HAL Id: inria-00071609
https://hal.inria.fr/inria-00071609
Submitted on 23 May 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,
Reachability Analysis over Term Rewriting Systems
Guillaume Feuillade, Thomas Genet, Valérie Viet Triem Tong
To cite this version:
Guillaume Feuillade, Thomas Genet, Valérie Viet Triem Tong. Reachability Analysis over Term Rewriting Systems. [Research Report] RR-4970, INRIA. 2003. �inria-00071609�
ISRN INRIA/RR--4970--FR+ENG
a p p o r t
d e r e c h e r c h e
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
Reachability Analysis over Term Rewriting Systems
Guillaume Feuillade , Thomas Genet , Valérie Viet Triem Tong
N˚4970
23 Octobre 2003
THÈMES 1 et 2
" ! $# !%& ' (*)+,'#-
.0/1324265/798 :$8;/1324245=<8?>[email protected]>MN5=23O;PQ138MR138JKS@TPQ138;7U@TBDIV
W!XZY[+\^]`_`\acbNdfeg^]h\^ikjmlG\aT]hno]paqY[+\^]rd*stgumvw\yxwz|{|v~}vw\x
\aT}ikx~}jZx]n[N=z|xwv~JjZ\
qzkp\aco\aTi|uZo\
ei|mzJ aTm\t q\^}XZ\ }Xm\uN|J;kdUbkSt}aqz|m q\ybk|JydUJZik{J\^]
GC^m|| W!Xmv~]ik=\ ']hjm q |\^n]']zJ[+\$ah\Q}Xmumv~JjZ\^]CikuZ`aqzz|x~]¡¢zJ 'i|}XZv£\^ ;vwum{ q\^iJ}XZikZv£xwv¤apntikuZi|x£no]hvw]
z J\ ah\ q[¥ q\¦ qv¤aqv£um{`]hn]ah\^[]§CW!Xm\¨}z| q\©z|¡mahXmz;]\ªah\Q}Xmumv~;jm\^]Cv~]Cic{|\^um\ qv~}$ah q\\!ikjmahz|[ikaqit}z|[+mxw\«
aqv£zJuGikxw{|zJ hv£ahXZ[¬j]\Q+ahz+}zJ[Zjoah\cv£uikuG\lmi|}a¨z| ¨ikmm qzlov£[ikah\^+¦!inahXm\`]h\aªz|¡'o\Q]h}\uZmi|u;aq]t®¢z|
q\^iJ}XZikZx£\cah\^ h[]¯§ªW!XZvw]cikxw{|z| qv£ahXm[°Xi|]!=\\u0vw[+mxw\[+\u;ah\QRv£uaqXm\NW!vw[Nmjm±Gahzz|x4§ª²Zjm hahXm\^ h[+z| q\|³
¦¨\]XZz¦´ahXZika©}x~i|]q]\Q]C¦v¤aqX q\{Jjmx~ik ]\aq]$z|¡=o\Q]h}\uZmi|u;aq]Czk¡=ahXm\xwv£ah\ iaqjm q\¨}z| q h\Q]=z|uZZ]aqzy]=\^}v¤µ}
vwuZ]aqi|uZ}\Q]Tz|¡$ahXm\ah q\\ikjoaqz|[iaiS}zJ[Zx£\ahvwz|uLi|x£{Jz| qv¤aqXm[i|uZH}^iku0aqX;j]c=\N\¶S}vw\u;ahxwnH}zJ[Zjoah\Q
nNW!vw[NZjm±D§C·Tu\l;aq\uZ]hvwz|uzk¡ZaqXm\}zJ[Zx£\ahvwz|u+ikxw{|z| qv£ahXm[¸aqz`}z|uZmv¤aqv£zJuZikx;ah\^ h[¹ h\^¦ hv£ahvwum{`]no]ah\[]
i|uZ]zJ[\yi|mmxwvw}^iahvwz|u]ik q\ti|xw]hz+m h\Q]\^u;ah\^§
º0»;¼D½q¾N¿ ÀC| W'\ q[e\¦ qv¤aqv£um{Sno]ah\^[+]^³me\Qi|}XZi|mv£xwv£apn|³mW' h\^\`·TjoahzJ[iaqi
Á~Â,ÃhÄ6Å^Æ!ÃÇCÈwÄ6É4ÊË
Unité de recherche INRIA Rennes
\a'i| aqvw}x£\ q\{| qz|jZ\jmuy\^uZ]\^[Nmxw\o\aq\^}Xmumv~;jm\^]o\^]ahvwumg\Q]!xi|uZikxwno]\iahah\^v£{JuZikmvwxwv¤aqg
]hjm !xw\^]!]no]ahY^[\Q]!o\c qggQ} qv¤aqjm q\|§iNah\^}XZumvw;jm\`m qvwuZ}vwZikxw\T\Q]pajmuRikxw{|zJ hv£ahXZ[\c{|g^umg qvw;jm\to\y}zJ[«
Zx£gahvwz|uo\Q]'i|joahzJ[+ikah\Q]ik qm h\;jmv;=\ q[\aCo\ª}ikx~}jZx£\^ 'o\$¡izJuy\lmi|}ah\zJjikmm qzo}Xmg\$x\uZ]h\[mx£\
m\^]Tm\^]q}\umiku;aq]®¢zJj0ah\^ h[+\^]ci|}^}\^]q]hv£mxw\^]¯§ \ati|x£{Jz| qv¤aqXm[+\y\^]acvw[+mxwi|u;ahgZikuZ]Txz|joaqv£xW!vw[Nmjm±D§
Tz|jZ]¨[+z|u;aq hzJuZ]¨g{Ji|x£\^[+\u;a!;jm\`xw\^]}xwiJ]h]h\^]¨inJi|uJa!o\^]!\^uZ]h\[NZx£\Q]¨m\`m\^]q}\umiku;aq]! qg{Jjmxwv£\^ q]^³;;jm\
xz|uEah qz|jm J\0mikuZ]Sxwi xwv¤ahahg^ qikahjm q\|³!}zJ h q\^]hzJuZo\^uJa´o\Q]vwuZ]paikuZ}\^]S]h=g^}v£µ;jm\Q]So\0xi|x£{Jz| qv¤aqXm[+\
m\G}zJ[Zx£gahvwz|u ikjmahz|[ikah\^]^§u }z|uZ]hg^;jm\^uZ}\J³C}\^]}x~i|]q]\Q]y hg^{|jmxwvwY q\^]y=\jm J\u;a! ah q\G}i|xw}jmxwg\^]
m\y¡i"z|uH\¶}^i|}\yZik tW!v£[mjm±D§#zJjZ]Z hzJz;]zJuZ]g{;ikxw\[+\u;aTjZum\N\l;aq\uZ]hvwz|uHo\xikxw{|z| qv£ahXm[+\No\
}z|[+mxwgaqv£zJui|j}^i|]o\Q]]no]ahY[+\Q]o\y hg^g^} hv£ahjm q\`}z|uov¤aqv£zJumum\^xw]i|v£uZ]hv;jm\o\Q]ikmmxwv~}iaqv£zJuZ]^§
$¹¿ Q ½ "% on]ahY^[+\^]o\y qggQ} qv¤aqjm h\J³o·¨aah\^v£{JuZikZv£xwv¤aqg|³Z·TjoahzJ[iah\Q]ik qm h\Q]
-D C
stvw |\^uiGah\^ h[ q\¦ qv¤aqv£uZ{ ]hn]ah\^[/. i|uZHap¦¨zG{J hzJjmuZRaq\ q[]10SikuZ32³,¦ª\¡¢zo}jZ]`zJuLm qz v£um{ikjo«
aqz|[iaqvw}^ikxwx£n ahXia405769892zJ 10;:5+6<892§yW!Xmv~]Tm qz|Zx£\^[Xi|]t]\^ |\ ikxCikmZx£v~}ikahvwz|uZ]Tv£u\^;jZiaqv£zJuZikx
Z hzzk¡]cjZ]h\^Lv£uLahXm\^z| q\[m qz ;vwum{ z| tv£um hzz|¡©i|]q]v~]paiku;aq]ti|]c¦¨\xwxiJ]TvwuL J\ qv¤µ=}iaqv£zJuH¦Xm\^ h\Nah\ q[
q\¦ qv£ahvwum{0]no]ah\[]y}^iku?\Sj]\QLaqzR[zoo\^xm qz|{J qi|[+]^§W!Xm\ q\^i|}Xikmvwx£v£apn0m qz|mxw\[ vw]y±umz¦uahz
=\+o\^}vwmi|mxw\N¡¢zJ `W'\ q[ e\^¦ hv£ahvwum{0no]paq\[]+®WeT0¡¢z| y]XZz| ha¯T¦Xmvw}X?ik q\aq\ q[vwuZikahvwum{Z§4=Tz¦ª\^ J«
\^ ^³©v£uEikjoaqz|[iaq\^ m\^ojZ}ahvwz|uEikuZ v£uE |\^ hv£µ}ikahvwz|u³]hno]paq\[]}z|u]v~o\ q\^ v£uEm i|}aqvw}\ i| h\ qi| h\^x£n
aq\ q[+v£uZikahvwum{0ikuZ³\ J\u?¦Xm\u?aqXm\n?ik q\|³i|joahzJ[+ikahv~}i|x£xwn0m qz ;vwum{ahXZ\vw `ah\ q[+v£uiahvwz|u v~]yov£¶}jmx£a^§
cu ahXm\0z|ahXm\^ +XZikuZ³© q\^i|}Xikmvwx£v£apn´v~]±umz¦u9ahz?=\Ho\^}vwmi|mxw\ zJuE]h\ J\ ikx!]nu;aqiJ}ahv~}}x~i|]q]\Q]z|¡
aq\ q[ q\¦ qv¤aqv£uZ{R]hno]paq\[]®¢uZzkaum\Q}\^]q]qik qv£xwnRah\^ h[+vwuZiaqv£um{0uZz| }zJu?>Zjm\^u;a¯§RcuaqXmzJ]h\S}x~i|]q]h\^]^³,ahXm\
aq\^}XmuZvw;jm\j]\QahzSm qz |\y q\^iJ}XZikZv£xwv¤apnGvw]T qikahXm\^ TovA@=\^ h\^uJa`ikuZRv~]i|]h\^Rz|uRaqXm\N}z|[+mjoaiahvwz|u0z|¡
aqXm\G]h\a<.CB?DFEG`zk¡H.«6m\^]q}\umiku;aq]G®¢z| 4.«4 q\^iJ}XZikmxw\ah\^ h[]¯tzk¡iku vwumv¤aqvwi|xª]h\az|¡¨aq\ q[]4E§R²mz|
aqXmzJ]h\ }xwiJ]h]h\^]^³I.CB?DFEJGNvw]+iL h\^{|jmx~ik yaq h\^\ x~ikuZ{|jZi|{|\Gi|uZ }i|u´ahXjZ]=\ q\Z h\Q]\^uJaq\^ jZ]hvwum{iKLM
N?,$O,Z§$W' h\^\ti|joahzJ[+ikaqiNz@D\ !iµZuZv¤aq\t¦!inahz h\^m q\^]h\u;aªvwuoµZumv£ah\® h\^{|jmx~ik ¯]h\a]ªz|¡ q\^i|}Xikmxw\
aq\ q[]!¦Xm\u0iumz|u ah\^ h[+vwuZiaqv£uZ{aq\ q[ q\¦ qv¤aqv£uZ{]hno]paq\[ v~]!jmuZm\ T}z|uZ}\ qu§
P u`aqXmvw]'Zi|\^ ^³Qz|jm 'ikvw[ v~],aqzm qz|=zJ]h\i}z|[+[+z|u³Q]hv£[+mxw\|³\¶}v£\^u;a'ikuZ`vw[+mxw\[+\u;ah\Qikxw{|zJ hv£ahXm«
[¡¢z| $}zJ[Zjoahvwum{`±umz¦um\^}v~mi|mx£\¨ q\{|jZxwi| C}xwiJ]h]h\^]i|]C¦¨\xwxmi|]'ahzy}z|uZ]ah qjZ}a]hz|[+\!ikmm qzlov£[ikahvwz|u
¦XZ\uGv£avw]¨umz|a!m\^}v~mi|mx£\J§$W!Xmvw]!i|x£{Jz| qv¤aqXm[ vw]¨\^]q]h\u;ahv~ikxwx£niQR$TSUALFzk¡'i7LM4N?,$O,k³ahXjZ]
aik±vwum{i|o iku;aik{|\tzk¡$iku0i|x£{Jz| qv¤aqXm[ ]hv£[+vwxwi| !ahzahXm\V`u;jmahXo«XW¨\uZov£lY$ZS[ F]\bk^v£uRzJ qo\^ umzka
aqz q\^]ah qv~}a¨ahz+i]h=\^}v£µ}t]nu;aqiJ}aqvw}t}x~i|]q]¨zk¡aq\ q[° h\^¦ hv£ahvwum{]no]ah\[]!iku]MJN?X$+Xcv£u z| o\
aqzHo\^i|x\¶S}v£\^uJaqx£n¦v¤aqX´v£umµZumv£ah\G]h\a]zk¡! q\^i|}Xikmxw\Naq\ q[]m qzoojZ}\Q?;numz|um«3aq\ q[vwuZikahvwum{ah\ q[
q\¦ qv£ahvwum{]hno]paq\[]^§
W!Xmv~]`ikxw{|zJ hv£ahXm[v~]tv£[+mxw\[+\u;aq\^v£uahXm\O_a`cb4d)e)fNahzzJxH\w_^4§J=Tz¦ª\^ |\^ ^³Di|]c¦ª\¦vwx£x$]h\\v£uahXm\
¡¢zJx£xwz¦vwum{Z³Jz|jm ªv£[+mxw\[+\u;aiahvwz|uSmz;\Q]©uZzkaª}z |\ 9 co\^}vwmi|mxw\T}x~i|]q]©]hv£u}\aqXmvw]ª¦¨z|jmx~+XZi |\Tx£\Q
aqzGiku0vwum\¶}v£\^u;aTahzzJx3§T·c]ci|u0\lmik[+mxw\|³Z¡¢z| `o\^i|x£vwum{¦v£ahXHuZz|uHxw\¡ah«4xwv£uZ\^ik tWeTo]^³zJum\N}^iku0 q\µZum\
aqXm\i|x£{Jz| qv¤aqXm[ ¦¨\LZ hzJz;]\0nrikmZx£nvwum{ o\ah\ q[+v£uZvw]qiaqv£zJu i¡ah\^ G\Qi|}X ]ah\ zk¡yah q\\ikjoaqz|[iai
}z|[+mxw\aqv£zJu§gPu+aqXmv~]$¦¨inJ³|zJum\[inz|oaikvwuiy[+z| q\¨{J\um\^ qi|xahXm\^z| q\[¬}z |\^ hvwum{cahXm\Tumz|u+xw\¡a«6xwv£um\Qik
}^i|]h\N¦v£ahXmzJjoay h\Q]paq hv~}aqv£zJu§<=z¦¨\ J\ Q³D]hvwuZ}\+o\aq\ q[+v£umv~]qiahvwz|uLvw]`iku\lo=z|um\^uJaqvwi|x¤«4ahvw[+\zJ\^ qikahvwz|u³
aqXmv~]N¦¨z|jmx~ umz|a=\ q\^i|x£v~]paqvw}Sv£u Z qiJ}ahv~}\J§LW!XjZ]^³C¦¨\ }XZz;z;]\SahzL]ahv~}±?ahzHaqXm\Gi|]hvw}S}z|[+mxw\aqv£zJu
i|x£{Jz| qv¤aqXm[ikuZL{|vw |\N]hz|[+\}z|uZmv¤aqv£zJuZ]c]hjo¶S}vw\u;at¡¢z| `}z J\ qv£um{+aqXm\umz|ux£\¡a«6x£vwum\^i| t}^i|]h\NvwuL[ikun
Z qiJ}ahv~}i|x,}i|]h\^]^§
W!Xm\GZik=\ vw]yzJ h{;ikumv[h\Q i|]`¡¢zJx£xwz¦]§QPu ]h\^}aqv£zJu _S¦ª\ q\^}^ikxwx$ahXZ\SZi|]hv~}umzkaiaqv£zJuZ]`¡¢z| ah\ q[
q\¦ qv£ahvwum{]no]ah\^[+]ªikuZaq h\^\ci|joahzJ[+ikaqiZ§'W!Xm\^u³v£uS]h\^}ahvwz|uGb`¦¨\T q\^}^ikxwxoahXm\c±umz¦u h\^{|jmx~ik }xwiJ]h]h\^]
¡¢zJ To\Q]h}\uZmi|u;aq]^§¨\Q}ahvwz|u0+m q\^]h\u;a]!ahXm\ah q\\ikjmahz|[ikaqi+}zJ[Zx£\ahvwz|uHikxw{|zJ hv£ahXZ[ ikuZ aqXm\ q\^]hjmx¤a
¡¢zJ z J\ h«6i|mm qzlov£[iaqv£zJuLz|¡i.CB)DLEJGy¡¢zJ i|un?WeTj. iku ikun?v£umv£ahv~ikx! q\{Jjmxwi| x~ikum{JjZik{J\7E§YPu
]h\^}ahvwz|u?0¦ª\+{Jv£ J\+]hz|[+\S]hjo¶S}vw\u;aN}zJuZov£ahvwz|uZ]t¡¢zJ yahXZ\+ah q\\Sikjmahz|[ikaqi}z|[+mxw\aqv£zJu?ahzH}zJ[+mjoah\
\lmi|}aqx£nQ.CB?DFEG¡¢zJ `i|unRWeck. i|uZLi|unvwumv£ahv~ikx q\{|jZxwi| cx~ikum{JjZik{J\JE§<P uLahXmv~]y]\Q}aqv£zJuH¦ª\+ikx~]hz
]hXmz¦ XZz¦ q\{|jZxwi| ¨}xwiJ]h]h\^]!z|¡ahXZ\yx£v£ah\^ qikahjm q\t}^iku\yzJoaqi|v£uZ\^ jZ]vwum{ah q\\yi|joahzJ[+ikaqi}zJ[Zx£\ahvwz|u§
W!XZ\u´vwu ]\Q}ahvwz|uKl0¦ª\{Jv£ J\S]zJ[\S¡¢z| q[+i|x©iku m qiJ}aqvw}^ikx$aqz;zJxw]y¡¢z| N{Jjmv~ov£uZ{0ahXm\ ikmm qzlov£[ikahvwz|u
}z|uZ]ah qjZ}ahvwz|ur¦Xm\^um.CB)DLEJGGvw] umzka h\^{|jmx~ik Q§nP u ]h\^}ahvwz|upom³c]zJ[\ikmmxwv~}iaqv£zJuZ]Sz|¡<.CB)DLEJG ik q\
Z h\Q]\^uJaq\^rq]hjo¶S}vw\u;a}z|[+mxw\aq\um\Q]h]^³$]paq hzJum{HumzJuo«3aq\ q[+v£uZikahvwz|u´m qzzk¡iku´ h\Qi|}XZi|mvwx£v£apnHaq\^]ahvwum{Z§
P u´]h\^}ahvwz|u ³¦¨\+m q\^]h\u;a`ahXm\Gi|x£{Jz| qv¤aqXm[+vw}z|mahvw[v~]qiahvwz|u?zk¡![ia}Xmv£uZ{vwu´ikjoaqz|[iaiv£uj_a`cb4d)e)f
i|uZ+]zJ[+\v£uZmvw}^iahvwz|u]$z|u+v£aq]$\¶}v£\^uZ}nJ§$²'vwuZi|x£xwn|³;iku+\lah\^uZ]hv£zJuz|¡aqXm\aq h\^\ikjoaqz|[iait}z|[+mxw\aqv£zJu
i|x£{Jz| qv¤aqXm[ ¡¢z| }z|uZmv¤aqv£zJuZikxDaq\ q[ q\¦ qv¤aqv£um{+]hn]ah\^[]!vw]{Jv£ J\u v£u0]h\^}aqv£zJuZ§
y $#-?R +( C
zJ[+m h\^Xm\u]vw |\`]jZ h J\no]}i|u=\`¡¢z|jZuZRv£u \m³_^¡¢z| ah\ q[ q\¦ qv£ahvwum{]no]ah\[]^³mvwuY\lo³_ ^'¡¢z| !ah q\\
i|joahzJ[iaqiikuGaq h\^\`xwi|um{|jZi|{|\cahXm\^z| qn|§
\a =\SiGµumv¤aq\S]\ayzk¡¨]hn[N=z|x~]³\^i|}X i|]q]hz}vwikah\Q0¦v¤aqX´iku ik qv¤apn0¡¢jZuZ}aqv£zJu³Ci|uZx£\a
=\SiR}zJjmu;aqikZx£\]h\azk¡! ik qvwi|mxw\^]^§7D CG`o\^umzkaq\^]`aqXm\S]h\azk¡ªah\^ h[]^³'iku7D+G`o\umz|ah\Q]`ahXm\
]h\a`zk¡ª{| qz|jmuZ0ah\ q[]®¢ah\^ h[]t¦v¤aqXmz|jmat ik qv~ikmxw\^]¯§yW!Xm\+]\atz|¡© ik qvwi|mxw\^]czk¡ªiSah\ q[/2v~]`o\umz|ah\Q
n"!#$?DF2 G§yW!Xm\mz|[ikvwuLiku0 qi|um{|\Nzk¡©iS[i|mmvwum{G¦vwx£xC=\o\^umzkaq\^0 q\^]h=\^}aqv£ J\xwn n%'&)( iku
.*+$§$· ]jm]paqv¤aqjoahvwz|u vw]!i[i|mmvwum{-,0¡¢ hzJ[.°v£u;aqz-CD/01CG³;¦XZvw}X}ikuGjmumv~JjZ\xwn\t\lah\^uZo\Q
aqzi|uG\uoz|[+z| qmXmv~]h[¬z|¡2CD/01CG§ P6a]¨mz|[ikvwu3%'&)( D/, G¨v~]465"798;:)5<, :
=
5>J§$· =zJ]hv£ahvwz|u@?G¡¢z|
iGah\^ h[/2cvw]`i ¦ªzJ qHz |\
N§W!XZ\\^[mapnH]\QJjZ\uZ}\-Am\umz|ah\^]caqXm\Naqz|o«6[+zJ]at=zJ]hv£ahvwz|u§NW!XZ\+]h\a B@&0)DF2 G¨zk¡'=zJ]hv£ahvwz|uZ]!z|¡iah\^ h[ 2©v~]vwuZojZ}ahvw |\xwnGo\µZum\Q nUq
C
B@&0)D2 G =
46AD>yv¤¡ 2E7"
C
B@&0)DGF D2IHJLKDKLKLM2NMG G =
46AD>EOP4DQ1K?P:SRUTVQWTV+i|uZ-?"7*B@&0)D2NX,G1>
P6¡Y?Z7VB@&0)D2 G³'aqXm\uj2L:[Rm\umz|ah\^]ahXm\ ]jmmah\ q[ z|¡i2`ikaN=zJ]hv¤aqv£zJu?9ikuZY2]\0]^_[Rm\umz|ah\^]ahXm\Sah\ q[
zJoaqi|v£uZ\^9;n9 h\^mx~i|}\^[+\u;azk¡tahXm\H]hjmoaq\ q[ 2L:[ iaS=zJ]hv£ahvwz|u`? ;n ahXm\Raq\ q[ 0J§ ²Zz| Gi|u;n ah\ q[
077D CG³¦ª\ªo\umz|ah\ª;naB@&0DbD0 G,ahXm\¨]\a'z|¡o¡¢jmuZ}aqv£zJuZikx;=zJ]hv¤aqv£zJuZ]vwu0J³v3§\|§c4I?"70B@&0 D0G:1? :
=
ATikuZ".*&J&2 DL0S:[ G7d*>N¦XZ\ q\<.*&J&2 D2Gco\uZzkah\Q]aqXm\]hn[N=z|x'ikaT=zJ]hv¤aqv£zJuPATvwu]2§
zJu; J\ ]\^x£nJ³o¦ª\
m\umz|ah\`neB@&0)f9DL0G¨ahXZ\]\a!z|¡C i| hv~ikmxw\tz;]v£ahvwz|uZ]!vwu]0J³mv3§\|§gB@&0)f1D0 G =
B@&0)DL0GhWB@&0 b D0G§
·ah\ q[ h\^¦ hv£ahvwum{S]hn]ah\^[ . v~]TiS]h\aczk¡iM&',N?A iI5j;³D¦Xm\^ h\ikk37l7D CG³miT:7dR³
i|uZ9!E?D/iGno!#?DG§·¥ q\¦ qv£ah\y qjmx£\'ig5p+v~]4AGqsrXy® h\Q]§1c( srX¯v£¡\Qi|}XR ik qvwi|mxw\
z|¡gi® h\Q]§ck¯zo}}jm ]z|umxwnGzJuZ}\J§ª·¸ qjmxw\vw]x£vwum\^i| v£¡v£aTv~]=zkahX0xw\¡atikuZ qv£{JXJah«4xwvwum\^i| ^§©·¹WeT7.
v~]xwvwum\^i| N®¢ q\^]h§¨x£\¡a«6x£vwum\^i| ^³ hvw{|X;ah«4xwv£uZ\^ik ¯ªv¤¡\^ |\^ hnS q\¦ qv£ah\y qjmx£\'iI5jz|¡ .v~]xwvwum\^i| N®¢ q\^]h§!x£\¡a«
xwvwum\^i| ^³= hvw{|X;ah«4xwv£uZ\^ik ¯§cW!Xm\WeT;. vwuZojZ}\iS q\¦ qv£ahvwum{S q\x~iahvwz|u 5 6¹zJu0ah\^ h[]c¦XmzJ]h\ q\ >Z\lov£ J\
aq qi|uZ]hv¤aqv£ J\}xwzJ]hjm h\`v~]To\^umzkaq\^Rn]5jB
6
§W!Xm\]\aTzk¡ .«o\^]q}\^uZmiku;a]zk¡i]h\aTz|¡{J hzJjmuZ ah\^ h[]E
v~]<. B DLEJG
= 4 27o"D+G*: t0P7pE ]^§aQ§ 0;5 B6
21>;§Pu\ \lah\^uZ?ahXZvw]umzkaiaqv£zJu ahzHaq\ q[]vwu´ahXm\
¡¢zJx£xwz¦vwum{¦¨inUq'.CB DL0G
=
.CB)DN40>G§u\Nm\umz|ah\n0vwxwOD."G¨aqXm\]h\az|¡Caq\ q[]vw h q\^oj}vwmx£\yn7.
i|uZ ;nC.yFDLEJGªahXZ\]\azk¡ .«6umzJ h[ikxD¡¢zJ h[]!z|¡IE³mv4§\|§ .yFDFEJG
=
.CB DFEJG{zvwxwD."G§
\ae|=\iSµZumv£ah\+]\aczk¡©]hn[N=z|x~]³D¦v£ahXLi| hv£apn9}m³,}i|x£xw\^ XX§7D~O|9Gv~]`}i|x£xw\^aqXm\]h\a
z|¡DI(N?RF§t· M LFGv~]ciG h\^¦ hv£ah\ qjmxw\'<5³D¦Xm\ q\''7`CDOd|9GTi|uZP*7|N§t·
U$+_ 1kM LF v~]ciGah iku]v£ahvwz|ul45¦Xm\ q\'
=
JW7o|¹z| x
= F DG6HJLKLKDK{IDMG³F7` ³
?DGFrG
=
+$³Tiku
H
LKDKLKI
M
7|§&· z|aaqz|[«4jZ umzJuo«6m\ah\^ h[+vwumv~]paqvw}HµZumv£ah\ah q\\i|joahzJ[iahzJu
®¢ah q\\0ikjmahz|[ikahz|u ¡¢z| S]hXmz| ha¯v~]i Jji|o qjmmxw\"
=
0)|)|a ³ª¦Xm\^ h\|Zj|ikuV vw]
i9]\az|¡NumzJ h[ikxwv[h\^rah ikuZ]hv¤aqv£zJuZ]^§°· aq h\^\?i|joahzJ[+ikahzJu vw] X $ Fv¤¡NahXm\^ h\ ik q\Lumz9ap¦¨z
qjmxw\^]¦v£ahXEahXm\0]qik[+\x£\¡a«6XZikuZE]hvwo\J§EW!XZ\ q\¦ qv£ahvwum{ q\x~iaqv£zJu vwuZojZ}\^9n´ahXm\aq qi|uZ]v£ahvwz|u]z|¡
U®aqXm\´]\a"+¯ v~]m\umz|ah\^ n 5c§ W!Xm\?ah q\\?x~ikum{JjZik{J\H h\Q}zJ{|umv[h\Qrn i9]aqikah\` vwu vw]
D/3 G
= 4 2c797D/OG:2 5 B >J§W!Xm\x~ikuZ{|jZi|{|\! h\Q}zJ{|umv[h\QNn¸vw] D/G
=
D/eIG§·
aq h\^\x~ikum{JjZik{J\¨v~] q\{Jjmx~ik $v£¡ikuZ+zJumx£nv¤¡v£aª}^iku=\ h\Q}zJ{|umv[h\Qn+itah q\\Ti|joahzJ[iahzJu§ Wªnumz|aqiaqv£zJu
i|mjZ]h\|³o¦¨\`¦v£xwxzk¡aq\uRumz|ah\U@7" iku72 5;'79¬ q\^]h\Q}aqv£ J\xwn+¡¢z| '7|¸i|uZQ2'5p@7" §
,C ( G'N
W!XZ\LZiJ]v~}0 q\^i|}Xikmvwx£v£apn Z hzJmx£\^[ ¦¨\Li| h\H{Jz|vwum{´aqz }zJuZ]v~o\^ Gv~]SaqXm\H¡¢zJx£xwz¦v£uZ{ q?{|vw |\u i´ah\ q[
q\¦ qv£ahvwum{ ]hno]paq\[u. i|uZRap¦¨zSah\^ h[]<0+iku]2T}^ikuH¦¨\m\^}v~o\¦Xm\aqXm\ <0O5 B6
2zJ cuZzkamP uHahXZvw]
ik ha^³o¦¨\c¡¢zo}jZ]z|u ahXZ\y\lovw]ahvwum{]hz|xwjoahvwz|uZ]m\^]hv£{Jum\^G¡¢z| Zi| aqvw}jmx~ik }iJ]\Q]§
W!Xm\0]hv£[+mxw\^]a}i|]h\vw]¦Xm\^u . v~]ah\^ h[+vwuZiaqv£um{#qSaqz?o\Q}v~o\R¦Xm\aqXm\ C035 6 B
2Nz| umz|av£avw]
\^umz|jZ{|X ahz]\^\`v¤¡ 2E7Q.CB DL0G]hv£u}\9.CB)D0G!vw]¨µumv¤aq\ikuZR}z|[+mjoaikmxw\|§
urXm\^uj. v~]umz|aah\^ h[+vwuZiaqv£um{³$o\^}vwovwum{H q\^iJ}XZikZv£xwv¤apnLum\\Qm]]hz|[+\SiJmov£ahvwz|uZi|x¡¢z| q[ikx$aqzz|x~]³
uik[+\xwn+ah q\\`ikjoaqz|[iaim³vwu zJ qo\^ ¨ahzµZumv£ah\xwnS q\m q\^]h\u;a¨ahXm\`vwuoµZumv£ah\y]h\a .CB?DL0G¨ikuZSahXm\^u0}Xm\^}±+v£¡
27k.CB?DL0G§Hi|u;n ¦ªzJ h±o]i| h\yo\^ |zkaq\^ ahz+aqXm\N}z|uZ]ah qjZ}aqv£zJuRzk¡I.CB DLEJG¨¡¢zJ Ti+ h\^{|jmx~ik !x~ikum{JjZik{J\<E
i|uZiNaq\ q[ q\¦ qv¤aqv£uZ{]hno]paq\[ .¡¢jmx£µZxwx£vwum{S]hz|[+\` h\Q]paq hv~}aqv£zJuZ]q
C
.v~]\^v¤aqXm\ i{| qz|jZuZ Wec3\;³Z^4§
C i qv£{JX;a«6x£vwum\^i| i|uZr[+z|uZiJov~}LWeT \b^4³cv3§\|§ qv£{JX;a«6XZikuZr]hv~o\^] zk¡aqXm\? hjmxw\^]ik q\H\^v¤aqXm\
ik qvwi|mx£\Q]z| aq\ q[+]z|¡aqXm\!¡¢z| q[ F D/5 H LKLKDKk5 M GC¦Xm\ q\F"79¹i|uZ@5 H DKLKDKk5 M i| h\¨ ik qvwi|mx£\Q]§
C
ix£vwum\^i| ikuZ]\^[+v¤«6[+z|uZiJovw}tWeT \o^4³Zv3§\|§ qjmx£\Q]ik q\cxwvwum\^i| !i|uZGahXm\^v£ qv£{JX;a«6XZikuZ ]v~o\Q]ik q\
zk¡ªahXm\¡¢z| q[F D2 H LKDKLK 2 M Gc¦Xm\^ h\3F 7 ikuZ<Q
=
R$LKDKLKk+$³ 2 X v~]t\v£ahXm\^ yiG ik qv~ikmxw\zJ ti
{| qz|jmuSaq\ q[§
C
iho\^} h\Qi|]hv£uZ{!Weck\£_6^6³;¦XZ\ q\m\^} q\^iJ]vwum{![+\^i|uZ]$aqXZia¨\ J\ qn qv£{JX;a«6XZikuZ]hv~o\v~]©\^v¤aqXm\
i ik qvwi|mxw\|³mzJ i+ah\^ h[ F D2IH LKLKDK2NMG!¦XZ\ q\@F7" ³<$?DsFrG
=
+$³=ikuZ<Q
=
RDKLKLKI+$³ 2NX©vw]i
ik qvwi|mx£\J³oi{J hzJjmuZSah\ q[R³oz| iNah\^ h[°¦XZzJ]h\t i| hv~ikmxw\^]!ozumz|a!zo}^}jm vwuGaqXm\yxw\¡a«6XZi|uZ ]hv~o\|§
cuHahXm\zkaqXm\ cXZikuZ³¡¢zJ tiG{|vw |\^u0 h\^{|jmx~ik cxwi|um{|jZi|{|\4E³U. B DFEGv~]TuZzka`um\^}\^]q]hi| hvwx£n h\^{|jmx~ik Q³Z\^ |\^u
v£¡ .v~]i}z|u?>ZjZ\u;aikuZGah\^ h[+vwuZiaqv£um{xwv£um\Qik WeT3\w_ ^6§'P6¡ .vw]!uZzkam\^} q\^iJ]vwum{³|ahXm\^u".CB DFEG¨vw]
uZzkaum\^}\^]q]hi| hvwxwn h\^{|jmx~ik 1\w_D^6§
·TumzkaqXm\ h\^{|jmx~ik }x~i|]q]¦!i|]y¡¢zJjmuZ´n §Cegapn \b; ^!¦Xm\ q\G q\^]ah qvw}ahvwz|uZ]Nik q\S¦ª\Qik±J\ zJu´ahXm\
Wec ikuZ´]ah qz|um{J\ yzJuaqXm\G q\{Jjmx~ik yx~ikum{JjZik{J\OES§RW!XZ\GikxwmXZi|\a@ v~]]h\Zi| qikah\^?vwu;ahzLi0]h\aNz|¡
/ 1$O W%
=
4JFd:t i 5 '7Q. ]§a^§ .*&J&2 DGiLG
=
F2>`i|uZG}z|uZ]ah qjZ}ahz| ¨]n[zJxw]
=
Zhg%G§
W!XZ\ h\Q]paq hv~}aqv£zJuzJu+E¸vw]aqXm\¡¢zJx£xwz¦v£uZ{ qgE v~]$aqXm\T]h\azk¡,{J hzJjmuZ}z|u]paq hjZ}ahzJ $v£uZ]aqi|uZ}\Q]$zk¡i`xwv£uZ\^ik
aq\ q[ 2³ov3§\|§ E = 4 2N, >`¦Xm\ q\92E797D/01CGªvw]!xwv£uZ\^ik i|uZ*, 5;CD! G§$W!Xm\` q\^]ah qvw}ahvwz|uZ]ªz|u7.
i| h\cahXZ\`¡¢z|xwx£z¦vwum{ qC¡¢zJ \^i|}X qjmx£\Ui 5
_|§v~]!xwv£um\Qik
bo§¨¡¢z| t\^iJ}XHz;]v£ahvwz|u*?7B@&0DbD/Gc]hjZ}X0aqXZia :[ = F DF2IH)LKDKLKM2NMGTi|uZlF7l% ¦¨\XZi |\yaqXZia
¡¢z| i|x£x{Q
=
RWKDKLKN+$³ 2NXvw]i ik qvwi|mxw\tzJ i{| qz|jmuZSah\^ h[
m§¨ahXm\^ h\yv~]!umz+um\Q]paq\^ ¡¢jmuZ}ahvwz|u0]n[zJxw]!vwu9
" C G'N#-`'-¨N#R¨'
P uj\w_|_ ^4³¦ª\ym qz|=zJ]h\^RikMON?X$+XY$TSUA Fikxw{|zJ hv£ahXm[ ¡¢z| z J\ h«6i|mm qzlov£[iaqv£uZ{4.CB DFEJG
¡¢zJ xw\¡a«6xwv£um\Qik Daq\ q[ q\¦ qv¤aqv£uZ{!]hno]paq\[]i|uZ`i! h\^{|jmx~ik Dx~ikum{JjZik{J\ ES§'W!Xm\}z|[+mxw\ahvwz|u`v~]Zi| qi|[+\ah qv[h\^
nGi|ui|Z]ah i|}aqv£zJuS¡¢jmu}ahvwz|u [+i|mmvwum{ah\^ h[]¨ahzS]aqikah\Q]!zk¡aqXm\ikjmahz|[ikahz|u§
\aªj]$µZ ]pa¨ h\Q}i|x£xoaqXm\aq h\^\Tikjmahz|[ikaqi}z|[+mxw\ahvwz|uSi|x£{Jz| qv¤aqXm[R§aqik hahvwum{y¡¢ qz|[ i`aq h\^\Tikjoaqz|[i«
aqz|u
=
0)|)| )ªi|uZGiNx£\¡a«6x£vwum\Qik WeTC.H³ahXZ\ti|v£[&z|¡ahXm\yi|mm qzlvw[iaqv£zJuSikxw{|z| qv£ahXm[
v~]$aqz}zJ[Zjoah\Tiyah q\\ikjmahz|[ikahz|u3=]hjZ}XahXZika DGG#nK.CB D D/GG§·mZ hzlovw[+ikahvwz|uZ]$i| h\j]\Q
aqz?]hXmz¦ aqXZiaah\^ h[] h\Q}zJ{|umv[h\Q ;n iLah q\\ikjoaqz|[iaqz|uV Rik q\Gumz|a q\^iJ}XZikZx£\Sn´ q\¦ qv¤aqv£uZ{
aq\ q[]yzk¡ DGGy¦v£ahX .H³v3§\|§ 0"7 DGG 2-7 D/ G I0 57698+2§0²mz| NahXmv~]^³'v£av~]\^umz|jm{JX:
aqz]Xmz¦ ahXZika D/G z DG G
=
v4§\J§£³m}z|[+mjoaq\tahXm\i|joahzJ[+ikahzJuG q\^}zJ{|umv[hvwum{NahXm\yvwu;ah\ ]h\^}aqv£zJu
i|uZ]Xmz¦ ahXZikaahXm\y q\^}z|{JumvAh^\^Gxwi|um{|jZi|{|\cvw]\^[+oapn|§
W!Xm\aq\^}Xmumv~;jm\+}z|u]v~]pa]tv£u ]j}}\Q]h]hvw |\xwn0}zJ[Zjoahvwum{ ah q\\+ikjoaqz|[iai0 H ³J³gKLKLKy]hjZ}XHaqXZia
Q } DGX,Ge D/X2H GNi|uZ´v£¡907 D/XXG³]hjZ}X´aqXZiaC0]576 2`aqXm\u 2e7 DGX2H G³jmu;aqv£x
¦¨\N{J\ayikuLi|joahzJ[iahzJulS¦v¤aqX7
N ]j}XHahXia D/G
=
D/2H G§W!XjZ]^³v~]`iµmlo=z|vwuJa
i|uZikx~]zR |\^ hv£µZ\Q] D/ G'nn. B D DGGG§ 0z| q\Z h\Q}v~]\^x£nJ³ahz0}z|uZ]ah qjZ}aX2H¡¢ qz|[ X³'¦ª\
iJ}Xmvw\ |\i"R$TSUALF;,XS¦Xmv~}XG}zJuZ]hvw]aq]©v£uµuZovwum{QLFS =\ap¦¨\\^u"5j6 ikuZ"5 §$²mz|
i ]jZZ]paqv¤aqjoahvwz|u, < 5 | ikuZiS qjmxw\-i 57Y.H³iG} hv£ahv~}i|x'Zi|v£ tv~]ti|uHvwuZ]paikuZ}\-iG, zk¡Eiª]j}X
aqXZiacahXm\^ h\N\lovw]aq]ae7 | ]qiahv~]¡¢n;vwum{*iG, 5 B
ikuZ9J, :5jB
§T²Zz| a),´ahzG=\N q\^}z|{JumvAh^\^Ri|]ahXm\
]qik[+\`]paiaq\ikuZGahXjZ]![+zoo\xDaqXm\y q\¦ qv¤aqv£um{zk¡gi/,v£u;aqz-J,³mv£av~]!\umzJjm{|X ahztpz|vwu ahXm\} hv£ahv~}i|x,Zikvw q
! " #
$ %
!'&)(
%
i|uZ iJmraqXm\?um\¦ aq qi|uZ]hv¤aqv£zJuoJ,u5 ahzX2Hk§ =z¦¨\ |\^ ^³ahXm\ah ikuZ]hv£ahvwz|uoJ,u5 ´v~]umzka
uZ\^}\Q]h]qik qvwx£nyz|¡=aqXm\¡¢zJ h[ F D/6HJLKDKLKIDM G 5;JikuZ+]hzyXZi|]aqzy\Tumz| q[ikxwvAh^\^NµZ q]a^§²mzJ \lmi|[Zx£\J³kahz
uZz| q[+i|x£v[h\iaq qi|uZ]hv¤aqv£zJu0zk¡ahXm\¡¢z| q[ F D+*UDG G]-,gD/JG G 5 ³¦¨\yum\\QRahzSµZuZ0]hz|[+\N]aqiaq\^] H .$I./
i|uZ q\mx~i|}\ahXm\ m q\ v£zJjZ]yaq qi|uZ]hv¤aqv£zJu´;n iH]h\azk¡umzJ h[ikxwv[h\^?aq qi|uZ]hv¤aqv£zJuZ]q046j5 H 0*UDG H G5
1 2, DG G 5p./ 1F D/1 I1/ G 5p>J§
·c]h]hjm[+\`ahXZika H I1 I1/yik q\`um\¦¸]paiaq\^]^³ahXm\^uHi|movwum{ahXZ\`ah ikuZ]hv¤aqv£zJuRv¤a]\^x¤¡z| v£aq]uZz| q[+i|x£v[h\Q
¡¢zJ h[ oz\^]$umz|a[ik±|\i|u;novc@D\ q\u}\|§ z¦y³Ji|]q]jm[+\¨ahXiaE H =
1k³kaqXm\umzJ h[ikxwv[h\^N¡¢z| q[=\^}z|[+\^]
4)35 6HJ3*rD/6HG<5 6H)2, DGJ[G<5 / 1F D/6HJI / G<5 >J§SW!Xmv~]y]h\azk¡!umzJ h[ikxwv[h\^Lah iku]v£ahvwz|uZ]t q\m q\«
]h\u;a]`ahXm\ h\^{|jmx~ik ]h\azk¡umz|u´uZz| q[+i|x£v[h\QHaq qi|uZ]hv¤aqv£zJuZ]yzk¡!aqXm\S¡¢zJ h[;F D4* B)DG G]-,gD/JG G5 ¦Xmv~}X
}z|u;aqi|v£u]ahXZ\Naq qi|uZ]v£ahvwz|uL¦ª\¦¨i|u;ah\^0ahz iJmHvwumv£ahv~ikxwx£nRmjma`i|xw]hzG[ikunRzkaqXm\ ]^§9=T\uZ}\|³DahXZvw]tv~]ci|u
i|mm qzlov£[iaqv£zJu§lu?\R}z|jZxw´Xi |\G[iJo\ i|u \ J\u [+zJ h\o qiJ]paqvw} ikmZ hzlovw[+ikahvwz|u n´vwm\u;ahv£¡¢nv£um{
)H)
/
¦v£ahX"³o¡¢zJ v£uZ]aqi|uZ}\J§
²Zz| \^ |\ qnRah iku]v£ahvwz|u³ahXm\^ h\\lovw]aq]yi|u?\Q;jmv£ i|x£\^uJa]h\az|¡¨umzJ h[i|x£v[h\QHaq qi|uZ]v£ahvwz|u]§Tz| q[+i|x¤«
v[h^ikahvwz|uH}z|uZ]hvw]aq]Tv£u?o\^}z|[+=zJ]hv£um{ i+ah ikuZ]hv£ahvwz|u 0J5 ³Dvwu;ahz iG]\a65P&))( DL05 Gzk¡uZz| q[+i|x£v[h\Q
738:9<;>=:?A@0=ABC?A;>DEBC;>F
tHG
;>I>IKJL@
G
@0M2N@
t
@0O6;
t
BP9<@RQFI>I>F
G ; t<S<T
aq qi|uZ]hv¤aqv£zJuZ]§$W!Xm\y[+\ahXmzoR}zJuZ]v~]aq]!vwuRi|Z]ah i|}aqv£uZ{]hjmoaq\ q[+]T06,z|¡'0N]§a^§ 06 :7`|¸nG]aqikah\Q]!zk¡|§
u?\`µZ ]pao\µZum\`aqXm\ikZ]ah i|}ahvwz|uG¡¢jmuZ}aqv£zJu0i|]¨¡¢z|xwxwz¦]q
» ¿ F1 LM FqN?F g +7 Tkq4$+ R1i<9|/7 TNqJ,, L<
i|Z]ah i|}aqv£zJu3qN?LF $OS#J C$O_ Q6g(N?MF]X7+,,
4)F D/)H)DKLKLK LM G:FP70 DsFrG
= + <@6H)DKLKDKILM07|U>5 |
P uGahXm\c¡¢z|xwx£z¦vwum{³|¡¢zJ ¨}z|[+mxw\ah\QSikjmahz|[ikaqim³;¦¨\ci|]q]hjm[+\ahXiax| v~]ªi]\a¨z|¡]paiaq\^]¨}z|u;aikvwumv£uZ{
]aqikah\Q]!zk¡Cah ikuZ]hv¤aqv£zJuZ]°iJ]!¦ª\^x£xiJ]]paiah\Q]zk¡'ahXm\y ikuZ{|\`zk¡R©§ PuRZi| aqvw}jmx~ik Q³;v£¡CahXm\y ikum{J\cz|¡R vw]
vwuoµZuZv¤aq\S®¡¢z| vwuZ]aqi|uZ}\J³mv¤¡$}zJ[+mx£\ahvwz|uRoz\^]!umz|aah\^ h[+vwuZiaq\Q¯©ahXm\^u0]z+v~]@|§
» ¿ F1 LM F XX W R7Q kq$O <P| " 1Nq,, Le O
( M F-qN?LF <q IRDI(N?MLFC2#7"DO`|9G<J MF]XXJkq
21E UX17 <2N&1?gD2 G1 ' / 1C
4qi2#7`| "2N&1? D2 G = 21
4qi2
= F DF2
H
LKDKLKM2
M
G<72N&1?
D2 G =
aDsF D2N&1?
DF2
H
G]LKLKDK 2N&1?
DF2
M G GGD
» ¿ $+_ FqN?LF W Ck 9kq$+ 1a| Q kqXX a0+5
pKM F L[ 0o7 7D~O|9G <do7 |U7 n LRLFqN?U F !U3
5l&)6(gDL05pGJNqumz| q[ikxwvAh^\^aq qi|uZ]hv¤aqv£zJuZ]4<<N G 1"
4qZ0
=
5P&))( gDL015;G
=
4qZ0U7|u<0O:
=
5P&))( DL015;G
=
40Z5;>$a
! 4qZ0
= F D2 H LKDKLK2 M G 5P&))( DL095;G
=
4)F D2N&1?" DF2IH GDKLKDK{2N&1?" D2NM#GG 5;>EO
M X$# H
5P&))( DF2NXg5 2N&1? D2NX,GGD
%'& )( %»*+g
=
4)F<0*< m>Q @
=
0)|)| 1H&gM|
=
46.I)H) / <-, >$#| =
4)
> @
=
4)F DG
H G 5;
3*rD/
H
I
H G 5;
H
5;
H >
C
!U+A (N ( RRR(#_ ;
H
MOq A&' (. D/eI
H
GO kqJX $
N? P41*< m>'/D D/3
H G =
7D4.* Im>G1 DG3I
G = DGJG
=
4)F D/5G:)5P7 DG3I
H
G>S
C 0
= F D4*rD/ H F DG GMG G < H a LM FqN?U F'46 5; , F D/ , G5p./ 0*UDG H I./ G5
1J> J!UiU$+_ LF"NqHM FF D+*UDG H 1F D/?GGMG 5; &'O MLF H aq A&' (.
5l&)6(0/DGF D+*UDG6HJ F D/?GMGG 5;. G =
4)F DG G 5j $3*rD/6HJI / G 5p 1F D/1,G 5; / IO5;1,>S
» ¿32n q\{|jZxwi| xwi|um{|jZi|{|\y]hjmZ]ahv£ahjoaqv£zJu4 |@r,N LN?F+ N?,$O,"
&' Jkq+,, | QpRSSUFFV, c 5 |-5;p76 ,< / F ,
$+S $p, CD/01CG5 CD6|9GL85Ol UXY :99DI|@ 7G]] ONq;M,(N?A;[)(N ()
N LN?LF< N?i@| <@l
»
¿ i,XS;kqZN?X$+XkR$TSUALF g =
0)|)|
9<MN?,$O r
X . j!9* MF3qN?LF<;!U+,XS $ZSA,1kN?X$+X 6D/JG
JCLMN?X$+X
0)|)|
1N k
=
O
6
f
5P&))( D/J,35;G
» ¿ FN?X$+X $TSUA F g x jM N?,$O, 1. !9*n /
MF'qN?U F
C 6 =
C ML2H
6 = 6 D/
M
6
Gcq +7
N
C
<B
6 = M M
6
Tzkah\RaqXZia \ |\^u9v£¡<B
6
}ikuZumzka=\0µZumv£ah\^x£nE}z|[+mjmah\^ vwu {|\^um\ ikx4³©vwur[ikun }iJ]\Q]ahXm\^ h\
\lovw]aq]Si uZiaqjm qi|xH 7
N
]j}X9aqXZia
6
vw]Si´µmlozJv£u;a^³v4§\|§
6 DG
6 G =
6 § Pu ahXm\
¡¢zJx£xwz¦vwum{m qz|=zJ]hv¤aqv£zJu³;¦ª\t{|vw |\t]zJ[\t]jm¶}v£\^u;a¨}zJuZov£ahvwz|uZ]ª¡¢zJ ªmjZv£x~ovwum{i|uSz |\^ «ikZm hzlovw[iahvwz|u
i|joahzJ[iahzJu"!rz|¡'aqXm\]\azk¡I.«6o\Q]h}\uZZiku;aq]¨zk¡$i h\^{|jmx~ik !x~ikum{JjZik{J\c q\^}z|{JumvAh^\^G;n0§
»
¿#g N?X$+Xn k. !9*i. <d q AGqGrXU
<F q1
U2c7"CD+G t%$ $ 5;7D/OG]t i 5 -77. L[ ]2
=
i&$C5 B '
(
t ,7 99DI|@ CG ][;2 5 B ' i/,;5 B '
Tzkah\ªahXia¡¢z| C\ J\ qntxw\¡ah«4xwvwum\^i| Wec1.¹aq hvw vwi|x£xwny]hikahv~]p¡¢n`aqXm\¨x£\¡a«6x£vwum\^i| hv£apny}zJuZov£ahvwz|uN¦v£ahX+ikun
aq h\^\Nikjmahz|[ikahz|u§W!Xmvw]t}zJuZov£ahvwz|u0v~]³=vwu0¡i|}a^³Dum\^}\^]q]hi| hnS¡¢z| TuZz|uHxw\¡ah«4xwv£uZ\^ik tWeTD§Dez|jZ{|Xmxwn|³ahXm\
Z hzJmx£\^[ ¦v¤aqX umzJuGxw\¡ah«4xwv£uZ\^ik ! qjmxw\^]ªvw]ªahXZ\c¡¢zJx£xwz¦vwum{ qCx£\aF D/5I5G 5 *rD5UGª\`iN qjmxw\cz|¡ .i|uZSxw\a
=\Niaq h\^\Nikjoaqz|[iaqz|u¦XmzJ]h\]h\aTz|¡Caq qi|uZ]hv¤aqv£zJuZ]}zJuJaikvwuZ] F DG H H Ga5 i|uZPF D/1 I1/ G 5p §
·Tx¤aqXmz|jZ{|X¦ª\y}i|u }z|uZ]ah qjZ}ai ikxwvw]hjmZ]ahv£ahjoaqv£zJu,
=
465 5;6HJ>t¡¢z| [ia}Xmv£uZ{aqXm\` h\^¦ hv£ah\t qjmx£\
zJuahXm\`µZ ]aah ikuZ]hv¤aqv£zJu³mv£aTv~]umzkaaqXm\N}^i|]h\c¡¢zJ ahXZ\]\Q}z|u zJum\|§¨W!Xm\]h\[iku;ahv~}]!z|¡i}z|[+mxw\aqv£zJu
=\ap¦¨\\^u´ hjZx£\0F D/5I5GO5 *rD5Giku?ah ikuZ]hv¤aqv£zJuF D/ I / G5 .S¦ªzJjmx~ \GahzHµuZ ahXZ\ }zJ[+[zJu
x~ikuZ{|jZi|{|\Tz|¡ah\^ h[]! q\^}z|{|uZvAh^\^=zkaqX n* i|uZ* / §W!Xmv~]}i|uG=\`z|oaikvwum\^ nS}z|[+mjmahvwum{iNum\^¦
aq h\^\ i|joahzJ[+ikahzJu¨¦v¤aqXEi]\az|¡c]aqiaq\^]9| !]hjZ}X´aqXZiaP| ¨v~]+ovw]pz|vwu;a¡¢ qz|[ ]aqikah\^]zk¡ iku
t `7 | D/sIG
=
DG3I GYz DG3I / G§LW!Xm\^u³CahzL\^uZ aqXm\ }z|[+mxw\ahvwz|u ]ah\^´v¤a¦ªzJjmx~´\
\^umz|jZ{|X ahzi|m aq qi|uZ]v£ahvwz|u]ªz|¡g@Dahz3¬¦v¤aqXahXm\yum\^¦ aq qi|uZ]hv¤aqv£zJu *rD/G 5;.|§
cu+aqXm\zkaqXm\ ©XZikuZ³|z|uZ\T}i|u q\[i| h±yaqXZia©ahXm\uZz|uo«6x£vwum\Qik qv¤apnZ hzJmx£\^[ ¦¨z|jZxw+ov~]hi|m=\^ik $¦v£ahX
m\ah\^ h[+vwumv~]paqvw}cikjoaqz|[iai]vwuZ}\¡¢z| !ikun+o\aq\ q[vwumv~]paqvw}cikjoaqz|[iaqz|ue *),+ ikuZ¡¢zJ ¨i|x£x=]paiah\Q]ES JZz|¡
*) +¦ª\aq hvw vwi|x£xwnNXi |\ D/3 Gz DG3IJG
=
§'=z¦¨\ J\ Q³|o\ah\ q[+v£uZvAhQiahvwz|uz|¡i`ah q\\Ti|joahzJ[iahzJu
[inS q\^]hjmx£av£u0iku\lo=z|um\^u;ahv~ikx,mxwz¦!«4jZ z|¡ahXZ\yu;jZ[N=\ z|¡C]aqiaq\^]1\l^6§
· ]hz|xwjoaqv£zJu³kvwu\ap¦ª\^\uahXm\!ap¦¨zym q\ vwz|jZ]zJum\^]^³kv~]ahzyjZ]h\!ahXZ\4AGqGrXU<LFo\µZum\Q
i|z J\n\uZ]hjm qv£uZ{o\ah\ q[+v£uZvw]h[ ¡¢z| iN]hjmZ]h\a!zk¡C]paiah\Q]@7| ¦Xmvw}Xik q\aqz=\c[ikaq}Xm\QSn+ahXm\
uZz|uSxwv£uZ\^ik ª ik qvwi|mx£\Q]z|¡,ahXm\tumz|uxwvwum\^i| ª qjmxw\^]
§$²mzJ ©vwuZ]paikuZ}\|³z|u+aqXm\txwiJ]pa¨\lmik[+mxw\|³;v¤a!v~]©\^umz|jm{JX
aqzSmjmvwx~RahXm\NµZ ]pac} hv£ahv~}i|xZi|v£ Q³iJmRaqXm\yah iku]v£ahvwz|u *rD/ H Gi5 ³Diku0±|\^\P.I1/No\ah\ q[+v£uZvw]ahv~}k³
v4§\|§G]hjZ}XahXZika DG<B
6
I.Ggz D/<B
6
./ G =
§eu?\umz¦ m\µZum\+aqXmv~]N}zJuZov£ahvwz|u }i|x£xw\^ $TSUA
[/qsrXLS¦XZvw}X vw[+mxwv£\Q]aqXm\Gxw\¡ah«4xwv£uZ\^ik qv£apn?}z|uZov£ahvwz|u§\a- \iku i|joahzJ[+ikahzJu³ i15 Ri
q\¦ qv£ah\ hjmxw\z |\ xCD/01CG³W4D5 HJLKDKLKk5 >+ahXm\]h\a`zk¡¨ i| hv~ikZx£\Q]TumzJuxwvwum\^i| tvwudi!i|uZ&i]\a`z|¡
i| hv~ikmxw\^]tov~]paqv£u}ay¡¢ qz|[R§+\aUw6+ D/iG=\+ahXZ\ikvw ODGi/GMEJGc¦Xm\^ h\i/$m\umz|ah\^]taqXm\ah\^ h[ ¦XZ\ q\
uZz|ux£vwum\^i| ik qvwi|mx£\Q]!ik q\t q\uik[+\^ikuZQE¬vw]i+]h\az|¡C}zJuZ]ah ikvwuJaQ§
w6+ D/iG
=
D/iN
G v¤¡YiCvw]!\^v¤aqXm\ Ti+}z|uZ]aqi|uJazJ !i
i| hv~ikZx£\cahXZikaToz\^]!umz|a
ikm=\^i| ¨vwu4D5 H LKDKLK{I5 >
=
D ]465
=
<>G v¤¡YiCvw]i+ ik qv~ikmxw\a5l7l465 H DKLKDK{k5 >
ikuZSv£¡$i¡¢ q\^]hX i| hv~ikmxw\tzk¡
=
DGF D2 H LKDKLK{M2 M
G
MX#2H
E XG v¤¡Yi
= F DF2IH)LKDKLKM2NM G¨ikuZ
w6+ DF2NXLG
= D2N
X
MEX,G©¡¢z| Ti|x£xQ
=
RWKDKLKN+$§
» ¿ *$TSUAA/qsrXURLk<LFOjN?X$+X <QY!9*Q. q]hv£[«
Zx£v£µZ\^xw\¡ah«4xwv£uZ\^ik qv£apnG}zJuZov£ahvwz|ujqWq J N?[ i 5 -77. N k w6+ D/iG
=
D/iG/REJG-
D/5
=
G#7;E3 ,d7 99DI|@ CG] S '7`| i
,]5
B '
0,'D/5G
=
Q:
=
=
,'DG
= (
DG3I Gz D/3 G =
¿ ( ¿ ¿4 *$TSUAAGqGrXU+$TSUFA/qsrXURL
¿¿ qU CUZq373 F <N 1Y eiT5 M7"9A9
(MN?<QX $ 2MM( _ 1; ]"XXUYkqxZ"N LN?F $ < 5CD+GN R '2
= i$
<72J5jB'
<<3 M7C|@r,N LN?Fl,~7+99DI|@ CGCN R
245jB' i/,liG,p5jB'
& 1 q 2T1kX1Nq#ia 2Z9,<NqEi//gAr2
=
iG;&gM 5;CD/OGD
!U ZSM A$/<1; QRM#)(kQ2-i2 +7F AU &'xi
= <
MS L< 4U"<LF H "2<4kq<Eq $ F D2IHJLKLKDK2NMGD g2
=
i/ N R;
8:9<;>=:;>=
G 9 M-B ;>= D0M2I>I>@3O6I>F.D0M2I>I O<@EBC@3?! ;t
;>=PBP;>DRBP?P@3@ M#" BPF$! M-BM ;
t&%('*),+4T
S 4 SH)LKDKLK K$>5 CD+G4& " UX D
G = 2
/qJ2+5jB'
K aN ,$ Nq2QM
RRR(#_ j 0 <YM;M mXX')H)DKLKLKI1 N RKi2
5
q RTVT 5
LN i0|@r,N LN?F*,
m4 SH6LKDKLK{ K$><5 | G + @,
D
G = 5< 92a5 B' i,
diG,a5 B' i& k "?RS 1< M7+d|r,N N?LFP,799DI|@ CGCN Rj
2 5 B' i/, i/,;5jB' c+ MRaAH& OF A X <&
N RQ
,,DX,G
=
DX<,,D
G =
&'eLX :
=
X
=
J7 M HkqTE
! T2NX
= 2
!UQ F ] "]N q CZA1S7NqF A 7D X*
G7&' "&
N?_"LN H|@r,N LN?F*, N kgiG,
= i, 7!U <F ! Z_JN RN
21]XNqi !U 4[R$4X7"R MF F
¿ ( ¿ ¿gT. 3 !9*m
=
6|@6| 1-O<
= 6|
)|
kL& jLM
N?,$O,N " U. ! qO1[/qsrXL+<LF< 5 .CB?D D9G G D G
q
a -/a<
i 5 -77." 7|a,P7 99DI|aG CG2i/,;5jB' k$ZSF J,]5jB'
¿¿ T" / F1#k,$ 2CNq9.CB D D9G G7N Yt07 DG+L[ "0C5jB
6
2LT
N LF _ +Nq 3LF 05 B6
21 & SUMOiq10J5 B6
2 O05 B'
3&'
'7|a3 72'5 B'
&g F;$ZScF4g2#7 DGL
4q42
=
0Y 9O0l7 D9G1<& CQt `7 |aKL[]2
=
0k5jB'
]M 1
-/I Uat '7|a;L[ a2 5jB'
4q40+5
6
21 lt06#7CD/OG+][+0+5jB
6
06 5 6
2LTk<N FY?RS "RS SF13,
095 B6
06a& XY Yt -7|a]L[i065 B' 3M1 9065
6
21 R76 L
N?Ai5 7m."J3N LN?F $ J< CSF"? 069N i&$
=
06:[
<
2 =
06s\ $S^[ i;N F kq X$-rXN SjMON?X$+XQ&' U$+_ 1kM LF1
qZ06#5 B' ON X$ NqT06a1R N F A @- X7XXJNq'| U'
i&$
= 0 :[ '& Z() 2t 7| ][Ei&$C5 B' <40 \ ^[ 5 B' &g'A N TM&m
$"5jB' J g2!#$?DGiLG
=
4D5 HJLKDKLK{I5 >Q J 4F [kqiIT*#URi. ! LqC
AGqGrXU"<LF & 9( MJ76 F,l7 99DI|@ 7G1N Rk 2i$75jB' i/,;5 B'
J J]T M" 6 LJ$++XXx"7|/N #,
=
465mX 5 DX:mQ
=
RWKDKLK <> <
5mX$ 5 B' LXEq xQ
=
RWKDKLK {e M$ 5mX$Y5 B' DX<& ()T E $j5jB' J,W0 )Z
J,35jB' J/ & () H $75jB' J <7 N 2 =
0D\ $S^[5jB'
P u?ahXZvw]`µ q]a`ahXm\^z| q\[R³¦¨\]Xmz¦¹ahXZikaN}zJ[Zx£\ahvwz|u ikxw¦¨ino]cz |\ h«ikmm qzlov£[ikah\yaqXm\S]\azk¡!o\«
]q}\^uZmi|uJa]¨¡¢z| WeTm]ikuZ ah q\\yi|joahzJ[+ikaqi]hikahv~]p¡¢nvwum{ahXm\yxw\¡ah«4xwvwum\^i| hv£apnG}zJuZov£ahvwz|u§