4.00/1.81	YES
4.02/1.84	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.02/1.84	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.02/1.84	
4.02/1.84	
4.02/1.84	Termination w.r.t. Q of the given QTRS could be proven:
4.02/1.84	
4.02/1.84	(0) QTRS
4.02/1.84	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.02/1.84	(2) QTRS
4.02/1.84	(3) Strip Symbols Proof [SOUND, 0 ms]
4.02/1.84	(4) QTRS
4.02/1.84	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
4.02/1.84	(6) YES
4.02/1.84	
4.02/1.84	
4.02/1.84	----------------------------------------
4.02/1.84	
4.02/1.84	(0)
4.02/1.84	Obligation:
4.02/1.84	Q restricted rewrite system:
4.02/1.84	The TRS R consists of the following rules:
4.02/1.84	
4.02/1.84	   a(b(b(a(a(a(a(a(a(a(x1)))))))))) -> a(a(a(a(a(a(a(a(b(b(a(b(b(x1)))))))))))))
4.02/1.84	
4.02/1.84	Q is empty.
4.02/1.84	
4.02/1.84	----------------------------------------
4.02/1.84	
4.02/1.84	(1) QTRS Reverse (EQUIVALENT)
4.02/1.84	We applied the QTRS Reverse Processor [REVERSE].
4.02/1.84	----------------------------------------
4.02/1.84	
4.02/1.84	(2)
4.02/1.84	Obligation:
4.02/1.84	Q restricted rewrite system:
4.02/1.84	The TRS R consists of the following rules:
4.02/1.84	
4.02/1.84	   a(a(a(a(a(a(a(b(b(a(x1)))))))))) -> b(b(a(b(b(a(a(a(a(a(a(a(a(x1)))))))))))))
4.02/1.84	
4.02/1.84	Q is empty.
4.02/1.84	
4.02/1.84	----------------------------------------
4.02/1.84	
4.02/1.84	(3) Strip Symbols Proof (SOUND)
4.02/1.84	We were given the following TRS:
4.02/1.84	
4.02/1.84	   a(a(a(a(a(a(a(b(b(a(x1)))))))))) -> b(b(a(b(b(a(a(a(a(a(a(a(a(x1)))))))))))))
4.02/1.84	
4.02/1.84	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.02/1.84	
4.02/1.84	   a(a(a(a(a(a(a(b(b(x))))))))) -> b(b(a(b(b(a(a(a(a(a(a(a(x))))))))))))
4.02/1.84	
4.02/1.84	----------------------------------------
4.02/1.84	
4.02/1.84	(4)
4.02/1.84	Obligation:
4.02/1.84	Q restricted rewrite system:
4.02/1.84	The TRS R consists of the following rules:
4.02/1.84	
4.02/1.84	   a(a(a(a(a(a(a(b(b(x))))))))) -> b(b(a(b(b(a(a(a(a(a(a(a(x))))))))))))
4.02/1.84	
4.02/1.84	Q is empty.
4.02/1.84	
4.02/1.84	----------------------------------------
4.02/1.84	
4.02/1.84	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.02/1.84	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.02/1.84	The following rules were used to construct the certificate:
4.02/1.84	
4.02/1.84	   a(a(a(a(a(a(a(b(b(x))))))))) -> b(b(a(b(b(a(a(a(a(a(a(a(x))))))))))))
4.02/1.84	
4.02/1.84	The certificate found is represented by the following graph.
4.02/1.84	The certificate consists of the following enumerated nodes:
4.02/1.84	508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531
4.02/1.84	
4.02/1.84	Node 508 is start node and node 509 is final node.
4.02/1.84	
4.02/1.84	Those nodes are connected through the following edges:
4.02/1.84	
4.02/1.84	* 508 to 510 labelled b_1(0)* 509 to 509 labelled #_1(0)* 510 to 511 labelled b_1(0)* 511 to 512 labelled a_1(0)* 512 to 513 labelled b_1(0)* 513 to 514 labelled b_1(0)* 514 to 515 labelled a_1(0)* 514 to 521 labelled b_1(1)* 515 to 516 labelled a_1(0)* 515 to 521 labelled b_1(1)* 516 to 517 labelled a_1(0)* 516 to 521 labelled b_1(1)* 517 to 518 labelled a_1(0)* 517 to 521 labelled b_1(1)* 518 to 519 labelled a_1(0)* 518 to 521 labelled b_1(1)* 519 to 520 labelled a_1(0)* 519 to 521 labelled b_1(1)* 520 to 509 labelled a_1(0)* 520 to 521 labelled b_1(1)* 521 to 522 labelled b_1(1)* 522 to 523 labelled a_1(1)* 523 to 524 labelled b_1(1)* 524 to 525 labelled b_1(1)* 525 to 526 labelled a_1(1)* 525 to 521 labelled b_1(1)* 526 to 527 labelled a_1(1)* 526 to 521 labelled b_1(1)* 527 to 528 labelled a_1(1)* 527 to 521 labelled b_1(1)* 528 to 529 labelled a_1(1)* 528 to 521 labelled b_1(1)* 529 to 530 labelled a_1(1)* 529 to 521 labelled b_1(1)* 530 to 531 labelled a_1(1)* 530 to 521 labelled b_1(1)* 531 to 509 labelled a_1(1)* 531 to 521 labelled b_1(1)
4.02/1.84	
4.02/1.84	
4.02/1.84	----------------------------------------
4.02/1.84	
4.02/1.84	(6)
4.02/1.84	YES
4.02/1.87	EOF