4.07/1.75	YES
4.07/1.76	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.07/1.76	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.07/1.76	
4.07/1.76	
4.07/1.76	Termination w.r.t. Q of the given QTRS could be proven:
4.07/1.76	
4.07/1.76	(0) QTRS
4.07/1.76	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.07/1.76	(2) QTRS
4.07/1.76	(3) Strip Symbols Proof [SOUND, 0 ms]
4.07/1.76	(4) QTRS
4.07/1.76	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
4.07/1.76	(6) YES
4.07/1.76	
4.07/1.76	
4.07/1.76	----------------------------------------
4.07/1.76	
4.07/1.76	(0)
4.07/1.76	Obligation:
4.07/1.76	Q restricted rewrite system:
4.07/1.76	The TRS R consists of the following rules:
4.07/1.76	
4.07/1.76	   a(b(a(a(a(a(a(x1))))))) -> a(a(a(a(a(a(b(a(b(a(a(b(a(b(x1))))))))))))))
4.07/1.76	
4.07/1.76	Q is empty.
4.07/1.76	
4.07/1.76	----------------------------------------
4.07/1.76	
4.07/1.76	(1) QTRS Reverse (EQUIVALENT)
4.07/1.76	We applied the QTRS Reverse Processor [REVERSE].
4.07/1.76	----------------------------------------
4.07/1.76	
4.07/1.76	(2)
4.07/1.76	Obligation:
4.07/1.76	Q restricted rewrite system:
4.07/1.76	The TRS R consists of the following rules:
4.07/1.76	
4.07/1.76	   a(a(a(a(a(b(a(x1))))))) -> b(a(b(a(a(b(a(b(a(a(a(a(a(a(x1))))))))))))))
4.07/1.76	
4.07/1.76	Q is empty.
4.07/1.76	
4.07/1.76	----------------------------------------
4.07/1.76	
4.07/1.76	(3) Strip Symbols Proof (SOUND)
4.07/1.76	We were given the following TRS:
4.07/1.76	
4.07/1.76	   a(a(a(a(a(b(a(x1))))))) -> b(a(b(a(a(b(a(b(a(a(a(a(a(a(x1))))))))))))))
4.07/1.76	
4.07/1.76	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.07/1.76	
4.07/1.76	   a(a(a(a(a(b(x)))))) -> b(a(b(a(a(b(a(b(a(a(a(a(a(x)))))))))))))
4.07/1.76	
4.07/1.76	----------------------------------------
4.07/1.76	
4.07/1.76	(4)
4.07/1.76	Obligation:
4.07/1.76	Q restricted rewrite system:
4.07/1.76	The TRS R consists of the following rules:
4.07/1.76	
4.07/1.76	   a(a(a(a(a(b(x)))))) -> b(a(b(a(a(b(a(b(a(a(a(a(a(x)))))))))))))
4.07/1.76	
4.07/1.76	Q is empty.
4.07/1.76	
4.07/1.76	----------------------------------------
4.07/1.76	
4.07/1.76	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.07/1.76	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.07/1.76	The following rules were used to construct the certificate:
4.07/1.76	
4.07/1.76	   a(a(a(a(a(b(x)))))) -> b(a(b(a(a(b(a(b(a(a(a(a(a(x)))))))))))))
4.07/1.76	
4.07/1.76	The certificate found is represented by the following graph.
4.07/1.76	The certificate consists of the following enumerated nodes:
4.07/1.76	486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511
4.07/1.76	
4.07/1.76	Node 486 is start node and node 487 is final node.
4.07/1.76	
4.07/1.76	Those nodes are connected through the following edges:
4.07/1.76	
4.07/1.76	* 486 to 488 labelled b_1(0)* 487 to 487 labelled #_1(0)* 488 to 489 labelled a_1(0)* 489 to 490 labelled b_1(0)* 490 to 491 labelled a_1(0)* 491 to 492 labelled a_1(0)* 492 to 493 labelled b_1(0)* 493 to 494 labelled a_1(0)* 494 to 495 labelled b_1(0)* 495 to 496 labelled a_1(0)* 495 to 500 labelled b_1(1)* 496 to 497 labelled a_1(0)* 496 to 500 labelled b_1(1)* 497 to 498 labelled a_1(0)* 497 to 500 labelled b_1(1)* 498 to 499 labelled a_1(0)* 498 to 500 labelled b_1(1)* 499 to 487 labelled a_1(0)* 499 to 500 labelled b_1(1)* 500 to 501 labelled a_1(1)* 501 to 502 labelled b_1(1)* 502 to 503 labelled a_1(1)* 503 to 504 labelled a_1(1)* 504 to 505 labelled b_1(1)* 505 to 506 labelled a_1(1)* 506 to 507 labelled b_1(1)* 507 to 508 labelled a_1(1)* 507 to 500 labelled b_1(1)* 508 to 509 labelled a_1(1)* 508 to 500 labelled b_1(1)* 509 to 510 labelled a_1(1)* 509 to 500 labelled b_1(1)* 510 to 511 labelled a_1(1)* 510 to 500 labelled b_1(1)* 511 to 487 labelled a_1(1)* 511 to 500 labelled b_1(1)
4.07/1.76	
4.07/1.76	
4.07/1.76	----------------------------------------
4.07/1.76	
4.07/1.76	(6)
4.07/1.76	YES
4.12/1.79	EOF