3.47/1.68	YES
3.47/1.71	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.47/1.71	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.47/1.71	
3.47/1.71	
3.47/1.71	Termination w.r.t. Q of the given QTRS could be proven:
3.47/1.71	
3.47/1.71	(0) QTRS
3.47/1.71	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.47/1.71	(2) QTRS
3.47/1.71	(3) Strip Symbols Proof [SOUND, 0 ms]
3.47/1.71	(4) QTRS
3.47/1.71	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.47/1.71	(6) YES
3.47/1.71	
3.47/1.71	
3.47/1.71	----------------------------------------
3.47/1.71	
3.47/1.71	(0)
3.47/1.71	Obligation:
3.47/1.71	Q restricted rewrite system:
3.47/1.71	The TRS R consists of the following rules:
3.47/1.71	
3.47/1.71	   a(b(a(a(a(a(a(a(a(x1))))))))) -> a(a(a(a(a(a(a(a(b(a(b(a(b(x1)))))))))))))
3.47/1.71	
3.47/1.71	Q is empty.
3.47/1.71	
3.47/1.71	----------------------------------------
3.47/1.71	
3.47/1.71	(1) QTRS Reverse (EQUIVALENT)
3.47/1.71	We applied the QTRS Reverse Processor [REVERSE].
3.47/1.71	----------------------------------------
3.47/1.71	
3.47/1.71	(2)
3.47/1.71	Obligation:
3.47/1.71	Q restricted rewrite system:
3.47/1.71	The TRS R consists of the following rules:
3.47/1.71	
3.47/1.71	   a(a(a(a(a(a(a(b(a(x1))))))))) -> b(a(b(a(b(a(a(a(a(a(a(a(a(x1)))))))))))))
3.47/1.71	
3.47/1.71	Q is empty.
3.47/1.71	
3.47/1.71	----------------------------------------
3.47/1.71	
3.47/1.71	(3) Strip Symbols Proof (SOUND)
3.47/1.71	We were given the following TRS:
3.47/1.71	
3.47/1.71	   a(a(a(a(a(a(a(b(a(x1))))))))) -> b(a(b(a(b(a(a(a(a(a(a(a(a(x1)))))))))))))
3.47/1.71	
3.47/1.71	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.47/1.71	
3.47/1.71	   a(a(a(a(a(a(a(b(x)))))))) -> b(a(b(a(b(a(a(a(a(a(a(a(x))))))))))))
3.47/1.71	
3.47/1.71	----------------------------------------
3.47/1.71	
3.47/1.71	(4)
3.47/1.71	Obligation:
3.47/1.71	Q restricted rewrite system:
3.47/1.71	The TRS R consists of the following rules:
3.47/1.71	
3.47/1.71	   a(a(a(a(a(a(a(b(x)))))))) -> b(a(b(a(b(a(a(a(a(a(a(a(x))))))))))))
3.47/1.71	
3.47/1.71	Q is empty.
3.47/1.71	
3.47/1.71	----------------------------------------
3.47/1.71	
3.47/1.71	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.47/1.71	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.47/1.71	The following rules were used to construct the certificate:
3.47/1.71	
3.47/1.71	   a(a(a(a(a(a(a(b(x)))))))) -> b(a(b(a(b(a(a(a(a(a(a(a(x))))))))))))
3.47/1.71	
3.47/1.71	The certificate found is represented by the following graph.
3.47/1.71	The certificate consists of the following enumerated nodes:
3.47/1.71	280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303
3.47/1.71	
3.47/1.71	Node 280 is start node and node 281 is final node.
3.47/1.71	
3.47/1.71	Those nodes are connected through the following edges:
3.47/1.71	
3.47/1.71	* 280 to 282 labelled b_1(0)* 281 to 281 labelled #_1(0)* 282 to 283 labelled a_1(0)* 283 to 284 labelled b_1(0)* 284 to 285 labelled a_1(0)* 285 to 286 labelled b_1(0)* 286 to 287 labelled a_1(0)* 286 to 293 labelled b_1(1)* 287 to 288 labelled a_1(0)* 287 to 293 labelled b_1(1)* 288 to 289 labelled a_1(0)* 288 to 293 labelled b_1(1)* 289 to 290 labelled a_1(0)* 289 to 293 labelled b_1(1)* 290 to 291 labelled a_1(0)* 290 to 293 labelled b_1(1)* 291 to 292 labelled a_1(0)* 291 to 293 labelled b_1(1)* 292 to 281 labelled a_1(0)* 292 to 293 labelled b_1(1)* 293 to 294 labelled a_1(1)* 294 to 295 labelled b_1(1)* 295 to 296 labelled a_1(1)* 296 to 297 labelled b_1(1)* 297 to 298 labelled a_1(1)* 297 to 293 labelled b_1(1)* 298 to 299 labelled a_1(1)* 298 to 293 labelled b_1(1)* 299 to 300 labelled a_1(1)* 299 to 293 labelled b_1(1)* 300 to 301 labelled a_1(1)* 300 to 293 labelled b_1(1)* 301 to 302 labelled a_1(1)* 301 to 293 labelled b_1(1)* 302 to 303 labelled a_1(1)* 302 to 293 labelled b_1(1)* 303 to 281 labelled a_1(1)* 303 to 293 labelled b_1(1)
3.47/1.71	
3.47/1.71	
3.47/1.71	----------------------------------------
3.47/1.71	
3.47/1.71	(6)
3.47/1.71	YES
3.82/1.72	EOF