4.80/2.04	NO
5.16/2.06	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
5.16/2.06	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.16/2.06	
5.16/2.06	
5.16/2.06	Termination w.r.t. Q of the given QTRS could be disproven:
5.16/2.06	
5.16/2.06	(0) QTRS
5.16/2.06	(1) NonTerminationProof [COMPLETE, 145 ms]
5.16/2.06	(2) NO
5.16/2.06	
5.16/2.06	
5.16/2.06	----------------------------------------
5.16/2.06	
5.16/2.06	(0)
5.16/2.06	Obligation:
5.16/2.06	Q restricted rewrite system:
5.16/2.06	The TRS R consists of the following rules:
5.16/2.06	
5.16/2.06	   a(a(a(x1))) -> b(b(c(a(a(x1)))))
5.16/2.06	   b(b(x1)) -> c(a(b(x1)))
5.16/2.06	   c(x1) -> x1
5.16/2.06	
5.16/2.06	Q is empty.
5.16/2.06	
5.16/2.06	----------------------------------------
5.16/2.06	
5.16/2.06	(1) NonTerminationProof (COMPLETE)
5.16/2.06	We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.
5.16/2.06	
5.16/2.06	Found the self-embedding DerivationStructure: 
5.16/2.06	"(b)^k+3 -> (b)^2k a a b"
5.16/2.06	(b)^k+3 -> (b)^2k a a b
5.16/2.06	by Overlapping Derivationstructures"(b)^k+3 -> (a)^k+2 b
5.16/2.06	by Equivalent"b (b)^k+2 -> (a)^k+2 b
5.16/2.06	by Overlap u with m (ol1)"b (b)^k+2 -> (c a)^k+2 b
5.16/2.06	by Operation lift"b (b)^k+1 -> (c a)^k+1 b
5.16/2.06	by Operation lift"b (b)^k -> (c a)^k b
5.16/2.06	by Selfoverlapping OC am2"b b -> c a b
5.16/2.06	by original rule (OC 1)"""""c -> 
5.16/2.06	by original rule (OC 1)""""(a)^k+2 -> (b)^2k a a
5.16/2.06	by Equivalent"a a (a)^k -> (b b)^k a a
5.16/2.06	by Overlap u with m (ol1)"a a (a)^k -> (b b c)^k a a
5.16/2.06	by Selfoverlapping OC am2"a a a -> b b c a a
5.16/2.06	by original rule (OC 1)"""c -> 
5.16/2.06	by original rule (OC 1)"""
5.16/2.06	
5.16/2.06	----------------------------------------
5.16/2.06	
5.16/2.06	(2)
5.16/2.06	NO
5.27/2.26	EOF