3.42/1.63	NO
3.42/1.64	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.42/1.64	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.42/1.64	
3.42/1.64	
3.42/1.64	Termination w.r.t. Q of the given QTRS could be disproven:
3.42/1.64	
3.42/1.64	(0) QTRS
3.42/1.64	(1) NonTerminationProof [COMPLETE, 0 ms]
3.42/1.64	(2) NO
3.42/1.64	
3.42/1.64	
3.42/1.64	----------------------------------------
3.42/1.64	
3.42/1.64	(0)
3.42/1.64	Obligation:
3.42/1.64	Q restricted rewrite system:
3.42/1.64	The TRS R consists of the following rules:
3.42/1.64	
3.42/1.64	   b(c(x1)) -> d(c(x1))
3.42/1.64	   b(d(x1)) -> d(b(x1))
3.42/1.64	   a(d(x1)) -> a(b(b(x1)))
3.42/1.64	
3.42/1.64	Q is empty.
3.42/1.64	
3.42/1.64	----------------------------------------
3.42/1.64	
3.42/1.64	(1) NonTerminationProof (COMPLETE)
3.42/1.64	We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.
3.42/1.64	
3.42/1.64	Found the self-embedding DerivationStructure: 
3.42/1.64	"a (b)^k d c -> a (b)^k+1 d c"
3.42/1.64	a (b)^k d c -> a (b)^k+1 d c
3.42/1.64	by Overlap u with r (ol3)"a (b)^k d -> a (b)^k+1 b
3.42/1.64	by Operation expand"a (b)^k d -> a (b)^k+2
3.42/1.64	by Equivalent"a (b)^k d -> a b b (b)^k
3.42/1.64	by Overlap u with l (ol4)"(b)^k d -> d (b)^k
3.42/1.64	by Selfoverlapping OC am1"b d -> d b
3.42/1.64	by original rule (OC 1)"""a d -> a b b
3.42/1.64	by original rule (OC 1)"""""b c -> d c
3.42/1.64	by original rule (OC 1)"
3.42/1.64	
3.42/1.64	----------------------------------------
3.42/1.64	
3.42/1.64	(2)
3.42/1.64	NO
3.58/1.71	EOF