41.56/11.51	NO
41.56/11.52	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
41.56/11.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
41.56/11.52	
41.56/11.52	
41.56/11.52	Termination w.r.t. Q of the given QTRS could be disproven:
41.56/11.52	
41.56/11.52	(0) QTRS
41.56/11.52	(1) NonTerminationProof [COMPLETE, 2449 ms]
41.56/11.52	(2) NO
41.56/11.52	
41.56/11.52	
41.56/11.52	----------------------------------------
41.56/11.52	
41.56/11.52	(0)
41.56/11.52	Obligation:
41.56/11.52	Q restricted rewrite system:
41.56/11.52	The TRS R consists of the following rules:
41.56/11.52	
41.56/11.52	   c(c(x1)) -> b(b(x1))
41.56/11.52	   a(b(x1)) -> a(c(b(x1)))
41.56/11.52	   b(a(x1)) -> b(b(x1))
41.56/11.52	   b(c(x1)) -> c(a(a(x1)))
41.56/11.52	
41.56/11.52	Q is empty.
41.56/11.52	
41.56/11.52	----------------------------------------
41.56/11.52	
41.56/11.52	(1) NonTerminationProof (COMPLETE)
41.56/11.52	We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.
41.56/11.52	
41.56/11.52	Found the self-embedding DerivationStructure: 
41.56/11.52	"a b b (a)^k c b -> a b b (a)^2k+4 c b"
41.56/11.52	a b b (a)^k c b -> a b b (a)^2k+4 c b
41.56/11.52	by Equivalent"a b b (a)^k c b -> a b b a a (a)^2k+2 c b
41.56/11.52	by Overlap u with l (ol4)"b (a)^k c b -> c (a)^2k+2 c b
41.56/11.52	by Equivalent"b (a)^k c b -> c (a a)^k a a c b
41.56/11.52	by Overlapping Derivationstructures"b (a)^k c b -> (b)^k c a a c b
41.56/11.52	by Overlap u with r (ol3)"b (a)^k -> (b)^k b
41.56/11.52	by Selfoverlapping OC am2"b a -> b b
41.56/11.52	by original rule (OC 1)"""b c b -> c a a c b
41.56/11.52	by OverlapClosure OC 2"b c -> c a a
41.56/11.52	by original rule (OC 1)""a b -> a c b
41.56/11.52	by original rule (OC 1)""""(b)^k c -> c (a a)^k
41.56/11.52	by Selfoverlapping OC am1"b c -> c a a
41.56/11.52	by original rule (OC 1)"""""a b c -> a b b a a
41.56/11.52	by OverlapClosure OC 3"a b c -> a c c a a
41.56/11.52	by OverlapClosure OC 2"a b -> a c b
41.56/11.52	by original rule (OC 1)""b c -> c a a
41.56/11.52	by original rule (OC 1)"""c c -> b b
41.56/11.52	by original rule (OC 1)"""
41.56/11.52	
41.56/11.52	----------------------------------------
41.56/11.52	
41.56/11.52	(2)
41.56/11.52	NO
41.96/11.62	EOF