3.15/1.63	YES
3.15/1.65	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.15/1.65	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.15/1.65	
3.15/1.65	
3.15/1.65	Termination w.r.t. Q of the given QTRS could be proven:
3.15/1.65	
3.15/1.65	(0) QTRS
3.15/1.65	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.15/1.65	(2) QTRS
3.15/1.65	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.15/1.65	(4) YES
3.15/1.65	
3.15/1.65	
3.15/1.65	----------------------------------------
3.15/1.65	
3.15/1.65	(0)
3.15/1.65	Obligation:
3.15/1.65	Q restricted rewrite system:
3.15/1.65	The TRS R consists of the following rules:
3.15/1.65	
3.15/1.65	   b(c(a(b(b(c(x1)))))) -> a(b(c(b(b(c(a(x1)))))))
3.15/1.65	
3.15/1.65	Q is empty.
3.15/1.65	
3.15/1.65	----------------------------------------
3.15/1.65	
3.15/1.65	(1) QTRS Reverse (EQUIVALENT)
3.15/1.65	We applied the QTRS Reverse Processor [REVERSE].
3.15/1.65	----------------------------------------
3.15/1.65	
3.15/1.65	(2)
3.15/1.65	Obligation:
3.15/1.65	Q restricted rewrite system:
3.15/1.65	The TRS R consists of the following rules:
3.15/1.65	
3.15/1.65	   c(b(b(a(c(b(x1)))))) -> a(c(b(b(c(b(a(x1)))))))
3.15/1.65	
3.15/1.65	Q is empty.
3.15/1.65	
3.15/1.65	----------------------------------------
3.15/1.65	
3.15/1.65	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
3.15/1.65	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 0. This implies Q-termination of R.
3.15/1.65	The following rules were used to construct the certificate:
3.15/1.65	
3.15/1.65	   c(b(b(a(c(b(x1)))))) -> a(c(b(b(c(b(a(x1)))))))
3.15/1.65	
3.15/1.65	The certificate found is represented by the following graph.
3.15/1.65	The certificate consists of the following enumerated nodes:
3.15/1.65	15, 16, 17, 18, 19, 20, 21, 22
3.15/1.65	
3.15/1.65	Node 15 is start node and node 16 is final node.
3.15/1.65	
3.15/1.65	Those nodes are connected through the following edges:
3.15/1.65	
3.15/1.65	* 15 to 17 labelled a_1(0)* 16 to 16 labelled #_1(0)* 17 to 18 labelled c_1(0)* 18 to 19 labelled b_1(0)* 19 to 20 labelled b_1(0)* 20 to 21 labelled c_1(0)* 21 to 22 labelled b_1(0)* 22 to 16 labelled a_1(0)
3.15/1.65	
3.15/1.65	
3.15/1.65	----------------------------------------
3.15/1.65	
3.15/1.65	(4)
3.15/1.65	YES
3.15/1.68	EOF