3.99/1.80	YES
4.09/1.81	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
4.09/1.81	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.09/1.81	
4.09/1.81	
4.09/1.81	Termination w.r.t. Q of the given QTRS could be proven:
4.09/1.81	
4.09/1.81	(0) QTRS
4.09/1.81	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.09/1.81	(2) QTRS
4.09/1.81	(3) Strip Symbols Proof [SOUND, 0 ms]
4.09/1.81	(4) QTRS
4.09/1.81	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 2 ms]
4.09/1.81	(6) YES
4.09/1.81	
4.09/1.81	
4.09/1.81	----------------------------------------
4.09/1.81	
4.09/1.81	(0)
4.09/1.81	Obligation:
4.09/1.81	Q restricted rewrite system:
4.09/1.81	The TRS R consists of the following rules:
4.09/1.81	
4.09/1.81	   a(b(b(a(a(a(a(a(x1)))))))) -> a(a(a(a(a(a(b(b(a(b(b(x1)))))))))))
4.09/1.81	
4.09/1.81	Q is empty.
4.09/1.81	
4.09/1.81	----------------------------------------
4.09/1.81	
4.09/1.81	(1) QTRS Reverse (EQUIVALENT)
4.09/1.81	We applied the QTRS Reverse Processor [REVERSE].
4.09/1.81	----------------------------------------
4.09/1.81	
4.09/1.81	(2)
4.09/1.81	Obligation:
4.09/1.81	Q restricted rewrite system:
4.09/1.81	The TRS R consists of the following rules:
4.09/1.81	
4.09/1.81	   a(a(a(a(a(b(b(a(x1)))))))) -> b(b(a(b(b(a(a(a(a(a(a(x1)))))))))))
4.09/1.81	
4.09/1.81	Q is empty.
4.09/1.81	
4.09/1.81	----------------------------------------
4.09/1.81	
4.09/1.81	(3) Strip Symbols Proof (SOUND)
4.09/1.81	We were given the following TRS:
4.09/1.81	
4.09/1.81	   a(a(a(a(a(b(b(a(x1)))))))) -> b(b(a(b(b(a(a(a(a(a(a(x1)))))))))))
4.09/1.81	
4.09/1.81	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.09/1.81	
4.09/1.81	   a(a(a(a(a(b(b(x))))))) -> b(b(a(b(b(a(a(a(a(a(x))))))))))
4.09/1.81	
4.09/1.81	----------------------------------------
4.09/1.81	
4.09/1.81	(4)
4.09/1.81	Obligation:
4.09/1.81	Q restricted rewrite system:
4.09/1.81	The TRS R consists of the following rules:
4.09/1.81	
4.09/1.81	   a(a(a(a(a(b(b(x))))))) -> b(b(a(b(b(a(a(a(a(a(x))))))))))
4.09/1.81	
4.09/1.81	Q is empty.
4.09/1.81	
4.09/1.81	----------------------------------------
4.09/1.81	
4.09/1.81	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.09/1.81	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.09/1.81	The following rules were used to construct the certificate:
4.09/1.81	
4.09/1.81	   a(a(a(a(a(b(b(x))))))) -> b(b(a(b(b(a(a(a(a(a(x))))))))))
4.09/1.81	
4.09/1.81	The certificate found is represented by the following graph.
4.09/1.81	The certificate consists of the following enumerated nodes:
4.09/1.81	489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508
4.09/1.81	
4.09/1.81	Node 489 is start node and node 490 is final node.
4.09/1.81	
4.09/1.81	Those nodes are connected through the following edges:
4.09/1.81	
4.09/1.81	* 489 to 491 labelled b_1(0)* 490 to 490 labelled #_1(0)* 491 to 492 labelled b_1(0)* 492 to 493 labelled a_1(0)* 493 to 494 labelled b_1(0)* 494 to 495 labelled b_1(0)* 495 to 496 labelled a_1(0)* 495 to 500 labelled b_1(1)* 496 to 497 labelled a_1(0)* 496 to 500 labelled b_1(1)* 497 to 498 labelled a_1(0)* 497 to 500 labelled b_1(1)* 498 to 499 labelled a_1(0)* 498 to 500 labelled b_1(1)* 499 to 490 labelled a_1(0)* 499 to 500 labelled b_1(1)* 500 to 501 labelled b_1(1)* 501 to 502 labelled a_1(1)* 502 to 503 labelled b_1(1)* 503 to 504 labelled b_1(1)* 504 to 505 labelled a_1(1)* 504 to 500 labelled b_1(1)* 505 to 506 labelled a_1(1)* 505 to 500 labelled b_1(1)* 506 to 507 labelled a_1(1)* 506 to 500 labelled b_1(1)* 507 to 508 labelled a_1(1)* 507 to 500 labelled b_1(1)* 508 to 490 labelled a_1(1)* 508 to 500 labelled b_1(1)
4.09/1.81	
4.09/1.81	
4.09/1.81	----------------------------------------
4.09/1.81	
4.09/1.81	(6)
4.09/1.81	YES
4.16/1.86	EOF