4.19/1.83	YES
4.31/1.89	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.31/1.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.31/1.89	
4.31/1.89	
4.31/1.89	Termination w.r.t. Q of the given QTRS could be proven:
4.31/1.89	
4.31/1.89	(0) QTRS
4.31/1.89	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.31/1.89	(2) QTRS
4.31/1.89	(3) Strip Symbols Proof [SOUND, 0 ms]
4.31/1.89	(4) QTRS
4.31/1.89	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
4.31/1.89	(6) YES
4.31/1.89	
4.31/1.89	
4.31/1.89	----------------------------------------
4.31/1.89	
4.31/1.89	(0)
4.31/1.89	Obligation:
4.31/1.89	Q restricted rewrite system:
4.31/1.89	The TRS R consists of the following rules:
4.31/1.89	
4.31/1.89	   a(b(a(a(a(b(a(a(x1)))))))) -> a(a(a(b(a(a(a(b(a(b(a(a(a(b(x1))))))))))))))
4.31/1.89	
4.31/1.89	Q is empty.
4.31/1.89	
4.31/1.89	----------------------------------------
4.31/1.89	
4.31/1.89	(1) QTRS Reverse (EQUIVALENT)
4.31/1.89	We applied the QTRS Reverse Processor [REVERSE].
4.31/1.89	----------------------------------------
4.31/1.89	
4.31/1.89	(2)
4.31/1.89	Obligation:
4.31/1.89	Q restricted rewrite system:
4.31/1.89	The TRS R consists of the following rules:
4.31/1.89	
4.31/1.89	   a(a(b(a(a(a(b(a(x1)))))))) -> b(a(a(a(b(a(b(a(a(a(b(a(a(a(x1))))))))))))))
4.31/1.89	
4.31/1.89	Q is empty.
4.31/1.89	
4.31/1.89	----------------------------------------
4.31/1.89	
4.31/1.89	(3) Strip Symbols Proof (SOUND)
4.31/1.89	We were given the following TRS:
4.31/1.89	
4.31/1.89	   a(a(b(a(a(a(b(a(x1)))))))) -> b(a(a(a(b(a(b(a(a(a(b(a(a(a(x1))))))))))))))
4.31/1.89	
4.31/1.89	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.31/1.89	
4.31/1.89	   a(a(b(a(a(a(b(x))))))) -> b(a(a(a(b(a(b(a(a(a(b(a(a(x)))))))))))))
4.31/1.89	
4.31/1.89	----------------------------------------
4.31/1.89	
4.31/1.89	(4)
4.31/1.89	Obligation:
4.31/1.89	Q restricted rewrite system:
4.31/1.89	The TRS R consists of the following rules:
4.31/1.89	
4.31/1.89	   a(a(b(a(a(a(b(x))))))) -> b(a(a(a(b(a(b(a(a(a(b(a(a(x)))))))))))))
4.31/1.89	
4.31/1.89	Q is empty.
4.31/1.89	
4.31/1.89	----------------------------------------
4.31/1.89	
4.31/1.89	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.31/1.89	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.31/1.89	The following rules were used to construct the certificate:
4.31/1.89	
4.31/1.89	   a(a(b(a(a(a(b(x))))))) -> b(a(a(a(b(a(b(a(a(a(b(a(a(x)))))))))))))
4.31/1.89	
4.31/1.89	The certificate found is represented by the following graph.
4.31/1.89	The certificate consists of the following enumerated nodes:
4.31/1.89	587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612
4.31/1.89	
4.31/1.89	Node 587 is start node and node 588 is final node.
4.31/1.89	
4.31/1.89	Those nodes are connected through the following edges:
4.31/1.89	
4.31/1.89	* 587 to 589 labelled b_1(0)* 588 to 588 labelled #_1(0)* 589 to 590 labelled a_1(0)* 590 to 591 labelled a_1(0)* 591 to 592 labelled a_1(0)* 592 to 593 labelled b_1(0)* 593 to 594 labelled a_1(0)* 594 to 595 labelled b_1(0)* 595 to 596 labelled a_1(0)* 596 to 597 labelled a_1(0)* 596 to 601 labelled b_1(1)* 597 to 598 labelled a_1(0)* 598 to 599 labelled b_1(0)* 599 to 600 labelled a_1(0)* 599 to 601 labelled b_1(1)* 600 to 588 labelled a_1(0)* 600 to 601 labelled b_1(1)* 601 to 602 labelled a_1(1)* 602 to 603 labelled a_1(1)* 603 to 604 labelled a_1(1)* 604 to 605 labelled b_1(1)* 605 to 606 labelled a_1(1)* 606 to 607 labelled b_1(1)* 607 to 608 labelled a_1(1)* 608 to 609 labelled a_1(1)* 608 to 601 labelled b_1(1)* 609 to 610 labelled a_1(1)* 610 to 611 labelled b_1(1)* 611 to 612 labelled a_1(1)* 611 to 601 labelled b_1(1)* 612 to 588 labelled a_1(1)* 612 to 601 labelled b_1(1)
4.31/1.89	
4.31/1.89	
4.31/1.89	----------------------------------------
4.31/1.89	
4.31/1.89	(6)
4.31/1.89	YES
4.51/2.13	EOF