4.05/1.88	YES
4.05/1.89	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
4.05/1.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.05/1.89	
4.05/1.89	
4.05/1.89	Termination w.r.t. Q of the given QTRS could be proven:
4.05/1.89	
4.05/1.89	(0) QTRS
4.05/1.89	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.05/1.89	(2) QTRS
4.05/1.89	(3) Strip Symbols Proof [SOUND, 0 ms]
4.05/1.89	(4) QTRS
4.05/1.89	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 2 ms]
4.05/1.89	(6) YES
4.05/1.89	
4.05/1.89	
4.05/1.89	----------------------------------------
4.05/1.89	
4.05/1.89	(0)
4.05/1.89	Obligation:
4.05/1.89	Q restricted rewrite system:
4.05/1.89	The TRS R consists of the following rules:
4.05/1.89	
4.05/1.89	   a(b(a(b(a(b(a(a(b(a(b(a(x1)))))))))))) -> a(a(b(a(b(a(a(b(a(b(a(b(a(b(x1))))))))))))))
4.05/1.89	
4.05/1.89	Q is empty.
4.05/1.89	
4.05/1.89	----------------------------------------
4.05/1.89	
4.05/1.89	(1) QTRS Reverse (EQUIVALENT)
4.05/1.89	We applied the QTRS Reverse Processor [REVERSE].
4.05/1.89	----------------------------------------
4.05/1.89	
4.05/1.89	(2)
4.05/1.89	Obligation:
4.05/1.89	Q restricted rewrite system:
4.05/1.89	The TRS R consists of the following rules:
4.05/1.89	
4.05/1.89	   a(b(a(b(a(a(b(a(b(a(b(a(x1)))))))))))) -> b(a(b(a(b(a(b(a(a(b(a(b(a(a(x1))))))))))))))
4.05/1.89	
4.05/1.89	Q is empty.
4.05/1.89	
4.05/1.89	----------------------------------------
4.05/1.89	
4.05/1.89	(3) Strip Symbols Proof (SOUND)
4.05/1.89	We were given the following TRS:
4.05/1.89	
4.05/1.89	   a(b(a(b(a(a(b(a(b(a(b(a(x1)))))))))))) -> b(a(b(a(b(a(b(a(a(b(a(b(a(a(x1))))))))))))))
4.05/1.89	
4.05/1.89	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.05/1.89	
4.05/1.89	   a(b(a(b(a(a(b(a(b(a(b(x))))))))))) -> b(a(b(a(b(a(b(a(a(b(a(b(a(x)))))))))))))
4.05/1.89	
4.05/1.89	----------------------------------------
4.05/1.89	
4.05/1.89	(4)
4.05/1.89	Obligation:
4.05/1.89	Q restricted rewrite system:
4.05/1.89	The TRS R consists of the following rules:
4.05/1.89	
4.05/1.89	   a(b(a(b(a(a(b(a(b(a(b(x))))))))))) -> b(a(b(a(b(a(b(a(a(b(a(b(a(x)))))))))))))
4.05/1.89	
4.05/1.89	Q is empty.
4.05/1.89	
4.05/1.89	----------------------------------------
4.05/1.89	
4.05/1.89	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.05/1.89	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.05/1.89	The following rules were used to construct the certificate:
4.05/1.89	
4.05/1.89	   a(b(a(b(a(a(b(a(b(a(b(x))))))))))) -> b(a(b(a(b(a(b(a(a(b(a(b(a(x)))))))))))))
4.05/1.89	
4.05/1.89	The certificate found is represented by the following graph.
4.05/1.89	The certificate consists of the following enumerated nodes:
4.05/1.89	565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590
4.05/1.89	
4.05/1.89	Node 565 is start node and node 566 is final node.
4.05/1.89	
4.05/1.89	Those nodes are connected through the following edges:
4.05/1.89	
4.05/1.89	* 565 to 567 labelled b_1(0)* 566 to 566 labelled #_1(0)* 567 to 568 labelled a_1(0)* 568 to 569 labelled b_1(0)* 569 to 570 labelled a_1(0)* 569 to 579 labelled b_1(1)* 570 to 571 labelled b_1(0)* 571 to 572 labelled a_1(0)* 572 to 573 labelled b_1(0)* 573 to 574 labelled a_1(0)* 574 to 575 labelled a_1(0)* 574 to 579 labelled b_1(1)* 575 to 576 labelled b_1(0)* 576 to 577 labelled a_1(0)* 576 to 579 labelled b_1(1)* 577 to 578 labelled b_1(0)* 578 to 566 labelled a_1(0)* 578 to 579 labelled b_1(1)* 579 to 580 labelled a_1(1)* 580 to 581 labelled b_1(1)* 581 to 582 labelled a_1(1)* 581 to 579 labelled b_1(1)* 582 to 583 labelled b_1(1)* 583 to 584 labelled a_1(1)* 584 to 585 labelled b_1(1)* 585 to 586 labelled a_1(1)* 586 to 587 labelled a_1(1)* 586 to 579 labelled b_1(1)* 587 to 588 labelled b_1(1)* 588 to 589 labelled a_1(1)* 588 to 579 labelled b_1(1)* 589 to 590 labelled b_1(1)* 590 to 566 labelled a_1(1)* 590 to 579 labelled b_1(1)
4.05/1.89	
4.05/1.89	
4.05/1.89	----------------------------------------
4.05/1.89	
4.05/1.89	(6)
4.05/1.89	YES
4.29/1.95	EOF