4.14/1.81	YES
4.14/1.82	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
4.14/1.82	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.14/1.82	
4.14/1.82	
4.14/1.82	Termination w.r.t. Q of the given QTRS could be proven:
4.14/1.82	
4.14/1.82	(0) QTRS
4.14/1.82	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.14/1.82	(2) QTRS
4.14/1.82	(3) Strip Symbols Proof [SOUND, 0 ms]
4.14/1.82	(4) QTRS
4.14/1.82	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 2 ms]
4.14/1.82	(6) YES
4.14/1.82	
4.14/1.82	
4.14/1.82	----------------------------------------
4.14/1.82	
4.14/1.82	(0)
4.14/1.82	Obligation:
4.14/1.82	Q restricted rewrite system:
4.14/1.82	The TRS R consists of the following rules:
4.14/1.82	
4.14/1.82	   a(b(a(a(b(a(a(a(a(x1))))))))) -> a(a(a(a(a(b(a(a(b(a(a(b(x1))))))))))))
4.14/1.82	
4.14/1.82	Q is empty.
4.14/1.82	
4.14/1.82	----------------------------------------
4.14/1.82	
4.14/1.82	(1) QTRS Reverse (EQUIVALENT)
4.14/1.82	We applied the QTRS Reverse Processor [REVERSE].
4.14/1.82	----------------------------------------
4.14/1.82	
4.14/1.82	(2)
4.14/1.82	Obligation:
4.14/1.82	Q restricted rewrite system:
4.14/1.82	The TRS R consists of the following rules:
4.14/1.82	
4.14/1.82	   a(a(a(a(b(a(a(b(a(x1))))))))) -> b(a(a(b(a(a(b(a(a(a(a(a(x1))))))))))))
4.14/1.82	
4.14/1.82	Q is empty.
4.14/1.82	
4.14/1.82	----------------------------------------
4.14/1.82	
4.14/1.82	(3) Strip Symbols Proof (SOUND)
4.14/1.82	We were given the following TRS:
4.14/1.82	
4.14/1.82	   a(a(a(a(b(a(a(b(a(x1))))))))) -> b(a(a(b(a(a(b(a(a(a(a(a(x1))))))))))))
4.14/1.82	
4.14/1.82	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.14/1.82	
4.14/1.82	   a(a(a(a(b(a(a(b(x)))))))) -> b(a(a(b(a(a(b(a(a(a(a(x)))))))))))
4.14/1.82	
4.14/1.82	----------------------------------------
4.14/1.82	
4.14/1.82	(4)
4.14/1.82	Obligation:
4.14/1.82	Q restricted rewrite system:
4.14/1.82	The TRS R consists of the following rules:
4.14/1.82	
4.14/1.82	   a(a(a(a(b(a(a(b(x)))))))) -> b(a(a(b(a(a(b(a(a(a(a(x)))))))))))
4.14/1.82	
4.14/1.82	Q is empty.
4.14/1.82	
4.14/1.82	----------------------------------------
4.14/1.82	
4.14/1.82	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.14/1.82	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.14/1.82	The following rules were used to construct the certificate:
4.14/1.82	
4.14/1.82	   a(a(a(a(b(a(a(b(x)))))))) -> b(a(a(b(a(a(b(a(a(a(a(x)))))))))))
4.14/1.82	
4.14/1.82	The certificate found is represented by the following graph.
4.14/1.82	The certificate consists of the following enumerated nodes:
4.14/1.82	518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539
4.14/1.82	
4.14/1.82	Node 518 is start node and node 519 is final node.
4.14/1.82	
4.14/1.82	Those nodes are connected through the following edges:
4.14/1.82	
4.14/1.82	* 518 to 520 labelled b_1(0)* 519 to 519 labelled #_1(0)* 520 to 521 labelled a_1(0)* 521 to 522 labelled a_1(0)* 522 to 523 labelled b_1(0)* 523 to 524 labelled a_1(0)* 524 to 525 labelled a_1(0)* 525 to 526 labelled b_1(0)* 526 to 527 labelled a_1(0)* 526 to 530 labelled b_1(1)* 527 to 528 labelled a_1(0)* 527 to 530 labelled b_1(1)* 528 to 529 labelled a_1(0)* 528 to 530 labelled b_1(1)* 529 to 519 labelled a_1(0)* 529 to 530 labelled b_1(1)* 530 to 531 labelled a_1(1)* 531 to 532 labelled a_1(1)* 532 to 533 labelled b_1(1)* 533 to 534 labelled a_1(1)* 534 to 535 labelled a_1(1)* 535 to 536 labelled b_1(1)* 536 to 537 labelled a_1(1)* 536 to 530 labelled b_1(1)* 537 to 538 labelled a_1(1)* 537 to 530 labelled b_1(1)* 538 to 539 labelled a_1(1)* 538 to 530 labelled b_1(1)* 539 to 519 labelled a_1(1)* 539 to 530 labelled b_1(1)
4.14/1.82	
4.14/1.82	
4.14/1.82	----------------------------------------
4.14/1.82	
4.14/1.82	(6)
4.14/1.82	YES
4.14/1.85	EOF