52.10/14.26	NO
52.10/14.29	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
52.10/14.29	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
52.10/14.29	
52.10/14.29	
52.10/14.29	Termination w.r.t. Q of the given QTRS could be disproven:
52.10/14.29	
52.10/14.29	(0) QTRS
52.10/14.29	(1) NonTerminationProof [COMPLETE, 2666 ms]
52.10/14.29	(2) NO
52.10/14.29	
52.10/14.29	
52.10/14.29	----------------------------------------
52.10/14.29	
52.10/14.29	(0)
52.10/14.29	Obligation:
52.10/14.29	Q restricted rewrite system:
52.10/14.29	The TRS R consists of the following rules:
52.10/14.29	
52.10/14.29	   a(x1) -> x1
52.10/14.29	   a(a(b(x1))) -> c(c(c(x1)))
52.10/14.29	   c(x1) -> b(a(x1))
52.10/14.29	   c(b(x1)) -> x1
52.10/14.29	
52.10/14.29	Q is empty.
52.10/14.29	
52.10/14.29	----------------------------------------
52.10/14.29	
52.10/14.29	(1) NonTerminationProof (COMPLETE)
52.10/14.29	We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.
52.10/14.29	
52.10/14.29	Found the self-embedding DerivationStructure: 
52.10/14.29	"a a b a b a b -> b b a a b a b a b"
52.10/14.29	a a b a b a b -> b b a a b a b a b
52.10/14.29	by OverlapClosure OC 3"a a b a b a b -> b b a a c b a b
52.10/14.29	by OverlapClosure OC 2"a a b a b -> b b a a a
52.10/14.29	by OverlapClosure OC 3"a a b a b -> c a b a
52.10/14.29	by OverlapClosure OC 2"a a b -> c a
52.10/14.29	by OverlapClosure OC 3"a a b -> c c b a
52.10/14.29	by OverlapClosure OC 2"a a b -> c c c
52.10/14.29	by original rule (OC 1)""c -> b a
52.10/14.29	by original rule (OC 1)"""c b -> 
52.10/14.29	by original rule (OC 1)"""a a b -> a b a
52.10/14.29	by OverlapClosure OC 3"a a b -> c b a b a
52.10/14.29	by OverlapClosure OC 3"a a b -> c c b a
52.10/14.29	by OverlapClosure OC 2"a a b -> c c c
52.10/14.29	by original rule (OC 1)""c -> b a
52.10/14.29	by original rule (OC 1)"""c -> b a
52.10/14.29	by original rule (OC 1)"""c b -> 
52.10/14.29	by original rule (OC 1)""""c a b -> b b a a
52.10/14.29	by OverlapClosure OC 3"c a b -> b b a c b a
52.10/14.29	by OverlapClosure OC 2"c -> b a
52.10/14.29	by original rule (OC 1)""a a b -> b a c b a
52.10/14.29	by OverlapClosure OC 3"a a b -> c c b a
52.10/14.29	by OverlapClosure OC 2"a a b -> c c c
52.10/14.29	by original rule (OC 1)""c -> b a
52.10/14.29	by original rule (OC 1)"""c -> b a
52.10/14.29	by original rule (OC 1)""""c b -> 
52.10/14.29	by original rule (OC 1)""""a a b -> c b a b
52.10/14.29	by OverlapClosure OC 2"a a b -> c b a c
52.10/14.29	by OverlapClosure OC 3"a a b -> c c c
52.10/14.29	by original rule (OC 1)""c -> b a
52.10/14.29	by original rule (OC 1)"""c -> b
52.10/14.29	by OverlapClosure OC 2"c -> b a
52.10/14.29	by original rule (OC 1)""a -> 
52.10/14.29	by original rule (OC 1)"""""c -> b a
52.10/14.29	by original rule (OC 1)"
52.10/14.29	
52.10/14.29	----------------------------------------
52.10/14.29	
52.10/14.29	(2)
52.10/14.29	NO
52.50/14.37	EOF