3.51/1.69	YES
3.72/1.73	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.72/1.73	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.72/1.73	
3.72/1.73	
3.72/1.73	Termination w.r.t. Q of the given QTRS could be proven:
3.72/1.73	
3.72/1.73	(0) QTRS
3.72/1.73	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.72/1.73	(2) QTRS
3.72/1.73	(3) Strip Symbols Proof [SOUND, 0 ms]
3.72/1.73	(4) QTRS
3.72/1.73	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.72/1.73	(6) YES
3.72/1.73	
3.72/1.73	
3.72/1.73	----------------------------------------
3.72/1.73	
3.72/1.73	(0)
3.72/1.73	Obligation:
3.72/1.73	Q restricted rewrite system:
3.72/1.73	The TRS R consists of the following rules:
3.72/1.73	
3.72/1.73	   a(b(b(a(a(a(a(a(a(a(x1)))))))))) -> a(a(a(a(a(a(a(a(b(b(a(a(b(b(x1))))))))))))))
3.72/1.73	
3.72/1.73	Q is empty.
3.72/1.73	
3.72/1.73	----------------------------------------
3.72/1.73	
3.72/1.73	(1) QTRS Reverse (EQUIVALENT)
3.72/1.73	We applied the QTRS Reverse Processor [REVERSE].
3.72/1.73	----------------------------------------
3.72/1.73	
3.72/1.73	(2)
3.72/1.73	Obligation:
3.72/1.73	Q restricted rewrite system:
3.72/1.73	The TRS R consists of the following rules:
3.72/1.73	
3.72/1.73	   a(a(a(a(a(a(a(b(b(a(x1)))))))))) -> b(b(a(a(b(b(a(a(a(a(a(a(a(a(x1))))))))))))))
3.72/1.73	
3.72/1.73	Q is empty.
3.72/1.73	
3.72/1.73	----------------------------------------
3.72/1.73	
3.72/1.73	(3) Strip Symbols Proof (SOUND)
3.72/1.73	We were given the following TRS:
3.72/1.73	
3.72/1.73	   a(a(a(a(a(a(a(b(b(a(x1)))))))))) -> b(b(a(a(b(b(a(a(a(a(a(a(a(a(x1))))))))))))))
3.72/1.73	
3.72/1.73	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.72/1.73	
3.72/1.73	   a(a(a(a(a(a(a(b(b(x))))))))) -> b(b(a(a(b(b(a(a(a(a(a(a(a(x)))))))))))))
3.72/1.73	
3.72/1.73	----------------------------------------
3.72/1.73	
3.72/1.73	(4)
3.72/1.73	Obligation:
3.72/1.73	Q restricted rewrite system:
3.72/1.73	The TRS R consists of the following rules:
3.72/1.73	
3.72/1.73	   a(a(a(a(a(a(a(b(b(x))))))))) -> b(b(a(a(b(b(a(a(a(a(a(a(a(x)))))))))))))
3.72/1.73	
3.72/1.73	Q is empty.
3.72/1.73	
3.72/1.73	----------------------------------------
3.72/1.73	
3.72/1.73	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.72/1.73	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.72/1.73	The following rules were used to construct the certificate:
3.72/1.73	
3.72/1.73	   a(a(a(a(a(a(a(b(b(x))))))))) -> b(b(a(a(b(b(a(a(a(a(a(a(a(x)))))))))))))
3.72/1.73	
3.72/1.73	The certificate found is represented by the following graph.
3.72/1.73	The certificate consists of the following enumerated nodes:
3.72/1.73	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, 512
3.72/1.73	
3.72/1.73	Node 487 is start node and node 488 is final node.
3.72/1.73	
3.72/1.73	Those nodes are connected through the following edges:
3.72/1.73	
3.72/1.73	* 487 to 489 labelled b_1(0)* 488 to 488 labelled #_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 b_1(0)* 494 to 495 labelled a_1(0)* 494 to 501 labelled b_1(1)* 495 to 496 labelled a_1(0)* 495 to 501 labelled b_1(1)* 496 to 497 labelled a_1(0)* 496 to 501 labelled b_1(1)* 497 to 498 labelled a_1(0)* 497 to 501 labelled b_1(1)* 498 to 499 labelled a_1(0)* 498 to 501 labelled b_1(1)* 499 to 500 labelled a_1(0)* 499 to 501 labelled b_1(1)* 500 to 488 labelled a_1(0)* 500 to 501 labelled b_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 b_1(1)* 506 to 507 labelled a_1(1)* 506 to 501 labelled b_1(1)* 507 to 508 labelled a_1(1)* 507 to 501 labelled b_1(1)* 508 to 509 labelled a_1(1)* 508 to 501 labelled b_1(1)* 509 to 510 labelled a_1(1)* 509 to 501 labelled b_1(1)* 510 to 511 labelled a_1(1)* 510 to 501 labelled b_1(1)* 511 to 512 labelled a_1(1)* 511 to 501 labelled b_1(1)* 512 to 488 labelled a_1(1)* 512 to 501 labelled b_1(1)
3.72/1.73	
3.72/1.73	
3.72/1.73	----------------------------------------
3.72/1.73	
3.72/1.73	(6)
3.72/1.73	YES
3.75/2.44	EOF