3.71/1.73	YES
3.85/1.75	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.85/1.75	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.85/1.75	
3.85/1.75	
3.85/1.75	Termination w.r.t. Q of the given QTRS could be proven:
3.85/1.75	
3.85/1.75	(0) QTRS
3.85/1.75	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.85/1.75	(2) QTRS
3.85/1.75	(3) Strip Symbols Proof [SOUND, 0 ms]
3.85/1.75	(4) QTRS
3.85/1.75	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.85/1.75	(6) YES
3.85/1.75	
3.85/1.75	
3.85/1.75	----------------------------------------
3.85/1.75	
3.85/1.75	(0)
3.85/1.75	Obligation:
3.85/1.75	Q restricted rewrite system:
3.85/1.75	The TRS R consists of the following rules:
3.85/1.75	
3.85/1.75	   a(b(b(a(a(a(a(a(x1)))))))) -> a(a(a(a(a(a(b(b(a(a(a(a(b(b(x1))))))))))))))
3.85/1.75	
3.85/1.75	Q is empty.
3.85/1.75	
3.85/1.75	----------------------------------------
3.85/1.75	
3.85/1.75	(1) QTRS Reverse (EQUIVALENT)
3.85/1.75	We applied the QTRS Reverse Processor [REVERSE].
3.85/1.75	----------------------------------------
3.85/1.75	
3.85/1.75	(2)
3.85/1.75	Obligation:
3.85/1.75	Q restricted rewrite system:
3.85/1.75	The TRS R consists of the following rules:
3.85/1.75	
3.85/1.75	   a(a(a(a(a(b(b(a(x1)))))))) -> b(b(a(a(a(a(b(b(a(a(a(a(a(a(x1))))))))))))))
3.85/1.75	
3.85/1.75	Q is empty.
3.85/1.75	
3.85/1.75	----------------------------------------
3.85/1.75	
3.85/1.75	(3) Strip Symbols Proof (SOUND)
3.85/1.75	We were given the following TRS:
3.85/1.75	
3.85/1.75	   a(a(a(a(a(b(b(a(x1)))))))) -> b(b(a(a(a(a(b(b(a(a(a(a(a(a(x1))))))))))))))
3.85/1.75	
3.85/1.75	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.85/1.75	
3.85/1.75	   a(a(a(a(a(b(b(x))))))) -> b(b(a(a(a(a(b(b(a(a(a(a(a(x)))))))))))))
3.85/1.75	
3.85/1.75	----------------------------------------
3.85/1.75	
3.85/1.75	(4)
3.85/1.75	Obligation:
3.85/1.75	Q restricted rewrite system:
3.85/1.75	The TRS R consists of the following rules:
3.85/1.75	
3.85/1.75	   a(a(a(a(a(b(b(x))))))) -> b(b(a(a(a(a(b(b(a(a(a(a(a(x)))))))))))))
3.85/1.75	
3.85/1.75	Q is empty.
3.85/1.75	
3.85/1.75	----------------------------------------
3.85/1.75	
3.85/1.75	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.85/1.75	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.85/1.75	The following rules were used to construct the certificate:
3.85/1.75	
3.85/1.75	   a(a(a(a(a(b(b(x))))))) -> b(b(a(a(a(a(b(b(a(a(a(a(a(x)))))))))))))
3.85/1.75	
3.85/1.75	The certificate found is represented by the following graph.
3.85/1.75	The certificate consists of the following enumerated nodes:
3.85/1.75	448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473
3.85/1.75	
3.85/1.75	Node 448 is start node and node 449 is final node.
3.85/1.75	
3.85/1.75	Those nodes are connected through the following edges:
3.85/1.75	
3.85/1.75	* 448 to 450 labelled b_1(0)* 449 to 449 labelled #_1(0)* 450 to 451 labelled b_1(0)* 451 to 452 labelled a_1(0)* 452 to 453 labelled a_1(0)* 453 to 454 labelled a_1(0)* 454 to 455 labelled a_1(0)* 455 to 456 labelled b_1(0)* 456 to 457 labelled b_1(0)* 457 to 458 labelled a_1(0)* 457 to 462 labelled b_1(1)* 458 to 459 labelled a_1(0)* 458 to 462 labelled b_1(1)* 459 to 460 labelled a_1(0)* 459 to 462 labelled b_1(1)* 460 to 461 labelled a_1(0)* 460 to 462 labelled b_1(1)* 461 to 449 labelled a_1(0)* 461 to 462 labelled b_1(1)* 462 to 463 labelled b_1(1)* 463 to 464 labelled a_1(1)* 464 to 465 labelled a_1(1)* 465 to 466 labelled a_1(1)* 466 to 467 labelled a_1(1)* 467 to 468 labelled b_1(1)* 468 to 469 labelled b_1(1)* 469 to 470 labelled a_1(1)* 469 to 462 labelled b_1(1)* 470 to 471 labelled a_1(1)* 470 to 462 labelled b_1(1)* 471 to 472 labelled a_1(1)* 471 to 462 labelled b_1(1)* 472 to 473 labelled a_1(1)* 472 to 462 labelled b_1(1)* 473 to 449 labelled a_1(1)* 473 to 462 labelled b_1(1)
3.85/1.75	
3.85/1.75	
3.85/1.75	----------------------------------------
3.85/1.75	
3.85/1.75	(6)
3.85/1.75	YES
3.85/1.79	EOF