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d $t t&* p#Gˉ E UT$$9E9Mt&A9Mw490A4$9MUuMȋMuЋuŰ9}AEQ1DU~D$}t8@1ɉ<$Z88T$EE$!9E؉t$EE$9E}<$7X|$H P0DH@D7@QU4$T$.8Eu9uMUȃMhTЉ$7UEXLLFLPL$$7PUhTыP $D$Z8PЉf_0@U4Љ|BdL$D$$eMhpTʋP$D$7f_1@4Љ|E|$dt$<$dEu9us4}}u;uUEuXE9ur̋E1Ƀ}> U}u9uh$ ЉMȅt|T0 $u5UXF <u9s=;uluX9rË}$}1T$ $5Eȉ$5pM19ph D1@?.plD@DDD@pDxUhh 4hD?plDD@׉DDDt&D4D}J9M4dуd D@ p!ыxʋhTD9sDӥ444!<]_0D>L|0DE< TPD$4$$|:f_1DLLPLL$4$}#PuD _00L1||DuT<ЋxPL$4$#|8_01x1Du<ЃTtPT$4$i#|9_10tD2TE<΋P4$ЉD$#|9_11hB 耉D$ $!b\$ l$QK+t$|$1a )9s׉F)9r\$ t$|$l$Ít&' $|$Jí*t$)pNu&?$t$|$ ÐUS  ЋuX[]ÐUS[/*P6"Y[Usage: %s [options] [filename]... Reads in one or more TRSes and tries to prove termination for each. -d, --use-dependency-pairs try finding a proof by first applying dependency pairs -e, --prefer-exhaustive prefer the use of exhaustive traversal over random traversal --expect-srs force default system type to string rewrite system -l, --use-semantic-labelling try finding a proof that uses semantic labelling -p, --use-polynomials try finding a proof that uses polynomial interpretations -m, --more-thorough spend more time searching; the latter takes a natural value as argument --maximum-labelling-depth maximum number of times that semantic labelling is applied recursively -r, --use-recursive-path-order try finding a proof that uses recursive path order -s, --do-not-sort-rules do not sort rules of the input system to try to improve performance --transformation-style sets the style of the transformation that limits occuring symbol arity takes an argument {Left,Balanced,Right}, default : [Right] -t, --timeout timeout per system in seconds; both take a natural value as argument -v, --verbose be more verbose; the latter takes an argument in {0...5} -h, --help show this information --version show program versionWhen no input files are specified, standard input is read.Report bugs to J.v.d.Wulp@student.tue.nl. %s %s copyright 2004-2005, J. van der Wulp Invalid transformation style specified! Apply string reversal on both sides of all rules. In any generated proof the following is information is assumed and left implicit at times for the sake of readability. Polynomial interpretations range over the naturals excluding zero and one. The default polynomial interpretations for constant, unary and binary symbols to define a polynomial orderings are: two, the identity function and sum-minus-two respectively. Finally, for semantic labelling the default interpretation for a symbol is 0 and the labelling function is one that tuples its arguments. Consider the Term Rewriting System (TRS) specified by the following rules: [elapsed time %.4f seconds, source '%s'] Renamed variables for better algorithm performance: Reordered rules for better algorithm performance: Proof of (non-)termination found for (%u + %u) of %u rewrite systems in total. (skipped %u) , %u minutes and %.4f seconds! Established that TRS is essentially an SRS. A non-termination preserving transformation was successfully applied to the original TRS: Application of dummy elimination yields the following TRS : By adding the dependency pairs, the termination problem is transformed to the following relative termination problem. teparlause-dependency-pairsprefer-exhaustiveexpect-srsuse-semantic-labellinguse-polynomialsuse-recursive-path-ordersort-rulesmore-thoroughmaximum-labelling-depthtransformation-styletimeoutverboseversionhelpdelprsmt:hvLeft1.2.7BalancedRight [%s error %s]  since no rules remainTRS is terminating%s. DONT_KNOW  [%sinformation%s] Timer set to %u seconds! Parsing TRS (%s) Result : inconclusive YES NO timed out! Total amount of time spent: %u hoursnon-terminating terminating %u minutes and %.4f seconds! , 1 minute and %.4f seconds! 1 hour5$@hư>߼xV42??Timeout triggered! .srs.trs [%s warning %s] [HashTable] Resizing when at %d of %d elements (load factor %3f). [HashTable] Resizing hash table after %d subsequent collissions. [HashTable] Collision triggered resize! [HashTable] Key totals : %u / %u (%4f) Assuming TPDB specification format. Ignoring input from `%s' as file does not exist. ),(VAR(RULES ->= -> (TPDB-RT) ,%s} Terms : {Rules : {->=->Variable set : {Number of variables %d Number of symbols %d Number of terms %d Number of rules %d Symbols : {,(%s,%d) [%s fatal %s] Syntax error around line %d. On line %d : expected '->' Context sensitive or other unsupported strategy found; aborting! TPDB extended with relative termination requested! On line %d : expected '(' but found '%c' Theory section found in input TRS which is currently not supported! At line %d : symbol '%s' occurs with different arities. Conditional term rewriting systems not supported! At line %d : expected a symbol! Variable section specifies '%s' as variable, but a previous section already used it as function or constant! _x_On line %d : expected ',' Ignoring strategy, trying to prove generic termination! _%u %s, %sCandidate symbols for dummy elimination! Proof of relative termination found using a polynomial ordering over : Termination follows from a proof of termination with the following rule%s removed : Termination follows from a proof of termination for the remaining rule%s : No rules remain, hence termination is proved! [polynomial orderings] Proceeding with %u deviation%s from the default! [polynomial orderings] Exhaustive search strategy (<=%u non-default interpretations). Proof of termination found using the following polynomial interpretation : Proof of relative termination found since no strict rules are present. All remaining rules are non-strict so termination is proved! Proof of relative termination found using a polynomial ordering : [polynomial orderings] Proceeding with the default interpretation! [polynomial orderings] Exhaustive search strategy (<=%u non-default interpretations). ,X_{%d}%s[%s](X_{0}Remaining rules: ?AbulFG??=???+@&?>>>8N>Fa aZa``O`__`Z_ZeH8}:NCߩZ qB6[polynomial orderings] Random search strategy (x%u + 1). y1]P1D <;S;';::m: :;;6;Proof of termination found using RPO with the embedding order and the following symbol precedence : Proof of termination found using LPO with the embedding order and For any symbol f lex(f) is a lexicographic precedence of f specified as a permutation. %s > %s lex(%s) = [,%u] 5,+,#,,,,+++++++p+b+WWWWWuWgWNW:W,WWWVVVXXXXXXXhXTXFX+XX XWW%vuuuumuIu%uutttqtMtqlss`s {(%s,%s),(%s,%s) %s -> {%s,q [%s](p%s) = %s [%s] = 1 //P//..<.--M--,p000138/877R776y6n9988 :9,63B?BAAAWAA@@K@ @??k??f>BEEECEEDDMDDCCmC(CBB arguments are the same for %s [%u] Proceeding with %u deviation%s from the default symbol interpretation! %u effective quasi-models found of %u generated quasi-models! %u effective models found of %u generated models! %u interpretations checked in total! [%u] Proceeding with generation of %u random interpretations! With semantic labelling over the booleans using the following %smodel : Resulting labelled system : Interpretation is a %smodel and yields an effective labelling : the following labelled system is generated : In summary, the remaining rules are : The labelling can be removed leaving a subset of the rules of the original system : Proof of non-termination, looping derivation starting in Proof of non-termination, variable %s is unbound in : Proof of non-termination, left-hand side is a subterm of the right-hand side in : . X_{%u}^{%u}X_{%u}%.2f + Number of variables : %d Number of coefficients : %d Textual representation : Coefficients : [Dimensions : [,(%d,%d),%.2f3 L w h   4$oԓoo zʗڗ *:JZjzʘژ *:JZjz p@{0 E W b y     Ӄ     ?????? @? @ @? @ @???????? @? @??? @@ ?          `  @       Ф   ` Ф    X H X 8 X (     p h p ` ?????? @? @ @? @ @???????? @? @??? @@ ?@              `  @     Ш   ` Ш     x  h ` H ` 0     ?????? @? @ @? @ @???????? @? @??? @@ ?  @ ` @ `  `  `  `  `  `  ` ` P    P   ` خ Ȯ خ  خ     p     ?????? @? @ @? @ @???????? @? @??? @@ ? `     `  @            ` P    P         Ȳ   0 ( 0  ?????? @? @ @? @ @???????? @? @??? @@ ?          `  @       е   ` е    X H X 8 X (     p h p ` ?????? @? @ @? @ @???????? @? @??? @@ ?@              `  @     й   ` й     x  h ` H ` 0     ! i    g i v         Ș  ՘   Ž     C[-G][ o"c4Eg.]Ut"K ]P+)RWGCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7)GCC: (GNU) 3.4.3-20050110 (Gentoo Linux 3.4.3.20050110-r1, ssp-3.4.3.20050110-0, pie-8.7.7).shstrtab.interp.note.ABI-tag.hash.dynsym.dynstr.gnu.version.gnu.version_r.rel.dyn.rel.plt.init.text.fini.rodata.eh_frame.ctors.dtors.jcr.dynamic.got.got.plt.data.bss.comment 44HH !hh,' / 7oDoԓPS $$\ 44 eLL`dd@kqw ww &            ! 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