10.87/3.64	NO
12.17/3.97	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
12.17/3.97	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
12.17/3.97	
12.17/3.97	
12.17/3.97	Termination w.r.t. Q of the given QTRS could be disproven:
12.17/3.97	
12.17/3.97	(0) QTRS
12.17/3.97	(1) NonTerminationProof [COMPLETE, 957 ms]
12.17/3.97	(2) NO
12.17/3.97	
12.17/3.97	
12.17/3.97	----------------------------------------
12.17/3.97	
12.17/3.97	(0)
12.17/3.97	Obligation:
12.17/3.97	Q restricted rewrite system:
12.17/3.97	The TRS R consists of the following rules:
12.17/3.97	
12.17/3.97	   b(b(x1)) -> b(a(x1))
12.17/3.97	   a(b(x1)) -> b(c(c(x1)))
12.17/3.97	   a(c(x1)) -> a(a(x1))
12.17/3.97	   c(a(x1)) -> b(a(a(x1)))
12.17/3.97	
12.17/3.97	Q is empty.
12.17/3.97	
12.17/3.97	----------------------------------------
12.17/3.97	
12.17/3.97	(1) NonTerminationProof (COMPLETE)
12.17/3.97	We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.
12.17/3.97	
12.17/3.97	Found the self-embedding DerivationStructure: 
12.17/3.97	"b a (c)^k b a -> b a (c)^2k+1 b a a"
12.17/3.97	b a (c)^k b a -> b a (c)^2k+1 b a a
12.17/3.97	by Overlap u with l (ol4)"a (c)^k b a -> b (c)^2k+1 b a a
12.17/3.97	by Equivalent"a (c)^k b a -> b (c c)^k c b a a
12.17/3.97	by Overlapping Derivationstructures"a (c)^k b a -> (a)^k b c b a a
12.17/3.97	by Overlap u with r (ol3)"a (c)^k -> (a)^k a
12.17/3.97	by Selfoverlapping OC am2"a c -> a a
12.17/3.97	by original rule (OC 1)"""a b a -> b c b a a
12.17/3.97	by OverlapClosure OC 2"a b -> b c c
12.17/3.97	by original rule (OC 1)""c a -> b a a
12.17/3.97	by original rule (OC 1)""""(a)^k b -> b (c c)^k
12.17/3.97	by Selfoverlapping OC am1"a b -> b c c
12.17/3.97	by original rule (OC 1)"""""b b -> b a
12.17/3.97	by original rule (OC 1)"
12.17/3.97	
12.17/3.97	----------------------------------------
12.17/3.97	
12.17/3.97	(2)
12.17/3.97	NO
12.38/4.06	EOF