48.17/13.24	NO
49.15/13.27	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
49.15/13.27	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
49.15/13.27	
49.15/13.27	
49.15/13.27	Termination w.r.t. Q of the given QTRS could be disproven:
49.15/13.27	
49.15/13.27	(0) QTRS
49.15/13.27	(1) NonTerminationProof [COMPLETE, 2642 ms]
49.15/13.27	(2) NO
49.15/13.27	
49.15/13.27	
49.15/13.27	----------------------------------------
49.15/13.27	
49.15/13.27	(0)
49.15/13.27	Obligation:
49.15/13.27	Q restricted rewrite system:
49.15/13.27	The TRS R consists of the following rules:
49.15/13.27	
49.15/13.27	   c(b(x1)) -> b(a(x1))
49.15/13.27	   a(c(x1)) -> a(b(c(x1)))
49.15/13.27	   b(b(x1)) -> b(c(x1))
49.15/13.27	   c(a(x1)) -> c(c(c(x1)))
49.15/13.27	
49.15/13.27	Q is empty.
49.15/13.27	
49.15/13.27	----------------------------------------
49.15/13.27	
49.15/13.27	(1) NonTerminationProof (COMPLETE)
49.15/13.27	We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.
49.15/13.27	
49.15/13.27	Found the self-embedding DerivationStructure: 
49.15/13.27	"b (c)^k+1 b c -> b (c)^2k+3 b c"
49.15/13.27	b (c)^k+1 b c -> b (c)^2k+3 b c
49.15/13.27	by Equivalent"b (c)^k+1 b c -> b (c c)^k+1 c b c
49.15/13.27	by Overlapping Derivationstructures"b (c)^k+1 b c -> b c (a)^k+1 b c
49.15/13.27	by Equivalent"b (c)^k+1 b c -> b c (a)^k a b c
49.15/13.27	by Overlap u with r (ol3)"b (c)^k+1 b -> b c (a)^k a
49.15/13.27	by Operation expand"b (c)^k+1 b -> b c (a)^k+1
49.15/13.27	by Overlap u with l (ol4)"(c)^k+1 b -> b (a)^k+1
49.15/13.27	by Operation lift"(c)^k b -> b (a)^k
49.15/13.27	by Selfoverlapping OC am1"c b -> b a
49.15/13.27	by original rule (OC 1)""""b b -> b c
49.15/13.27	by original rule (OC 1)""""a c -> a b c
49.15/13.27	by original rule (OC 1)""""c (a)^k+1 -> (c c)^k+1 c
49.15/13.27	by Operation lift"c (a)^k -> (c c)^k c
49.15/13.27	by Selfoverlapping OC am2"c a -> c c c
49.15/13.27	by original rule (OC 1)""""
49.15/13.27	
49.15/13.27	----------------------------------------
49.15/13.27	
49.15/13.27	(2)
49.15/13.27	NO
49.27/13.35	EOF