5.16/2.14	YES
5.35/2.18	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
5.35/2.18	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.35/2.18	
5.35/2.18	
5.35/2.18	Termination w.r.t. Q of the given QTRS could be proven:
5.35/2.18	
5.35/2.18	(0) QTRS
5.35/2.18	(1) QTRS Reverse [EQUIVALENT, 0 ms]
5.35/2.18	(2) QTRS
5.35/2.18	(3) QTRSRRRProof [EQUIVALENT, 13 ms]
5.35/2.18	(4) QTRS
5.35/2.18	(5) RisEmptyProof [EQUIVALENT, 0 ms]
5.35/2.18	(6) YES
5.35/2.18	
5.35/2.18	
5.35/2.18	----------------------------------------
5.35/2.18	
5.35/2.18	(0)
5.35/2.18	Obligation:
5.35/2.18	Q restricted rewrite system:
5.35/2.18	The TRS R consists of the following rules:
5.35/2.18	
5.35/2.18	   a(a(x1)) -> b(b(b(x1)))
5.35/2.18	   b(b(x1)) -> c(c(c(x1)))
5.35/2.18	   c(c(c(c(x1)))) -> a(b(x1))
5.35/2.18	
5.35/2.18	Q is empty.
5.35/2.18	
5.35/2.18	----------------------------------------
5.35/2.18	
5.35/2.18	(1) QTRS Reverse (EQUIVALENT)
5.35/2.18	We applied the QTRS Reverse Processor [REVERSE].
5.35/2.18	----------------------------------------
5.35/2.18	
5.35/2.18	(2)
5.35/2.18	Obligation:
5.35/2.18	Q restricted rewrite system:
5.35/2.18	The TRS R consists of the following rules:
5.35/2.18	
5.35/2.18	   a(a(x1)) -> b(b(b(x1)))
5.35/2.18	   b(b(x1)) -> c(c(c(x1)))
5.35/2.18	   c(c(c(c(x1)))) -> b(a(x1))
5.35/2.18	
5.35/2.18	Q is empty.
5.35/2.18	
5.35/2.18	----------------------------------------
5.35/2.18	
5.35/2.18	(3) QTRSRRRProof (EQUIVALENT)
5.35/2.18	Used ordering:
5.35/2.18	Polynomial interpretation [POLO]:
5.35/2.18	
5.35/2.18	   POL(a(x_1)) = 26 + x_1
5.35/2.18	   POL(b(x_1)) = 17 + x_1
5.35/2.18	   POL(c(x_1)) = 11 + x_1
5.35/2.18	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
5.35/2.18	
5.35/2.18	   a(a(x1)) -> b(b(b(x1)))
5.35/2.18	   b(b(x1)) -> c(c(c(x1)))
5.35/2.18	   c(c(c(c(x1)))) -> b(a(x1))
5.35/2.18	
5.35/2.18	
5.35/2.18	
5.35/2.18	
5.35/2.18	----------------------------------------
5.35/2.18	
5.35/2.18	(4)
5.35/2.18	Obligation:
5.35/2.18	Q restricted rewrite system:
5.35/2.18	R is empty.
5.35/2.18	Q is empty.
5.35/2.18	
5.35/2.18	----------------------------------------
5.35/2.18	
5.35/2.18	(5) RisEmptyProof (EQUIVALENT)
5.35/2.18	The TRS R is empty. Hence, termination is trivially proven.
5.35/2.18	----------------------------------------
5.35/2.18	
5.35/2.18	(6)
5.35/2.18	YES
5.35/2.23	EOF