516.59/131.51	NO
516.73/131.54	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
516.73/131.54	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
516.73/131.54	
516.73/131.54	
516.73/131.54	Termination of the given RelTRS could be disproven:
516.73/131.54	
516.73/131.54	(0) RelTRS
516.73/131.54	(1) RelTRSLoopFinderProof [COMPLETE, 30.4 s]
516.73/131.54	(2) NO
516.73/131.54	
516.73/131.54	
516.73/131.54	----------------------------------------
516.73/131.54	
516.73/131.54	(0)
516.73/131.54	Obligation:
516.73/131.54	Relative term rewrite system:
516.73/131.54	The relative TRS consists of the following R rules:
516.73/131.54	
516.73/131.54	   a(c(c(x1))) -> c(c(a(x1)))
516.73/131.54	   a(b(b(x1))) -> b(b(a(x1)))
516.73/131.54	   a(a(c(x1))) -> b(b(a(x1)))
516.73/131.54	   b(c(a(x1))) -> a(c(c(x1)))
516.73/131.54	
516.73/131.54	The relative TRS consists of the following S rules:
516.73/131.54	
516.73/131.54	   a(c(a(x1))) -> a(c(b(x1)))
516.73/131.54	   b(a(a(x1))) -> a(a(a(x1)))
516.73/131.54	
516.73/131.54	
516.73/131.54	----------------------------------------
516.73/131.54	
516.73/131.54	(1) RelTRSLoopFinderProof (COMPLETE)
516.73/131.54	The following loop was found:
516.73/131.54	
516.73/131.54	---------- Loop: ----------
516.73/131.54	
516.73/131.54	b(b(a(a(c(a(c(a(x1)))))))) -> b(b(a(a(c(b(c(a(x1)))))))) with rule a(c(a(x1'))) -> a(c(b(x1'))) at position [0,0,0] and matcher [x1' / c(a(x1))]
516.73/131.54	
516.73/131.54	b(b(a(a(c(b(c(a(x1)))))))) -> b(b(a(a(c(a(c(c(x1)))))))) with rule b(c(a(x1'))) -> a(c(c(x1'))) at position [0,0,0,0,0] and matcher [x1' / x1]
516.73/131.54	
516.73/131.54	b(b(a(a(c(a(c(c(x1)))))))) -> b(b(a(a(c(c(c(a(x1)))))))) with rule a(c(c(x1'))) -> c(c(a(x1'))) at position [0,0,0,0,0] and matcher [x1' / x1]
516.73/131.54	
516.73/131.54	b(b(a(a(c(c(c(a(x1)))))))) -> b(a(a(a(c(c(c(a(x1)))))))) with rule b(a(a(x1'))) -> a(a(a(x1'))) at position [0] and matcher [x1' / c(c(c(a(x1))))]
516.73/131.54	
516.73/131.54	b(a(a(a(c(c(c(a(x1)))))))) -> b(a(a(c(c(a(c(a(x1)))))))) with rule a(c(c(x1'))) -> c(c(a(x1'))) at position [0,0,0] and matcher [x1' / c(a(x1))]
516.73/131.54	
516.73/131.54	b(a(a(c(c(a(c(a(x1)))))))) -> a(a(a(c(c(a(c(a(x1)))))))) with rule b(a(a(x1'))) -> a(a(a(x1'))) at position [] and matcher [x1' / c(c(a(c(a(x1)))))]
516.73/131.54	
516.73/131.54	a(a(a(c(c(a(c(a(x1)))))))) -> a(b(b(a(c(a(c(a(x1)))))))) with rule a(a(c(x1'))) -> b(b(a(x1'))) at position [0] and matcher [x1' / c(a(c(a(x1))))]
516.73/131.54	
516.73/131.54	a(b(b(a(c(a(c(a(x1)))))))) -> b(b(a(a(c(a(c(a(x1)))))))) with rule a(b(b(x1'))) -> b(b(a(x1'))) at position [] and matcher [x1' / a(c(a(c(a(x1)))))]
516.73/131.54	
516.73/131.54	Now an instance of the first term with Matcher [ ] occurs in the last term at position [].
516.73/131.54	
516.73/131.54	Context: []
516.73/131.54	
516.73/131.54	Therefore, the relative TRS problem does not terminate.
516.73/131.54	----------------------------------------
516.73/131.54	
516.73/131.54	(2)
516.73/131.54	NO
516.82/131.59	EOF