3.36/1.79	YES
3.61/1.81	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.61/1.81	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.61/1.81	
3.61/1.81	
3.61/1.81	Termination w.r.t. Q of the given QTRS could be proven:
3.61/1.81	
3.61/1.81	(0) QTRS
3.61/1.81	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.61/1.81	(2) QTRS
3.61/1.81	(3) Strip Symbols Proof [SOUND, 1 ms]
3.61/1.81	(4) QTRS
3.61/1.81	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.61/1.81	(6) YES
3.61/1.81	
3.61/1.81	
3.61/1.81	----------------------------------------
3.61/1.81	
3.61/1.81	(0)
3.61/1.81	Obligation:
3.61/1.81	Q restricted rewrite system:
3.61/1.81	The TRS R consists of the following rules:
3.61/1.81	
3.61/1.81	   a(b(a(b(a(a(a(a(x1)))))))) -> a(a(a(a(a(b(a(b(a(a(b(a(b(x1)))))))))))))
3.61/1.81	
3.61/1.81	Q is empty.
3.61/1.81	
3.61/1.81	----------------------------------------
3.61/1.81	
3.61/1.81	(1) QTRS Reverse (EQUIVALENT)
3.61/1.81	We applied the QTRS Reverse Processor [REVERSE].
3.61/1.81	----------------------------------------
3.61/1.81	
3.61/1.81	(2)
3.61/1.81	Obligation:
3.61/1.81	Q restricted rewrite system:
3.61/1.81	The TRS R consists of the following rules:
3.61/1.81	
3.61/1.81	   a(a(a(a(b(a(b(a(x1)))))))) -> b(a(b(a(a(b(a(b(a(a(a(a(a(x1)))))))))))))
3.61/1.81	
3.61/1.81	Q is empty.
3.61/1.81	
3.61/1.81	----------------------------------------
3.61/1.81	
3.61/1.81	(3) Strip Symbols Proof (SOUND)
3.61/1.81	We were given the following TRS:
3.61/1.81	
3.61/1.81	   a(a(a(a(b(a(b(a(x1)))))))) -> b(a(b(a(a(b(a(b(a(a(a(a(a(x1)))))))))))))
3.61/1.81	
3.61/1.81	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.61/1.81	
3.61/1.81	   a(a(a(a(b(a(b(x))))))) -> b(a(b(a(a(b(a(b(a(a(a(a(x))))))))))))
3.61/1.81	
3.61/1.81	----------------------------------------
3.61/1.81	
3.61/1.81	(4)
3.61/1.81	Obligation:
3.61/1.81	Q restricted rewrite system:
3.61/1.81	The TRS R consists of the following rules:
3.61/1.81	
3.61/1.81	   a(a(a(a(b(a(b(x))))))) -> b(a(b(a(a(b(a(b(a(a(a(a(x))))))))))))
3.61/1.81	
3.61/1.81	Q is empty.
3.61/1.81	
3.61/1.81	----------------------------------------
3.61/1.81	
3.61/1.81	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.61/1.81	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.61/1.81	The following rules were used to construct the certificate:
3.61/1.81	
3.61/1.81	   a(a(a(a(b(a(b(x))))))) -> b(a(b(a(a(b(a(b(a(a(a(a(x))))))))))))
3.61/1.81	
3.61/1.81	The certificate found is represented by the following graph.
3.61/1.81	The certificate consists of the following enumerated nodes:
3.61/1.81	508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531
3.61/1.81	
3.61/1.81	Node 508 is start node and node 509 is final node.
3.61/1.81	
3.61/1.81	Those nodes are connected through the following edges:
3.61/1.81	
3.61/1.81	* 508 to 510 labelled b_1(0)* 509 to 509 labelled #_1(0)* 510 to 511 labelled a_1(0)* 511 to 512 labelled b_1(0)* 512 to 513 labelled a_1(0)* 513 to 514 labelled a_1(0)* 514 to 515 labelled b_1(0)* 515 to 516 labelled a_1(0)* 516 to 517 labelled b_1(0)* 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 a_1(1)* 522 to 523 labelled b_1(1)* 523 to 524 labelled a_1(1)* 524 to 525 labelled a_1(1)* 525 to 526 labelled b_1(1)* 526 to 527 labelled a_1(1)* 527 to 528 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)
3.61/1.81	
3.61/1.81	
3.61/1.81	----------------------------------------
3.61/1.81	
3.61/1.81	(6)
3.61/1.81	YES
3.84/2.17	EOF