3.61/1.71	YES
3.61/1.75	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.61/1.75	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.61/1.75	
3.61/1.75	
3.61/1.75	Termination w.r.t. Q of the given QTRS could be proven:
3.61/1.75	
3.61/1.75	(0) QTRS
3.61/1.75	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.61/1.75	(2) QTRS
3.61/1.75	(3) Strip Symbols Proof [SOUND, 0 ms]
3.61/1.75	(4) QTRS
3.61/1.75	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.61/1.75	(6) YES
3.61/1.75	
3.61/1.75	
3.61/1.75	----------------------------------------
3.61/1.75	
3.61/1.75	(0)
3.61/1.75	Obligation:
3.61/1.75	Q restricted rewrite system:
3.61/1.75	The TRS R consists of the following rules:
3.61/1.75	
3.61/1.75	   a(b(a(b(a(a(b(a(b(a(x1)))))))))) -> a(a(b(a(b(a(b(a(b(a(a(b(a(b(x1))))))))))))))
3.61/1.75	
3.61/1.75	Q is empty.
3.61/1.75	
3.61/1.75	----------------------------------------
3.61/1.75	
3.61/1.75	(1) QTRS Reverse (EQUIVALENT)
3.61/1.75	We applied the QTRS Reverse Processor [REVERSE].
3.61/1.75	----------------------------------------
3.61/1.75	
3.61/1.75	(2)
3.61/1.75	Obligation:
3.61/1.75	Q restricted rewrite system:
3.61/1.75	The TRS R consists of the following rules:
3.61/1.75	
3.61/1.75	   a(b(a(b(a(a(b(a(b(a(x1)))))))))) -> b(a(b(a(a(b(a(b(a(b(a(b(a(a(x1))))))))))))))
3.61/1.75	
3.61/1.75	Q is empty.
3.61/1.75	
3.61/1.75	----------------------------------------
3.61/1.75	
3.61/1.75	(3) Strip Symbols Proof (SOUND)
3.61/1.75	We were given the following TRS:
3.61/1.75	
3.61/1.75	   a(b(a(b(a(a(b(a(b(a(x1)))))))))) -> b(a(b(a(a(b(a(b(a(b(a(b(a(a(x1))))))))))))))
3.61/1.75	
3.61/1.75	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.61/1.75	
3.61/1.75	   a(b(a(b(a(a(b(a(b(x))))))))) -> b(a(b(a(a(b(a(b(a(b(a(b(a(x)))))))))))))
3.61/1.75	
3.61/1.75	----------------------------------------
3.61/1.75	
3.61/1.75	(4)
3.61/1.75	Obligation:
3.61/1.75	Q restricted rewrite system:
3.61/1.75	The TRS R consists of the following rules:
3.61/1.75	
3.61/1.75	   a(b(a(b(a(a(b(a(b(x))))))))) -> b(a(b(a(a(b(a(b(a(b(a(b(a(x)))))))))))))
3.61/1.75	
3.61/1.75	Q is empty.
3.61/1.75	
3.61/1.75	----------------------------------------
3.61/1.75	
3.61/1.75	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.61/1.75	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.61/1.75	The following rules were used to construct the certificate:
3.61/1.75	
3.61/1.75	   a(b(a(b(a(a(b(a(b(x))))))))) -> b(a(b(a(a(b(a(b(a(b(a(b(a(x)))))))))))))
3.61/1.75	
3.61/1.75	The certificate found is represented by the following graph.
3.61/1.75	The certificate consists of the following enumerated nodes:
3.61/1.75	233, 234, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518
3.61/1.75	
3.61/1.75	Node 233 is start node and node 234 is final node.
3.61/1.75	
3.61/1.75	Those nodes are connected through the following edges:
3.61/1.75	
3.61/1.75	* 233 to 495 labelled b_1(0)* 234 to 234 labelled #_1(0)* 495 to 496 labelled a_1(0)* 496 to 497 labelled b_1(0)* 497 to 498 labelled a_1(0)* 498 to 499 labelled a_1(0)* 499 to 500 labelled b_1(0)* 500 to 501 labelled a_1(0)* 501 to 502 labelled b_1(0)* 502 to 503 labelled a_1(0)* 502 to 507 labelled b_1(1)* 503 to 504 labelled b_1(0)* 504 to 505 labelled a_1(0)* 504 to 507 labelled b_1(1)* 505 to 506 labelled b_1(0)* 506 to 234 labelled a_1(0)* 506 to 507 labelled b_1(1)* 507 to 508 labelled a_1(1)* 508 to 509 labelled b_1(1)* 509 to 510 labelled a_1(1)* 510 to 511 labelled a_1(1)* 511 to 512 labelled b_1(1)* 512 to 513 labelled a_1(1)* 513 to 514 labelled b_1(1)* 514 to 515 labelled a_1(1)* 514 to 507 labelled b_1(1)* 515 to 516 labelled b_1(1)* 516 to 517 labelled a_1(1)* 516 to 507 labelled b_1(1)* 517 to 518 labelled b_1(1)* 518 to 234 labelled a_1(1)* 518 to 507 labelled b_1(1)
3.61/1.75	
3.61/1.75	
3.61/1.75	----------------------------------------
3.61/1.75	
3.61/1.75	(6)
3.61/1.75	YES
3.81/1.79	EOF