3.47/1.67	YES
3.72/1.72	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.72/1.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.72/1.72	
3.72/1.72	
3.72/1.72	Termination w.r.t. Q of the given QTRS could be proven:
3.72/1.72	
3.72/1.72	(0) QTRS
3.72/1.72	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.72/1.72	(2) QTRS
3.72/1.72	(3) Strip Symbols Proof [SOUND, 0 ms]
3.72/1.72	(4) QTRS
3.72/1.72	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.72/1.72	(6) YES
3.72/1.72	
3.72/1.72	
3.72/1.72	----------------------------------------
3.72/1.72	
3.72/1.72	(0)
3.72/1.72	Obligation:
3.72/1.72	Q restricted rewrite system:
3.72/1.72	The TRS R consists of the following rules:
3.72/1.72	
3.72/1.72	   a(b(a(a(a(a(a(a(a(x1))))))))) -> a(a(a(a(a(a(a(a(b(a(b(a(a(b(x1))))))))))))))
3.72/1.72	
3.72/1.72	Q is empty.
3.72/1.72	
3.72/1.72	----------------------------------------
3.72/1.72	
3.72/1.72	(1) QTRS Reverse (EQUIVALENT)
3.72/1.72	We applied the QTRS Reverse Processor [REVERSE].
3.72/1.72	----------------------------------------
3.72/1.72	
3.72/1.72	(2)
3.72/1.72	Obligation:
3.72/1.72	Q restricted rewrite system:
3.72/1.72	The TRS R consists of the following rules:
3.72/1.72	
3.72/1.72	   a(a(a(a(a(a(a(b(a(x1))))))))) -> b(a(a(b(a(b(a(a(a(a(a(a(a(a(x1))))))))))))))
3.72/1.72	
3.72/1.72	Q is empty.
3.72/1.72	
3.72/1.72	----------------------------------------
3.72/1.72	
3.72/1.72	(3) Strip Symbols Proof (SOUND)
3.72/1.72	We were given the following TRS:
3.72/1.72	
3.72/1.72	   a(a(a(a(a(a(a(b(a(x1))))))))) -> b(a(a(b(a(b(a(a(a(a(a(a(a(a(x1))))))))))))))
3.72/1.72	
3.72/1.72	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.72/1.72	
3.72/1.72	   a(a(a(a(a(a(a(b(x)))))))) -> b(a(a(b(a(b(a(a(a(a(a(a(a(x)))))))))))))
3.72/1.72	
3.72/1.72	----------------------------------------
3.72/1.72	
3.72/1.72	(4)
3.72/1.72	Obligation:
3.72/1.72	Q restricted rewrite system:
3.72/1.72	The TRS R consists of the following rules:
3.72/1.72	
3.72/1.72	   a(a(a(a(a(a(a(b(x)))))))) -> b(a(a(b(a(b(a(a(a(a(a(a(a(x)))))))))))))
3.72/1.72	
3.72/1.72	Q is empty.
3.72/1.72	
3.72/1.72	----------------------------------------
3.72/1.72	
3.72/1.72	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.72/1.72	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.72/1.72	The following rules were used to construct the certificate:
3.72/1.72	
3.72/1.72	   a(a(a(a(a(a(a(b(x)))))))) -> b(a(a(b(a(b(a(a(a(a(a(a(a(x)))))))))))))
3.72/1.72	
3.72/1.72	The certificate found is represented by the following graph.
3.72/1.72	The certificate consists of the following enumerated nodes:
3.72/1.72	397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422
3.72/1.72	
3.72/1.72	Node 397 is start node and node 398 is final node.
3.72/1.72	
3.72/1.72	Those nodes are connected through the following edges:
3.72/1.72	
3.72/1.72	* 397 to 399 labelled b_1(0)* 398 to 398 labelled #_1(0)* 399 to 400 labelled a_1(0)* 400 to 401 labelled a_1(0)* 401 to 402 labelled b_1(0)* 402 to 403 labelled a_1(0)* 403 to 404 labelled b_1(0)* 404 to 405 labelled a_1(0)* 404 to 411 labelled b_1(1)* 405 to 406 labelled a_1(0)* 405 to 411 labelled b_1(1)* 406 to 407 labelled a_1(0)* 406 to 411 labelled b_1(1)* 407 to 408 labelled a_1(0)* 407 to 411 labelled b_1(1)* 408 to 409 labelled a_1(0)* 408 to 411 labelled b_1(1)* 409 to 410 labelled a_1(0)* 409 to 411 labelled b_1(1)* 410 to 398 labelled a_1(0)* 410 to 411 labelled b_1(1)* 411 to 412 labelled a_1(1)* 412 to 413 labelled a_1(1)* 413 to 414 labelled b_1(1)* 414 to 415 labelled a_1(1)* 415 to 416 labelled b_1(1)* 416 to 417 labelled a_1(1)* 416 to 411 labelled b_1(1)* 417 to 418 labelled a_1(1)* 417 to 411 labelled b_1(1)* 418 to 419 labelled a_1(1)* 418 to 411 labelled b_1(1)* 419 to 420 labelled a_1(1)* 419 to 411 labelled b_1(1)* 420 to 421 labelled a_1(1)* 420 to 411 labelled b_1(1)* 421 to 422 labelled a_1(1)* 421 to 411 labelled b_1(1)* 422 to 398 labelled a_1(1)* 422 to 411 labelled b_1(1)
3.72/1.72	
3.72/1.72	
3.72/1.72	----------------------------------------
3.72/1.72	
3.72/1.72	(6)
3.72/1.72	YES
3.72/1.75	EOF