4.27/1.86	YES
4.27/1.89	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.27/1.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.27/1.89	
4.27/1.89	
4.27/1.89	Termination w.r.t. Q of the given QTRS could be proven:
4.27/1.89	
4.27/1.89	(0) QTRS
4.27/1.89	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.27/1.89	(2) QTRS
4.27/1.89	(3) Strip Symbols Proof [SOUND, 0 ms]
4.27/1.89	(4) QTRS
4.27/1.89	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
4.27/1.89	(6) YES
4.27/1.89	
4.27/1.89	
4.27/1.89	----------------------------------------
4.27/1.89	
4.27/1.89	(0)
4.27/1.89	Obligation:
4.27/1.89	Q restricted rewrite system:
4.27/1.89	The TRS R consists of the following rules:
4.27/1.89	
4.27/1.89	   a(b(a(a(a(a(a(a(a(a(x1)))))))))) -> a(a(a(a(a(a(a(a(a(b(a(a(a(b(x1))))))))))))))
4.27/1.89	
4.27/1.89	Q is empty.
4.27/1.89	
4.27/1.89	----------------------------------------
4.27/1.89	
4.27/1.89	(1) QTRS Reverse (EQUIVALENT)
4.27/1.89	We applied the QTRS Reverse Processor [REVERSE].
4.27/1.89	----------------------------------------
4.27/1.89	
4.27/1.89	(2)
4.27/1.89	Obligation:
4.27/1.89	Q restricted rewrite system:
4.27/1.89	The TRS R consists of the following rules:
4.27/1.89	
4.27/1.89	   a(a(a(a(a(a(a(a(b(a(x1)))))))))) -> b(a(a(a(b(a(a(a(a(a(a(a(a(a(x1))))))))))))))
4.27/1.89	
4.27/1.89	Q is empty.
4.27/1.89	
4.27/1.89	----------------------------------------
4.27/1.89	
4.27/1.89	(3) Strip Symbols Proof (SOUND)
4.27/1.89	We were given the following TRS:
4.27/1.89	
4.27/1.89	   a(a(a(a(a(a(a(a(b(a(x1)))))))))) -> b(a(a(a(b(a(a(a(a(a(a(a(a(a(x1))))))))))))))
4.27/1.89	
4.27/1.89	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.27/1.89	
4.27/1.89	   a(a(a(a(a(a(a(a(b(x))))))))) -> b(a(a(a(b(a(a(a(a(a(a(a(a(x)))))))))))))
4.27/1.89	
4.27/1.89	----------------------------------------
4.27/1.89	
4.27/1.89	(4)
4.27/1.89	Obligation:
4.27/1.89	Q restricted rewrite system:
4.27/1.89	The TRS R consists of the following rules:
4.27/1.89	
4.27/1.89	   a(a(a(a(a(a(a(a(b(x))))))))) -> b(a(a(a(b(a(a(a(a(a(a(a(a(x)))))))))))))
4.27/1.89	
4.27/1.89	Q is empty.
4.27/1.89	
4.27/1.89	----------------------------------------
4.27/1.89	
4.27/1.89	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.27/1.89	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.27/1.89	The following rules were used to construct the certificate:
4.27/1.89	
4.27/1.89	   a(a(a(a(a(a(a(a(b(x))))))))) -> b(a(a(a(b(a(a(a(a(a(a(a(a(x)))))))))))))
4.27/1.89	
4.27/1.89	The certificate found is represented by the following graph.
4.27/1.89	The certificate consists of the following enumerated nodes:
4.27/1.89	435, 436, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473
4.27/1.89	
4.27/1.89	Node 435 is start node and node 436 is final node.
4.27/1.89	
4.27/1.89	Those nodes are connected through the following edges:
4.27/1.89	
4.27/1.89	* 435 to 450 labelled b_1(0)* 436 to 436 labelled #_1(0)* 450 to 451 labelled a_1(0)* 451 to 452 labelled a_1(0)* 452 to 453 labelled a_1(0)* 453 to 454 labelled b_1(0)* 454 to 455 labelled a_1(0)* 454 to 462 labelled b_1(1)* 455 to 456 labelled a_1(0)* 455 to 462 labelled b_1(1)* 456 to 457 labelled a_1(0)* 456 to 462 labelled b_1(1)* 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 436 labelled a_1(0)* 461 to 462 labelled b_1(1)* 462 to 463 labelled a_1(1)* 463 to 464 labelled a_1(1)* 464 to 465 labelled a_1(1)* 465 to 466 labelled b_1(1)* 466 to 467 labelled a_1(1)* 466 to 462 labelled b_1(1)* 467 to 468 labelled a_1(1)* 467 to 462 labelled b_1(1)* 468 to 469 labelled a_1(1)* 468 to 462 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 436 labelled a_1(1)* 473 to 462 labelled b_1(1)
4.27/1.89	
4.27/1.89	
4.27/1.89	----------------------------------------
4.27/1.89	
4.27/1.89	(6)
4.27/1.89	YES
4.27/1.92	EOF