{z sv^qs sv
¤esZ|vp
v
v\y>s Mtqty^sv
7y
w,sqsu{w6y~'ª !Kt= ®
Zsqtyrr1w6(w6svuxw,yrq,z,uxyr zxprvu{w6y wt K]q,:qevp
eqtyrFÕÒ O0=6^N^ P B I:B Ò fX mk i!t m mIH f l g¢ f Zti f l Xi f g m i b  ÐXÑÏ:Ï¢µ Ø Ð rÈvÒv¡ 6db - mIH ftg b t d:¨+Ê
^¨Ó ft m§F¨¬ J # 3 1,7 "B.(,"/4) :}^,uxyw,p
Ksvw,pr3wtF\o6p^qsvuxw,y^qtzrqt¥uxw,qtsvux°qsu{w6yr w,3
v
¥eu¡sqsvuxw,ye}|
v\y>svuxy
q w6e
z{sv"q¥u{w6v|Zs w,3sv
"v\q,|uxprzxqtsvuxw,y]
w6
+Ð *Z +y1
Õ"w,3sv
"
À y
u{svuxw,y%wtFsvrux7zqsvuxw,yIÒ*p
uxqtzxyrÐX*Z^Â(q,}
z{6Ò7qtyrwt(sv
w>zxuxsv\u{y qt}
zx Ê
¸
"!
$#
%& % &
U('B=6EWX=6^
Ø ·
Øt Ð !!
Ò '
·
'
·
·
Â(q,}
z{ ÊÄ'V)D 13AI /8, IWIWZ .0I K>AV7I9jB>AD3//K.0Gh/:DG0V5D34=VCB¡a]>AIWV).0[]< V513VhB jIml/D3.0/5ImD36y4=/8D < D3>AVF9[] 13(V=*\)R/:47G0zh 6l >AGk6]Z0 j8D3/>AV)[Gp13VhV)jGF//D36F./ zhIWlXZ04< j5V=479IW/}D3.04=/ Gk47IW>A?'l]/8IWIY>AIV=V79 Gp¡D3.47/ G06 9V713'D3.FD3.>AI+j547IW/)R0z{/i)>AG-zhlp47[[0?'l]>AG0i ] 7 OD3V D3VKV)z]Dc47>AGFD3./ !/ NhZk4=?@>'D~l 4 03- 0 M /:
hQ # 4 - / 0!'^2 T/ j54=G-G0V5B13/547IWV7Gy47IC>AGFD3./`013ImDYj54=IW/ V79D3.0/[13VhV79D3VK6/813>A\|/D3.04=D 4 - / 4 06- 0 M /:
|Q 01'32 ,1c47G0IW>'D3>A\t>'D lXG0V5Bl]>@/8? 6]I+D3.0/ >AG0_/ NtZ04=D3>AV)>G ` !" $# +.- +>Û q A %3+ %.- % M /:
hQnx 47Gk6 # +.- A 0a4 03- 0 M /:
|Q l ] 7 OD3V R047G06X13/54=IWV)G47IC>AGFD3./ [13/\t>AV)ZICj547IW/) 7 [0[?A; !" $# +.- + Û q A`% + % - % M /:
hQnx 47Gk6 # +.- 4 Û q A$0 4 0 - 0 M /:
hQnx I (* R]B/ >AG9/1D3.04=!D 9 7 8 O7D3.0/13/ /8a]>@ImD3IY4 b IWZ0jc.FD3.k4dD de c b 4=Gk>6 (* b R gh9V=1/8\|/81W;l :D3.0/813/ /8a]>AImD3IY4 fq :~xIWZ0jc.pD3.k4dD ec fq :~x 4=GkH6 % (* fq :~xR 9 £@> ? >'D>AIY4IWZB + I:4=Gk>6 B 4 0 D B 4 I:4d13/ !/ NhZk4=? r /0 j5H I47&Z, IW/y.0/8V7139 /9D3V7.13/F/C9B V=/C13< A9{D3D3IW./8?A/+9 >AV7G01X!/ NhV)Z0G>A/-\747V7?A/9 GD3j.//I % (* qf:~x 47G06FIWZ0zImD3>'D3ZD3>A\t>AD~l2D3VK>AG9n/81CD3.k4=D qmOdx + %.- % + %.- fq :~x % % T/ [13Vhj8//56pBC>'D3.FD3./ [13VhV=9&ztloj8V)G0IW>@6]/813>AG0iKD3.0/9V)?A?AV5BC>AG0ioD B VIWZ0zb#j54=IW/_I 9
%
4 0 - 0 /
Ô
, .0/13/ >@I47Gp>AGk6/aiAGk6]/8a='D3. + # 4 0 >ADY.V)?@6I+D3.k4dD (* 0 T/ jV7G0IW>@6/81CD3./IW/ D BVKj547IW/8I>AGpD3Z]13G 7 7 IWIWZAIY47GF>AG06/8a AI+j547IW/)R B / '47DI+.9V7V)?A?@?@6V5ICBCD3I_.k9 4dD (* 0 GXD3.0>AIYj547IW/)R + Ûq + % - % M /:
)Qx + Ûq + % - qf:~x8M /:
hQnx % % + Ûq + %.- fq :~x / + - / 4 06- 0 M /:
)Qx % 0 ¼
¼ ½
+
+
¼
+
# ½
, .0>AICjV7y
À
w,y
ux°qtsvuxw,ysvy
zxux¦,eu{ysv
q,vwt7v\q,|vu{mp
zqsvuxw,yMFy
w%¥svq]zqD ux"y
\ svw\qtz1:u{svk
r¥~u¡sqsu{w6y%¥rz{u u{svzx|, U B=6EWX=6^ 8 B I = ti m m i × sÙ ~  ÐXÑÏ:Ï¢µ Ø Ð rÈvÒvÒ (× (*0+ Ù b § + %%( × ' ٠¢
:
wwtVwtVsvr w,e
zx sy
\vPsv
w, w63vu{mp
zxqtsvuxw,yeuKuxeu{zqts¤q w6e
z{sv"q¥u{w6v|Zs w,¤
v
¥eu¡sqsvuxw,y:u{sv~v\I s svw%svrq6uxy
w6
\¢rqt¥uxw,Èv|Zs / w6yrvuxs"wt3sv
e w6z{zx svuxw,yw,3zqD w,:q6|~vu{mp
zqsvuxw,ykqty^~w,(s
w6vz{uZsuxyk qt}rz{Ór ('
#
¶
#
%
% %
Ð~ e! 2!Ò
Ø,Ð~ e! 2!Ò Ø,Ð~ !e K!K! ~Ð 2!ÒvÒ ·
·
·
·
·
·
·
·
·
·
' µ
'
~Ð tØ Ð ! Ò!SÒ!S! Ð~
KØ,!Ð~ KÒ !Ò Ø,Ð~ !K! Ð K!ÒÒS!e ·
·
·
·
·
·
·
·
·
·
·
·
Â(q,}
z{ÓÄK¨:¥u{w67w,¥:\q,uxy
U B=6EWX=6^ B8I = ti m m i ×sÙ ~  ÐXÑÏ:Ï¢ µ Ø Ð rÈvÒvÒ (× (*0/ Ù b § / %%×u{svuxw,yswrvw6"¢
k
Ó^ÕÔ D3WVKXIWEJ/E/ *D3}.04=L]DCZ0[>'DY[{IWV)Z IW 2/j8D3.k/I+4dD D3VK /Im(* Dc47z ?A>@IW.-B D3/./ []13jVd?@\|47/ >A< D3.kZ04=G0D 6 /81+D3 ./ 9V7 ?A?@V5 BC>AG0riXlJ4=IW IW/Z0'9 D >AIG0V7D.k4d1c6
*
#
O) ¡4=Gk6 4d13/G0V713'D347j8>AD5?AV)?0RGKG47/D3j8/5.0j6:V74=1cD D36].>@/ Gdi:B IWZ0D3/5Vz]4=^|D3 /8/8/8131&AG!/ NhZk47?A>'D = ?A/8a]>AjV)i=1c47[0.>Aj}V=1c6/813>AGiKV)G-[047>'13ICl V7 9&[] 13Vh j/9IW13ICV)D3&< /813AGk 6]Z0 x j8eD3>AV7q G BC >'D3x+.>'9 13/IW[{/j8D&D3V D3./9V7?@?AV5BC>AG0i b-/8>AD3./8 1 "!$#(q x "!$#8q x b-V=%1 & '!(#8(q Ox #) "!$#8q x 47G0*6 "!$#8q x "!$#q x , .0/ G/8atD+D BVKj547IW/8I6]>@ImD3>AGi)Z0>AIW.FD3./ [{V)IWIW>Az?@/Iml]GhDc47j8D3>Aj 9nV713A/G0j.0/ 4d\) / R{(* BC>'D3. R 942V=1ImDWIW13V)V)AG06Z0jD3>@V7G-D3V % (* % D3Vp6]/813>A\|/ Z % % Y, .0/813/89nV713/)R{9nV71 /47jc.H:EFHGkR + %.- % + %.- % # + %.- %HqA x rSlpIWZz0ImD3>'D3ZD3>A\t>'D lhRtB / .045\|/D3.k4dD # +.q;Phx + %P- % M /:
|Q + %.- % M /:
|Q %f'3) %f'*) /_LtNt>AG0Z0j47;/ ?kD3 ViB (* + %8D :EFS>AA/0 I Z] 1W D3 .0 w /813 A A>'/D:I9D3V).0?A?A4=V5D8BCeIKD3.k.k474dICD 4 IWZ0 w A6 I V7G0?'lX>'9 e /Gj/)R + %.- % M /:
hQ /8a][q x # %f'3) BC.>Aj.XD3V)i)/D3.0/81CBC>'D3.-!/ NhZk4dD3>AV)G q;P|x l]>A/?@6 I ! " # +.- + Û q A %('*) + % - % M /:
)Qx , ./ G0/a]D+D~B VKj47IW/I6>AImD3>AG0i7Z0>AIW.FD3.0/ [{V7IWIW>Az0?A/ Iml]GtDc4=j8D3>Aj 9V=13A9IG 0I30 4dPD3A*OZ)]r1cq#4=V7g)D3D3x/. 6 OR 0 b >@/IY47A?'AD3/G0ZI V=1c134=D3A4 IK0 /5# 47Im,lURD3V5V BC>@IWG/i/ D3.0>AG04=D47?A[]?'lh13R V)[{ "/8!$1W#5D~(q l A bA x V= 89 "!$#847(qG06 xC 47G0>@6 AGk476]G0Z06 j8D3 >AV70 G D3V= b (* J 0 D3V26/813>A\|/ b 0 L]Zz0ImD3>'D3ZD3>A\t>'D loG0V5Bl]>A/?@6I - b 4 0 - 0 0q /)x /G0j8/)R 12# 3 /a[(q x 4 q |x 4 03- 0 M /:
|Q 01'3215 9nV71yIWV7AI-/47ImlND3V_IW//D3.k4=>D (* >@@/89I w 3q :x (; 9x ; < #$B 4 0 D '947Gk62V7G0?'lo>'9 .047I+4IWZ0AG0j/ (* 4=GkH6 e c % 4=Gk6 >AICI34=D3Z]1c4=D3/56 R /AA/I+D3.k4=D+9nV71/547jcH. :F>G O7 />'D3.0/1 + % # + 4=GkH6 % (* R gh V71CD3./813/ >AI4 6 % (* 0 !6" % # %
# .+ - A f% '3) + %.- % / a e c % ce % % %
X«
¯
¼
«
«
¯
¼
¬ ;
% A>JGX?A/5D34d.013/ ?'lhjRhV7/5Gh47D3jc/8. atD - >AIR04 47GkG6oV713BC'D347. ?t9 V= "13!$< #8q( >AG% x BC.>A j ".o!$#84=q(?@%?[x13V7[{/81IWZzD3/813'[0D3[Z?'D3l>A\t>AG>'D i$lhR >@G06Zj8D3>AV)GND3V (* RCB / >AG9/1FD3.k4dD> + % - % + - q#f)x ~GGFV713D3Aj .2/8AD3l A xG #Q V7B1D3: /)I R 9Z]1WD3.0/813 ? e F@> ? e -@> ? 0 e % % % % 0 0 D3IW, .kAG0D3j .0/ 0 V7}+IW/Lt#8V7>@G95j /: D34=9n.V7Gk/:21 6 IWS>A F"/8R{I 13 /8V7IW9S[{D347/.0Gkj8/D36 IW>A\|/}+ /D ?'Blh# RVX>A+ GkDW1c6 4=Z9jj8V7/D331 >AGV)! V7Gy13F"AA?Aj8ZkD36]?'l / % # 0 7 I + % # 4 0 R{>'D9nV)?A?AVdBCID3.k4=CD # +.- +>%Û % # 4*0 Û 0 # +.- j54=Gyz{/ 6/13>@\)/56X9 13D V)< D5 S b , !"4 9 G g:V731 $ #+ V731 * # +X 0V=1/8\|/81Wlp47j8D3>AV7G + FFuSvw8R06/8`0G0/D3./9V7?A?@V5BC>AG0io>AGk6]/8aXIW/8D3_I 9
¯
¯
¯
¯
K
G
%c
#
c # #
! 0 cc $ c (c
#
B!:EFHG B < F>K B ;F B F B F B F
6 7 8# 8&
D+ % # + I D 40 # + I % D% # + I 0 D+0 # + I D+ b # + I D4b # + I -
" ! "$ %(
=4 Gk6 Q V=D3/SD3.04=D5R=6]Z0/D3V+D3.0/13/ImDW13>Aj8D3>AV)GIV)G DW1c47j8/GV713Û=< A %f'*)?> A% @
+ - +
C/ '
#
-
¬\
/ A
' 3>
CB A> ' > % E D
/ A %f'*) ) A
/
qmO)|x
0 ,L]>AO)A?@4=B13/ ?'lhj5R47>A9,GyA\|// %G D3! ./ c /!#NhZk+X4dD3>@V7, G .tZ0IR047i|4=>AGyZ0IW>AG0io4da>AV7] 7 O 47G06 #
c
w q
'
x
: Û:A
+ - +
> 0D
0!'^2
' >
B > ' > 0 D
/ A 0!'^2 2 A
/
qmO7Odx , L]>A.0G/8jGL/i Rl]>'>AD/?@9n6V)I ?A?AVdBCI D3.04=D w 3q( x8# w 3q x >'a 4=G + F w 3q(x % ,x / ' 3> / %('*) B ) > ' > % + Û q %f'*)?> 0 ,x / ' > / 01'32 B 27> ' > 0 + Ûq 0!'^2 > D D5 /!IWL]>@Nh>A6GZk/ j4=/ .0?A>A47D~GlIC.0IW>A47I&/g IWG0V7>AV1 /C$i=Im13DW/513#14=>Aj8D3D3/+¡?'1lD3V7IW.01'DY/Y9nD3V)/8?A?AEF13V5< BCV713IV7/GXzhVd\|lXD3/8.>@15G0/R)6D3?A/8Z.09nj8/ DWD3b#D3>A.0V)/84713GpGk@D+6D3/B.0/ V7/ 913j5D3>A47i7.0Gy.t/ DW6]b#4=.0/8z{1347Vd>AGk\|\|6// qmO5g)x % ,x / ' > / %('*) B )A> ' > % # + Û q %f'*) > 0 ,x / / 0 + Ûq 0!'^2 > ' > 01'32 B 2 > ' > 9n>AI+13V7/< '9>A47GkGk4762?A?'lhV7RdG0IW?'>AloG0j>'9E/ IW V:e>@Iq g 0!>'9k'^4=2Gk56 0 V)xSGg ?'l .F>'9 &~9e z{V7 D3Rd.X>AD j9V)V7?A?@?A?A/V5j8BCD3>AIV7D3G0.kIC4d4=D13q/g G0%f'3V))G] b#/% AAI[[?@/13VdD3\)/84=13z0< ?'lp13/8/!B+NhZk13>'47D3? >@GD3iV 4}D3/813< BC.0>Ajc.->AIC/>'D3.0/81b 9n13/8/)RkV=1V=9D3.0/9V713< LtZ0[[{V)IW/ D3.k4dD&D B VD3/813A\747?A/GhD5 T/C6>AImD3>AG0i7Z0>AIW.KD BV j547IW/8I b , ! 9 S, ./G-j?A/54d13?AlF47?AIWV R0IWV b 9n13/8 ,/ ! 47Gk 6U9S?@47Gi)>AI2Zk4=i)b /9 13//!/)NhUZ0>A, \747.?A//GGhD5j8R?@>A/Do4=13>A?'Iol G0 V=D2>AI2.k4d471c?A6_IWVTD3Vb 9nIW13///F/)UD3.kL]4dD2>AG0jD3.0S/ /8 l_4d4=13Gk/y6 47 ?AIWVT4d13DW/-1c4=j/ b 9n!/ 13NhV7Z0< >A\747 ?A&/GhRD5BCo.Lt>AjV.-R >A47ICjj8>AG0V7j1c?A6Z0>A6G/5iF6XD3V->@>G , . AV)G # j47GTz{/K6/813>A\|/56 gt Q V7D3/D3.04=D5R]9V=1/8\|/81WSl F-, q r+J+J+L s Û q;uvcw3xWxR]D3.0/9nV)?A?AVdBC>AGip.V)?@6_I 9 (* @> ? / >A, p
uxqtzxyr, ¢
v%:uxzxz:}^
vy>s ¬Ó
uxysv
p
zxz(6uxw,ykwtPs
u+rq,^rsvw6, s
:u¡sq]rq,q6*su{°\qsvuxw,ywtPs
¥
v\vvux, Iw¤7w, A@ B "Ò*r1 585; (tË,Ër ª 82® % NO LP Q I C m Rl fXi `+l m i!f fX = b b g mSR f -b mdr©qsvrqsux7µvux#Ð ¥ Ñ7w:yRqtyrT 8r +> :´s\
Ò ¤Ï¤rqt
q,y@qtyr É+q,z{z· 1w6yrw,yM y
u{sv\@Öuxy
6w6k ¬\Ë>Ô¬6 ªÕÔ\® 3 - ` +klnm g mmTH fXg b X¨f l f! b fXg b10 fXg b XXi k i m ! b g m i!fXg b X ,ÌÍyZ §3vw \v 1ssx 6~ЬË,Ë,Ó>Ò
1rÊ6Ê,Ê Ê,ÊÔ ª ¶® %K #" %$ $ & J6m l¥b m fXi4g b hmU ifX 5b 6g b m4d©k(m gji R m\u{y§3vw
u{y
> +Ï wtsv \¢Ï u{}y¥Ï¤w65Ë ;
Krp¨sv+svµ ux
q,yrk,V ^8
µP
vѢuxy
qt6svvyWÀ 6PqtvyrzT qt^8r^P¬\Ë,ÖÅË z{;rw61
P1^r>xÔP¶ ,
w6tz Ë Ô-Ó ,¶wtM*sp
ª Ë® ¡ `¿ kZlªm g m f ! b fXg b10 ftg b tVti i!ft 5b 6 bedb Rl ftg b t X6ti m m > b g m d g¢fXg m m ft b i d*~uxy ©qtsv
qsvuq,z]
w6p
yr
qtsvuxw,yrw,Ϥw,e
p
sv@µ
uxyr ¬\Ë,Ë,Êr+¿
qty^¦V+§u·:rx+6w,z·¢Ô¬6¬ w,6M*sp
_ w,sv~u{yϤw6e
psv%µu{yr 6+µ
u{y
6vWÀ 6Pvzqt^+¬\Ë,Ë,Êr¤r13ÓÔÊ Ó6¶,Ór ¨+Dq,u{zqt}rz{}|~qtyrw,y|w6pr¤²svkw,Z Y&[[ \ fXg b Xa k fXif llªml6k i!Åi!f d*
Ϥw6e>¨+Ï¢©I¬Ë]ЬË>Ô586Ò
MrÊ>Ô¬ Ê6¶tÓ^ ª{¬,¬ ® M; "< C+m¢k i mdm g¢fXg b X " m m g d>b m i m m g d fX > b g m f g¢ fXg¢f ¢uxy ¨+psvw6eqtsqµ>sprux3ÏÓ^¬, ª{¬\D ® NO 8 ` b g m i!f g b mk i g¢ l Xi k i! mdd f l m i!f d*Muxy´Ëtsv¨y
yprq,zKµ|IwtÀ vu{pr w6y]¢
w6vsvuqtz^¨+v^\*s3wt(Ϥw,e
p
sv¢µ uxy^ ,>,w6z - 6Ô,Ôw, 1 svp
} +wtsv\Kuxy Ϥw6rpsv+µ uxyr,IÏ7q6rqtyMrq,yr 6F¬Ê I¬
}11¬Ë6Ë6
µ
vuxy
6\
1,8r¬DÔ 8
¬\¶
23 4 XfXg b X
' ( %)5* ",+ -.' %* 4/ 0` m fXg b X¨f l f ! b fXg b10 ftg b t|">5 dm i
t-Åi m m Xi k i m ¨Ä
%
&
&
%
%
!
%
%
&
¬
ª{¬Ê® HG ",% / +` +klnm g m°b m i m m£d d g m Xi°f l f dd £i m Rl fXi m fX b i d* 8r^Ϥw,e
ps\^µ|sv µ u·x^t¶ÐZ¬\Ë,¶tÓÒ*
M
Ó6Ê6Ë >Ó 8 8r ª{¬Ót® ' bL ftg b t|fX t ii m 7§Ky>svu À¯Éqtzxz3ÌÍy>svvy^qsvuxw,y^qtz·KnKy
6z{À 7ww¤Ï zxu¡±FM¬Ë,¶6Ë
ª{¬ D® J6m k l Åf XbL f lªRl¥6d
f'g g¢Xi b f l 6uxy%§3vw
u{y
>3©q,v¦>svw6}^
w,vFµprmÀ e~µ
ww,zÎ Ër¬,$1w,6uxqty^ ¨+z{6}
q´wtµ^\ u{ ^qtsvuxw,y1 +¨P ¨µÌµuxr1^t;6Ê
Ó 8r ª{¬ 8® O /4 X ii m fX f g¢ fXg¢f X b > b g mdmTH m md*KuxyV ¿"ÌeϤw,y
À vyr 6¢Ö q,vzvvp
r,7¿"vq,y>|67§
