3.66/1.77	YES
3.94/1.81	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.94/1.81	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.94/1.81	
3.94/1.81	
3.94/1.81	Termination w.r.t. Q of the given QTRS could be proven:
3.94/1.81	
3.94/1.81	(0) QTRS
3.94/1.81	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.94/1.81	(2) QTRS
3.94/1.81	(3) Strip Symbols Proof [SOUND, 0 ms]
3.94/1.81	(4) QTRS
3.94/1.81	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.94/1.81	(6) YES
3.94/1.81	
3.94/1.81	
3.94/1.81	----------------------------------------
3.94/1.81	
3.94/1.81	(0)
3.94/1.81	Obligation:
3.94/1.81	Q restricted rewrite system:
3.94/1.81	The TRS R consists of the following rules:
3.94/1.81	
3.94/1.81	   a(b(a(a(a(a(a(a(a(x1))))))))) -> a(a(a(a(a(a(a(a(b(a(a(b(a(b(x1))))))))))))))
3.94/1.81	
3.94/1.81	Q is empty.
3.94/1.81	
3.94/1.81	----------------------------------------
3.94/1.81	
3.94/1.81	(1) QTRS Reverse (EQUIVALENT)
3.94/1.81	We applied the QTRS Reverse Processor [REVERSE].
3.94/1.81	----------------------------------------
3.94/1.81	
3.94/1.81	(2)
3.94/1.81	Obligation:
3.94/1.81	Q restricted rewrite system:
3.94/1.81	The TRS R consists of the following rules:
3.94/1.81	
3.94/1.81	   a(a(a(a(a(a(a(b(a(x1))))))))) -> b(a(b(a(a(b(a(a(a(a(a(a(a(a(x1))))))))))))))
3.94/1.81	
3.94/1.81	Q is empty.
3.94/1.81	
3.94/1.81	----------------------------------------
3.94/1.81	
3.94/1.81	(3) Strip Symbols Proof (SOUND)
3.94/1.81	We were given the following TRS:
3.94/1.81	
3.94/1.81	   a(a(a(a(a(a(a(b(a(x1))))))))) -> b(a(b(a(a(b(a(a(a(a(a(a(a(a(x1))))))))))))))
3.94/1.81	
3.94/1.81	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.94/1.81	
3.94/1.81	   a(a(a(a(a(a(a(b(x)))))))) -> b(a(b(a(a(b(a(a(a(a(a(a(a(x)))))))))))))
3.94/1.81	
3.94/1.81	----------------------------------------
3.94/1.81	
3.94/1.81	(4)
3.94/1.81	Obligation:
3.94/1.81	Q restricted rewrite system:
3.94/1.81	The TRS R consists of the following rules:
3.94/1.81	
3.94/1.81	   a(a(a(a(a(a(a(b(x)))))))) -> b(a(b(a(a(b(a(a(a(a(a(a(a(x)))))))))))))
3.94/1.81	
3.94/1.81	Q is empty.
3.94/1.81	
3.94/1.81	----------------------------------------
3.94/1.81	
3.94/1.81	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.94/1.81	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.94/1.81	The following rules were used to construct the certificate:
3.94/1.81	
3.94/1.81	   a(a(a(a(a(a(a(b(x)))))))) -> b(a(b(a(a(b(a(a(a(a(a(a(a(x)))))))))))))
3.94/1.81	
3.94/1.81	The certificate found is represented by the following graph.
3.94/1.81	The certificate consists of the following enumerated nodes:
3.94/1.81	349, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389
3.94/1.81	
3.94/1.81	Node 349 is start node and node 353 is final node.
3.94/1.81	
3.94/1.81	Those nodes are connected through the following edges:
3.94/1.81	
3.94/1.81	* 349 to 354 labelled b_1(0)* 353 to 353 labelled #_1(0)* 354 to 355 labelled a_1(0)* 355 to 356 labelled b_1(0)* 356 to 357 labelled a_1(0)* 357 to 358 labelled a_1(0)* 358 to 359 labelled b_1(0)* 359 to 360 labelled a_1(0)* 359 to 378 labelled b_1(1)* 360 to 361 labelled a_1(0)* 360 to 378 labelled b_1(1)* 361 to 362 labelled a_1(0)* 361 to 378 labelled b_1(1)* 362 to 363 labelled a_1(0)* 362 to 378 labelled b_1(1)* 363 to 364 labelled a_1(0)* 363 to 378 labelled b_1(1)* 364 to 365 labelled a_1(0)* 364 to 378 labelled b_1(1)* 365 to 353 labelled a_1(0)* 365 to 378 labelled b_1(1)* 378 to 379 labelled a_1(1)* 379 to 380 labelled b_1(1)* 380 to 381 labelled a_1(1)* 381 to 382 labelled a_1(1)* 382 to 383 labelled b_1(1)* 383 to 384 labelled a_1(1)* 383 to 378 labelled b_1(1)* 384 to 385 labelled a_1(1)* 384 to 378 labelled b_1(1)* 385 to 386 labelled a_1(1)* 385 to 378 labelled b_1(1)* 386 to 387 labelled a_1(1)* 386 to 378 labelled b_1(1)* 387 to 388 labelled a_1(1)* 387 to 378 labelled b_1(1)* 388 to 389 labelled a_1(1)* 388 to 378 labelled b_1(1)* 389 to 353 labelled a_1(1)* 389 to 378 labelled b_1(1)
3.94/1.81	
3.94/1.81	
3.94/1.81	----------------------------------------
3.94/1.81	
3.94/1.81	(6)
3.94/1.81	YES
3.94/1.88	EOF