************************************************** Claim { termination = Standard , system = (VAR x1) (RULES a -> , a b -> b c a a a , a c c -> b) , deadline = Just (Time -2040315399) } is false because of mirror image R' = { reverse(l) -> reverse(r) | (l -> r) in R } (VAR x1) (RULES a -> , b a -> a a a c b , c c a -> b) admits a looping transport system notation: http://dfa.imn.htwk-leipzig.de/matchbox/methods/loop.pdf pivot p = [ a , a ] block alphabet Gamma = [ [ a ] , [ c , b ] ] forall g in Gamma: g p ->^* p phi(g) where phi = listToFM [ ( [ a ] , [ [ a ] ] ) , ( [ c , b ] , [ [ a ] , [ c , b ] , [ c , b ] ] ) ] phi ([ a ]) = [ [ a ] ] because of Derivation { lhs = [ a ] , rhs = [ a ] , hash_value = -165557840 , strict = False , steps = [ ] } phi ([ c , b ]) = [ [ a ] , [ c , b ] , [ c , b ] ] because of Derivation { lhs = [ c , b , a , a ] , rhs = [ a , a , a , c , b , c , b ] , hash_value = 1612343866 , strict = True , steps = [ Step { rule = 1 , position = 1 } , Step { rule = 1 , position = 5 } , Step { rule = 0 , position = 1 } , Step { rule = 0 , position = 1 } , Step { rule = 0 , position = 1 } , Step { rule = 0 , position = 2 } , Step { rule = 2 , position = 0 } , Step { rule = 1 , position = 0 } ] } start s = [ c , b ] exponent k = 5 phi^k(s) contains s (.. p ..)^k this implies there is a loop starting at s p^k ************************************************** statistics: total atomic proof attempts number = 8, total = 5 maximal = [ Log { what = rfc match bounds (classical) , start = Time -2040321340 , end = Time -2040320836 , duration = 5 , success = False } ] successful atomic proof attempts number = 1, total = 0 maximal = [ Log { what = simplex , start = Time -2040321341 , end = Time -2040321341 , duration = 0 , success = True } ] failed atomic proof attempts number = 7, total = 5 maximal = [ Log { what = rfc match bounds (classical) , start = Time -2040321340 , end = Time -2040320836 , duration = 5 , success = False } ] ************************************************** matchbox general information (including details on proof methods): http://dfa.imn.htwk-leipzig.de/matchbox/ this matchbox implementation uses the SAT solver MiniSat by Niklas Een and Niklas Sörensson http://www.cs.chalmers.se/Cs/Research/FormalMethods/MiniSat/ matchbox process information arguments : --solver=/tmp/tmpongfjx/matchbox-2007-06-01/minisat --timeout-command=/tmp/tmpongfjx/matchbox-2007-06-01/timeout --tmpdir=tmp --timeout=60 /tmp/tmp.QYVnQi5rLy/a.srs started : Thu Jan 26 12:40:23 CET 2012 finished : Thu Jan 26 12:40:29 CET 2012 run system : Linux uc01-11 2.6.32-5-amd64 #1 SMP Wed Jan 12 03:40:32 UTC 2011 x86_64 release date : Fri Jun 1 17:36:44 CEST 2007 build date : Fri Jun 1 17:36:44 CEST 2007 build system : Linux dfa 2.6.8-2-k7 #1 Tue Aug 16 14:00:15 UTC 2005 i686 GNU/Linux used clock time: 6 secs