3.98/1.83	YES
4.10/1.87	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.10/1.87	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.10/1.87	
4.10/1.87	
4.10/1.87	Termination w.r.t. Q of the given QTRS could be proven:
4.10/1.87	
4.10/1.87	(0) QTRS
4.10/1.87	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.10/1.87	(2) QTRS
4.10/1.87	(3) Strip Symbols Proof [SOUND, 0 ms]
4.10/1.87	(4) QTRS
4.10/1.87	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
4.10/1.87	(6) YES
4.10/1.87	
4.10/1.87	
4.10/1.87	----------------------------------------
4.10/1.87	
4.10/1.87	(0)
4.10/1.87	Obligation:
4.10/1.87	Q restricted rewrite system:
4.10/1.87	The TRS R consists of the following rules:
4.10/1.87	
4.10/1.87	   a(b(a(a(a(a(a(a(x1)))))))) -> a(a(a(a(a(a(a(b(a(a(a(b(x1))))))))))))
4.10/1.87	
4.10/1.87	Q is empty.
4.10/1.87	
4.10/1.87	----------------------------------------
4.10/1.87	
4.10/1.87	(1) QTRS Reverse (EQUIVALENT)
4.10/1.87	We applied the QTRS Reverse Processor [REVERSE].
4.10/1.87	----------------------------------------
4.10/1.87	
4.10/1.87	(2)
4.10/1.87	Obligation:
4.10/1.87	Q restricted rewrite system:
4.10/1.87	The TRS R consists of the following rules:
4.10/1.87	
4.10/1.87	   a(a(a(a(a(a(b(a(x1)))))))) -> b(a(a(a(b(a(a(a(a(a(a(a(x1))))))))))))
4.10/1.87	
4.10/1.87	Q is empty.
4.10/1.87	
4.10/1.87	----------------------------------------
4.10/1.87	
4.10/1.87	(3) Strip Symbols Proof (SOUND)
4.10/1.87	We were given the following TRS:
4.10/1.87	
4.10/1.87	   a(a(a(a(a(a(b(a(x1)))))))) -> b(a(a(a(b(a(a(a(a(a(a(a(x1))))))))))))
4.10/1.87	
4.10/1.87	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.10/1.87	
4.10/1.87	   a(a(a(a(a(a(b(x))))))) -> b(a(a(a(b(a(a(a(a(a(a(x)))))))))))
4.10/1.87	
4.10/1.87	----------------------------------------
4.10/1.87	
4.10/1.87	(4)
4.10/1.87	Obligation:
4.10/1.87	Q restricted rewrite system:
4.10/1.87	The TRS R consists of the following rules:
4.10/1.87	
4.10/1.87	   a(a(a(a(a(a(b(x))))))) -> b(a(a(a(b(a(a(a(a(a(a(x)))))))))))
4.10/1.87	
4.10/1.87	Q is empty.
4.10/1.87	
4.10/1.87	----------------------------------------
4.10/1.87	
4.10/1.87	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.10/1.87	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.10/1.87	The following rules were used to construct the certificate:
4.10/1.87	
4.10/1.87	   a(a(a(a(a(a(b(x))))))) -> b(a(a(a(b(a(a(a(a(a(a(x)))))))))))
4.10/1.87	
4.10/1.87	The certificate found is represented by the following graph.
4.10/1.87	The certificate consists of the following enumerated nodes:
4.10/1.87	453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474
4.10/1.87	
4.10/1.87	Node 453 is start node and node 454 is final node.
4.10/1.87	
4.10/1.87	Those nodes are connected through the following edges:
4.10/1.87	
4.10/1.87	* 453 to 455 labelled b_1(0)* 454 to 454 labelled #_1(0)* 455 to 456 labelled a_1(0)* 456 to 457 labelled a_1(0)* 457 to 458 labelled a_1(0)* 458 to 459 labelled b_1(0)* 459 to 460 labelled a_1(0)* 459 to 465 labelled b_1(1)* 460 to 461 labelled a_1(0)* 460 to 465 labelled b_1(1)* 461 to 462 labelled a_1(0)* 461 to 465 labelled b_1(1)* 462 to 463 labelled a_1(0)* 462 to 465 labelled b_1(1)* 463 to 464 labelled a_1(0)* 463 to 465 labelled b_1(1)* 464 to 454 labelled a_1(0)* 464 to 465 labelled b_1(1)* 465 to 466 labelled a_1(1)* 466 to 467 labelled a_1(1)* 467 to 468 labelled a_1(1)* 468 to 469 labelled b_1(1)* 469 to 470 labelled a_1(1)* 469 to 465 labelled b_1(1)* 470 to 471 labelled a_1(1)* 470 to 465 labelled b_1(1)* 471 to 472 labelled a_1(1)* 471 to 465 labelled b_1(1)* 472 to 473 labelled a_1(1)* 472 to 465 labelled b_1(1)* 473 to 474 labelled a_1(1)* 473 to 465 labelled b_1(1)* 474 to 454 labelled a_1(1)* 474 to 465 labelled b_1(1)
4.10/1.87	
4.10/1.87	
4.10/1.87	----------------------------------------
4.10/1.87	
4.10/1.87	(6)
4.10/1.87	YES
4.10/1.89	EOF