3.89/1.79	YES
3.89/1.80	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.89/1.80	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.89/1.80	
3.89/1.80	
3.89/1.80	Termination w.r.t. Q of the given QTRS could be proven:
3.89/1.80	
3.89/1.80	(0) QTRS
3.89/1.80	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.89/1.80	(2) QTRS
3.89/1.80	(3) Strip Symbols Proof [SOUND, 0 ms]
3.89/1.80	(4) QTRS
3.89/1.80	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.89/1.80	(6) YES
3.89/1.80	
3.89/1.80	
3.89/1.80	----------------------------------------
3.89/1.80	
3.89/1.80	(0)
3.89/1.80	Obligation:
3.89/1.80	Q restricted rewrite system:
3.89/1.80	The TRS R consists of the following rules:
3.89/1.80	
3.89/1.80	   a(b(a(b(a(a(b(a(a(b(a(x1))))))))))) -> a(a(b(a(a(b(a(a(b(a(b(a(b(x1)))))))))))))
3.89/1.80	
3.89/1.80	Q is empty.
3.89/1.80	
3.89/1.80	----------------------------------------
3.89/1.80	
3.89/1.80	(1) QTRS Reverse (EQUIVALENT)
3.89/1.80	We applied the QTRS Reverse Processor [REVERSE].
3.89/1.80	----------------------------------------
3.89/1.80	
3.89/1.80	(2)
3.89/1.80	Obligation:
3.89/1.80	Q restricted rewrite system:
3.89/1.80	The TRS R consists of the following rules:
3.89/1.80	
3.89/1.80	   a(b(a(a(b(a(a(b(a(b(a(x1))))))))))) -> b(a(b(a(b(a(a(b(a(a(b(a(a(x1)))))))))))))
3.89/1.80	
3.89/1.80	Q is empty.
3.89/1.80	
3.89/1.80	----------------------------------------
3.89/1.80	
3.89/1.80	(3) Strip Symbols Proof (SOUND)
3.89/1.80	We were given the following TRS:
3.89/1.80	
3.89/1.80	   a(b(a(a(b(a(a(b(a(b(a(x1))))))))))) -> b(a(b(a(b(a(a(b(a(a(b(a(a(x1)))))))))))))
3.89/1.80	
3.89/1.80	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.89/1.80	
3.89/1.80	   a(b(a(a(b(a(a(b(a(b(x)))))))))) -> b(a(b(a(b(a(a(b(a(a(b(a(x))))))))))))
3.89/1.80	
3.89/1.80	----------------------------------------
3.89/1.80	
3.89/1.80	(4)
3.89/1.80	Obligation:
3.89/1.80	Q restricted rewrite system:
3.89/1.80	The TRS R consists of the following rules:
3.89/1.80	
3.89/1.80	   a(b(a(a(b(a(a(b(a(b(x)))))))))) -> b(a(b(a(b(a(a(b(a(a(b(a(x))))))))))))
3.89/1.80	
3.89/1.80	Q is empty.
3.89/1.80	
3.89/1.80	----------------------------------------
3.89/1.80	
3.89/1.80	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.89/1.80	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.89/1.80	The following rules were used to construct the certificate:
3.89/1.80	
3.89/1.80	   a(b(a(a(b(a(a(b(a(b(x)))))))))) -> b(a(b(a(b(a(a(b(a(a(b(a(x))))))))))))
3.89/1.80	
3.89/1.80	The certificate found is represented by the following graph.
3.89/1.80	The certificate consists of the following enumerated nodes:
3.89/1.80	566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589
3.89/1.80	
3.89/1.80	Node 566 is start node and node 567 is final node.
3.89/1.80	
3.89/1.80	Those nodes are connected through the following edges:
3.89/1.80	
3.89/1.80	* 566 to 568 labelled b_1(0)* 567 to 567 labelled #_1(0)* 568 to 569 labelled a_1(0)* 569 to 570 labelled b_1(0)* 570 to 571 labelled a_1(0)* 570 to 579 labelled b_1(1)* 571 to 572 labelled b_1(0)* 572 to 573 labelled a_1(0)* 573 to 574 labelled a_1(0)* 573 to 579 labelled b_1(1)* 574 to 575 labelled b_1(0)* 575 to 576 labelled a_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 567 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 a_1(1)* 584 to 579 labelled b_1(1)* 585 to 586 labelled b_1(1)* 586 to 587 labelled a_1(1)* 587 to 588 labelled a_1(1)* 587 to 579 labelled b_1(1)* 588 to 589 labelled b_1(1)* 589 to 567 labelled a_1(1)* 589 to 579 labelled b_1(1)
3.89/1.80	
3.89/1.80	
3.89/1.80	----------------------------------------
3.89/1.80	
3.89/1.80	(6)
3.89/1.80	YES
3.89/1.84	EOF