3.62/1.70	YES
3.62/1.71	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.62/1.71	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.62/1.71	
3.62/1.71	
3.62/1.71	Termination w.r.t. Q of the given QTRS could be proven:
3.62/1.71	
3.62/1.71	(0) QTRS
3.62/1.71	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.62/1.71	(2) QTRS
3.62/1.71	(3) Strip Symbols Proof [SOUND, 0 ms]
3.62/1.71	(4) QTRS
3.62/1.71	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.62/1.71	(6) YES
3.62/1.71	
3.62/1.71	
3.62/1.71	----------------------------------------
3.62/1.71	
3.62/1.71	(0)
3.62/1.71	Obligation:
3.62/1.71	Q restricted rewrite system:
3.62/1.71	The TRS R consists of the following rules:
3.62/1.71	
3.62/1.71	   a(b(a(a(b(a(b(a(x1)))))))) -> a(a(b(a(b(a(b(a(b(a(a(b(x1))))))))))))
3.62/1.71	
3.62/1.71	Q is empty.
3.62/1.71	
3.62/1.71	----------------------------------------
3.62/1.71	
3.62/1.71	(1) QTRS Reverse (EQUIVALENT)
3.62/1.71	We applied the QTRS Reverse Processor [REVERSE].
3.62/1.71	----------------------------------------
3.62/1.71	
3.62/1.71	(2)
3.62/1.71	Obligation:
3.62/1.71	Q restricted rewrite system:
3.62/1.71	The TRS R consists of the following rules:
3.62/1.71	
3.62/1.71	   a(b(a(b(a(a(b(a(x1)))))))) -> b(a(a(b(a(b(a(b(a(b(a(a(x1))))))))))))
3.62/1.71	
3.62/1.71	Q is empty.
3.62/1.71	
3.62/1.71	----------------------------------------
3.62/1.71	
3.62/1.71	(3) Strip Symbols Proof (SOUND)
3.62/1.71	We were given the following TRS:
3.62/1.71	
3.62/1.71	   a(b(a(b(a(a(b(a(x1)))))))) -> b(a(a(b(a(b(a(b(a(b(a(a(x1))))))))))))
3.62/1.71	
3.62/1.71	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.62/1.71	
3.62/1.71	   a(b(a(b(a(a(b(x))))))) -> b(a(a(b(a(b(a(b(a(b(a(x)))))))))))
3.62/1.71	
3.62/1.71	----------------------------------------
3.62/1.71	
3.62/1.71	(4)
3.62/1.71	Obligation:
3.62/1.71	Q restricted rewrite system:
3.62/1.71	The TRS R consists of the following rules:
3.62/1.71	
3.62/1.71	   a(b(a(b(a(a(b(x))))))) -> b(a(a(b(a(b(a(b(a(b(a(x)))))))))))
3.62/1.71	
3.62/1.71	Q is empty.
3.62/1.71	
3.62/1.71	----------------------------------------
3.62/1.71	
3.62/1.71	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.62/1.71	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.62/1.71	The following rules were used to construct the certificate:
3.62/1.71	
3.62/1.71	   a(b(a(b(a(a(b(x))))))) -> b(a(a(b(a(b(a(b(a(b(a(x)))))))))))
3.62/1.71	
3.62/1.71	The certificate found is represented by the following graph.
3.62/1.71	The certificate consists of the following enumerated nodes:
3.62/1.71	464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485
3.62/1.71	
3.62/1.71	Node 464 is start node and node 465 is final node.
3.62/1.71	
3.62/1.71	Those nodes are connected through the following edges:
3.62/1.71	
3.62/1.71	* 464 to 466 labelled b_1(0)* 465 to 465 labelled #_1(0)* 466 to 467 labelled a_1(0)* 467 to 468 labelled a_1(0)* 468 to 469 labelled b_1(0)* 469 to 470 labelled a_1(0)* 470 to 471 labelled b_1(0)* 471 to 472 labelled a_1(0)* 471 to 476 labelled b_1(1)* 472 to 473 labelled b_1(0)* 473 to 474 labelled a_1(0)* 473 to 476 labelled b_1(1)* 474 to 475 labelled b_1(0)* 475 to 465 labelled a_1(0)* 475 to 476 labelled b_1(1)* 476 to 477 labelled a_1(1)* 477 to 478 labelled a_1(1)* 478 to 479 labelled b_1(1)* 479 to 480 labelled a_1(1)* 480 to 481 labelled b_1(1)* 481 to 482 labelled a_1(1)* 481 to 476 labelled b_1(1)* 482 to 483 labelled b_1(1)* 483 to 484 labelled a_1(1)* 483 to 476 labelled b_1(1)* 484 to 485 labelled b_1(1)* 485 to 465 labelled a_1(1)* 485 to 476 labelled b_1(1)
3.62/1.71	
3.62/1.71	
3.62/1.71	----------------------------------------
3.62/1.71	
3.62/1.71	(6)
3.62/1.71	YES
3.62/1.74	EOF