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Termination Proofs Using gpo Ordering Constraints : Extended Version

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(1)Termination Proofs Using gpo Ordering Constraints : Extended Version Thomas Genet, Isabelle Gnaedig. To cite this version: Thomas Genet, Isabelle Gnaedig. Termination Proofs Using gpo Ordering Constraints : Extended Version. [Research Report] RR-3087, INRIA. 1997, pp.37. �inria-00073604�. HAL Id: inria-00073604 https://hal.inria.fr/inria-00073604 Submitted on 24 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Termination Proofs using gpo Ordering Constraints – extended version –. Thomas Genet and Isabelle Gnaedig. N ˚ 3087 January 1997 ` THEME 2. ISSN 0249-6399. apport de recherche.

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(134) ØZ×Ud—‹  q4‹7qMyâd†moqž×·Ø|n@yU}7qu{u«q4e `»xo‹JvmYŒnwyUs ptqZy{d  uâq~u ` d =@?A Œ:d1montuân@q4mJntu«yâd ptÙ _2B d uŠx1y   yƒu n@mZu  q:Œ:x1sd 3  (   Ø7× ` n@s ` d p|‹  dSyâyâd+yavmoqu«ntqMmOq4ÙyâxoW} `WÙ q  e~x1p@vntm U `W‹  q|qÙ y _ Ñ S 1 2 3› 2 Õ 1 . H( g "lU !

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(139) yâdu*qÙ  #  'H$l)  ØcqMmodÙ q  d Sv4s `  xop@d _ montuânwvpā Û ÚaÛ:y·v _  df_aÛ ` Úa=3Û:?GyhA × ` qZy{d  ÚaÛ9r  v‹ ` y ` vÅÜMd moq q  Œ:d  n@mo` r d+Œ:rMdv4m1Œ9× ` qMyâd `§yâxo}1y{uântuâx:u«ntqMm1yfv dOd+e‹ouƒz d sqMm1y{u vn@mMuCyâq4p@ÜZn@mor!q4m Û ÚaÛn@yCvMs ntd+Ü4dSŒ }|z v y{d ufq4Ù Œod+Œ:x1suân@q4m  xop@d+y __a` d+yâd `  xop@d+yā⁠u  vm1y{Ù q  e v Û ÚaÛf}|zv4Œ1Œ:ntm1r*` q  Œ:d  n@mor*d+Œor4d+yÄuâq~u ` d  ÚaÛfr  v4‹ ` ` v4m1«Œ! }|z sqMm1y{u x1U s>u«ntmo r

(140) u d_ sq d+yâ‹7q4m1Œ:n@mo r `§y{xo}Yyƒu«nÈu«x:uân@q4mcØ × qMyâdv ‹1‹optnws ` vuân@ q4m ׈n@ptp«‹  qžÜ|nwŒ:dfu d s q dSy{‹7q4mYŒ:ntm1r `W‹ q|qÙ y Û|qMptÜ|n@morOnwy‹ q|s d+y«y{dSŒ.n@m1Œ:d+‹Yd+m1Œ:d mZu«ptz$Ù q d+v4s Û ÚaÛ sq d+yâ‹YqMm1Œ:n@mor u«K qfd+` v4s `O d+×  ntuâd  xoptdMØovm1 ŒJd m1Œ1ya× ` d m ` moqCŒ:d+Œox1s>u«ntqMm   xop@dhv4‹o‹op@ntdSya vm|zCptqMmor4d _2B duˆKx1yaŒ:d m1quâdh}|z u dy{d uÄqÙcŒ:dSŒ:x1suân@q4m xoptdSy ØM}|z ~u dŒ:d+Œox1s>u«ntqMm d+p@vuân@q4mfq4mJÛ ÚaÛn@m1Œ:xYsd+Œf}|z ØMvmYŒf}Zz  u ` d*Ksu _2 v4/ m1yânÈu« ntÜMdsp@qMyâx  d*qÙ  _ B dK uhx1y s v4ptp K `» Œ:dSŒ:x1s` uân@q4m$‹  q:sd+y«yu ` dŒ: d+Œ:xYs>uân@q4m ‹  q|s d+y«y_ Œ:d 1modS` Œ }|z K Û ÚaÛJn@yˆy«v nwŒu«qf}Ydhn@m  `»moq eC` vpY Ù q e × d+mOmoqCŒ:dSŒ:x1suân@q4m xo` p@d· v‹o‹1ptn@d+yUu⁠qfntu Û|_ d+dhu d yâduˆq4Ù `§Œ:d+Œ:xYs>uân@q4m xoptdSyantm 1rMx d•MØ:× d d·vm d+Œ:rMd 

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(143) vCmod+× `»‹ q|qÙܞv n@v4}optd †qu«d·u vžu—m1q|Œod+y vmYŒ q4Ù u ` d K `»Œ:dSŒ:x1suân@q4m  xop@d+yh ex1y{u·v4pt×avÅz:yeCvu«s ` Œ:n@y{uâ_ n@ m1_ s_ u*=3mo?Gq:A Œ:d+yhq4Ù  _C_a` nwyh‹  d+Ü4d+mMu2yÙ  qMe v4ŒoŒontmor s z:sp@n@sÄntmodSZx1vp@nÈuƒz·q Œod ntmord+Œ:rMd+Oy d vp@×avÅz|ycÙ vpwy{dŠ× u i(v4m1Œ~s z|s ptnwsdSZxontܞv4ptd+m1sdŠd+Œ:rMd+Oy d v4pt×avÅz:y x1momod+s d+y«yâv  zfÙ q `  Œ:d+Œox1s>u«ntqMm1y i _  quâdˆv4p@yâqu vžumoq·yâ‹YdSsnwvpoy{u vžu«d r4zhnwy  dSZxon  d+Œ~× ` d m  xoptdSyv  dŠv4‹o‹op@ntdSŒ (d+nÈu ` d  Ù q  u ` d†s ` qMn@s d q4ف u ` d‹1vn  q4Ùmoq:Œ:d+_y+Ø6_aq `  Ù q   u ` dfs` ` q4U nwsd*q4 Ùu ` d   x1ptd~u⁠qOv4‹o‹op@z _ / yv  dSy{ x1pÈuSØYu ` d~‹  q:sdSyây—s v4«m. }Yd ‹Yv vp@ptd+pt n  dSŒvMyntuU nwy v4m yu«q·u d `»‹ q|qÙcyƒu xYs>uâx dMØZv4‹o‹op@n@s+«vžuân@q4mCq4Ù xop@d+yU s v4mC}Ydsq4mYsx d+` mZu qMmv Û ÚaÛ   ‹ q:s d+y«y{dS`y~s v4mv‹1‹optz Œod+Œ:x1suân@q4m xo p@d+ysqMm1sx d  mZuâp@z qMm‹1 v4n y*q4Ù_ mo_ q:Œ:& dSy~( q4نu d y«v( ef& dfÛ ÚaÛ6 Ø6‹ qžÜZnwŒ:dSŒ

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