3.96/1.95	YES
3.96/1.96	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.96/1.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.96/1.96	
3.96/1.96	
3.96/1.96	Termination w.r.t. Q of the given QTRS could be proven:
3.96/1.96	
3.96/1.96	(0) QTRS
3.96/1.96	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.96/1.96	(2) QTRS
3.96/1.96	(3) QTRSRRRProof [EQUIVALENT, 19 ms]
3.96/1.96	(4) QTRS
3.96/1.96	(5) RisEmptyProof [EQUIVALENT, 0 ms]
3.96/1.96	(6) YES
3.96/1.96	
3.96/1.96	
3.96/1.96	----------------------------------------
3.96/1.96	
3.96/1.96	(0)
3.96/1.96	Obligation:
3.96/1.96	Q restricted rewrite system:
3.96/1.96	The TRS R consists of the following rules:
3.96/1.96	
3.96/1.96	   a(x1) -> b(b(x1))
3.96/1.96	   b(b(b(x1))) -> a(x1)
3.96/1.96	
3.96/1.96	Q is empty.
3.96/1.96	
3.96/1.96	----------------------------------------
3.96/1.96	
3.96/1.96	(1) QTRS Reverse (EQUIVALENT)
3.96/1.96	We applied the QTRS Reverse Processor [REVERSE].
3.96/1.96	----------------------------------------
3.96/1.96	
3.96/1.96	(2)
3.96/1.96	Obligation:
3.96/1.96	Q restricted rewrite system:
3.96/1.96	The TRS R consists of the following rules:
3.96/1.96	
3.96/1.96	   a(x1) -> b(b(x1))
3.96/1.96	   b(b(b(x1))) -> a(x1)
3.96/1.96	
3.96/1.96	Q is empty.
3.96/1.96	
3.96/1.96	----------------------------------------
3.96/1.96	
3.96/1.96	(3) QTRSRRRProof (EQUIVALENT)
3.96/1.96	Used ordering:
3.96/1.96	Polynomial interpretation [POLO]:
3.96/1.96	
3.96/1.96	   POL(a(x_1)) = 5 + x_1
3.96/1.96	   POL(b(x_1)) = 2 + x_1
3.96/1.96	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.96/1.96	
3.96/1.96	   a(x1) -> b(b(x1))
3.96/1.96	   b(b(b(x1))) -> a(x1)
3.96/1.96	
3.96/1.96	
3.96/1.96	
3.96/1.96	
3.96/1.96	----------------------------------------
3.96/1.96	
3.96/1.96	(4)
3.96/1.96	Obligation:
3.96/1.96	Q restricted rewrite system:
3.96/1.96	R is empty.
3.96/1.96	Q is empty.
3.96/1.96	
3.96/1.96	----------------------------------------
3.96/1.96	
3.96/1.96	(5) RisEmptyProof (EQUIVALENT)
3.96/1.96	The TRS R is empty. Hence, termination is trivially proven.
3.96/1.96	----------------------------------------
3.96/1.96	
3.96/1.96	(6)
3.96/1.96	YES
4.27/1.99	EOF