3.73/1.84	YES
4.08/1.87	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
4.08/1.87	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.08/1.87	
4.08/1.87	
4.08/1.87	Termination w.r.t. Q of the given QTRS could be proven:
4.08/1.87	
4.08/1.87	(0) QTRS
4.08/1.87	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.08/1.87	(2) QTRS
4.08/1.87	(3) Strip Symbols Proof [SOUND, 0 ms]
4.08/1.87	(4) QTRS
4.08/1.87	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
4.08/1.87	(6) YES
4.08/1.87	
4.08/1.87	
4.08/1.87	----------------------------------------
4.08/1.87	
4.08/1.87	(0)
4.08/1.87	Obligation:
4.08/1.87	Q restricted rewrite system:
4.08/1.87	The TRS R consists of the following rules:
4.08/1.87	
4.08/1.87	   a(b(a(a(a(b(a(a(a(a(x1)))))))))) -> a(a(a(a(a(b(a(a(a(b(a(a(a(b(x1))))))))))))))
4.08/1.87	
4.08/1.87	Q is empty.
4.08/1.87	
4.08/1.87	----------------------------------------
4.08/1.87	
4.08/1.87	(1) QTRS Reverse (EQUIVALENT)
4.08/1.87	We applied the QTRS Reverse Processor [REVERSE].
4.08/1.87	----------------------------------------
4.08/1.87	
4.08/1.87	(2)
4.08/1.87	Obligation:
4.08/1.87	Q restricted rewrite system:
4.08/1.87	The TRS R consists of the following rules:
4.08/1.87	
4.08/1.87	   a(a(a(a(b(a(a(a(b(a(x1)))))))))) -> b(a(a(a(b(a(a(a(b(a(a(a(a(a(x1))))))))))))))
4.08/1.87	
4.08/1.87	Q is empty.
4.08/1.87	
4.08/1.87	----------------------------------------
4.08/1.87	
4.08/1.87	(3) Strip Symbols Proof (SOUND)
4.08/1.87	We were given the following TRS:
4.08/1.87	
4.08/1.87	   a(a(a(a(b(a(a(a(b(a(x1)))))))))) -> b(a(a(a(b(a(a(a(b(a(a(a(a(a(x1))))))))))))))
4.08/1.87	
4.08/1.87	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.08/1.87	
4.08/1.87	   a(a(a(a(b(a(a(a(b(x))))))))) -> b(a(a(a(b(a(a(a(b(a(a(a(a(x)))))))))))))
4.08/1.87	
4.08/1.87	----------------------------------------
4.08/1.87	
4.08/1.87	(4)
4.08/1.87	Obligation:
4.08/1.87	Q restricted rewrite system:
4.08/1.87	The TRS R consists of the following rules:
4.08/1.87	
4.08/1.87	   a(a(a(a(b(a(a(a(b(x))))))))) -> b(a(a(a(b(a(a(a(b(a(a(a(a(x)))))))))))))
4.08/1.87	
4.08/1.87	Q is empty.
4.08/1.87	
4.08/1.87	----------------------------------------
4.08/1.87	
4.08/1.87	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.08/1.87	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.08/1.87	The following rules were used to construct the certificate:
4.08/1.87	
4.08/1.87	   a(a(a(a(b(a(a(a(b(x))))))))) -> b(a(a(a(b(a(a(a(b(a(a(a(a(x)))))))))))))
4.08/1.87	
4.08/1.87	The certificate found is represented by the following graph.
4.08/1.87	The certificate consists of the following enumerated nodes:
4.08/1.87	549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574
4.08/1.87	
4.08/1.87	Node 549 is start node and node 550 is final node.
4.08/1.87	
4.08/1.87	Those nodes are connected through the following edges:
4.08/1.87	
4.08/1.87	* 549 to 551 labelled b_1(0)* 550 to 550 labelled #_1(0)* 551 to 552 labelled a_1(0)* 552 to 553 labelled a_1(0)* 553 to 554 labelled a_1(0)* 554 to 555 labelled b_1(0)* 555 to 556 labelled a_1(0)* 556 to 557 labelled a_1(0)* 557 to 558 labelled a_1(0)* 558 to 559 labelled b_1(0)* 559 to 560 labelled a_1(0)* 559 to 563 labelled b_1(1)* 560 to 561 labelled a_1(0)* 560 to 563 labelled b_1(1)* 561 to 562 labelled a_1(0)* 561 to 563 labelled b_1(1)* 562 to 550 labelled a_1(0)* 562 to 563 labelled b_1(1)* 563 to 564 labelled a_1(1)* 564 to 565 labelled a_1(1)* 565 to 566 labelled a_1(1)* 566 to 567 labelled b_1(1)* 567 to 568 labelled a_1(1)* 568 to 569 labelled a_1(1)* 569 to 570 labelled a_1(1)* 570 to 571 labelled b_1(1)* 571 to 572 labelled a_1(1)* 571 to 563 labelled b_1(1)* 572 to 573 labelled a_1(1)* 572 to 563 labelled b_1(1)* 573 to 574 labelled a_1(1)* 573 to 563 labelled b_1(1)* 574 to 550 labelled a_1(1)* 574 to 563 labelled b_1(1)
4.08/1.87	
4.08/1.87	
4.08/1.87	----------------------------------------
4.08/1.87	
4.08/1.87	(6)
4.08/1.87	YES
4.17/1.90	EOF