3.70/1.78	YES
3.70/1.80	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.70/1.80	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.70/1.80	
3.70/1.80	
3.70/1.80	Termination w.r.t. Q of the given QTRS could be proven:
3.70/1.80	
3.70/1.80	(0) QTRS
3.70/1.80	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.70/1.80	(2) QTRS
3.70/1.80	(3) Strip Symbols Proof [SOUND, 0 ms]
3.70/1.80	(4) QTRS
3.70/1.80	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.70/1.80	(6) YES
3.70/1.80	
3.70/1.80	
3.70/1.80	----------------------------------------
3.70/1.80	
3.70/1.80	(0)
3.70/1.80	Obligation:
3.70/1.80	Q restricted rewrite system:
3.70/1.80	The TRS R consists of the following rules:
3.70/1.80	
3.70/1.80	   a(b(a(b(a(a(a(a(a(a(a(x1))))))))))) -> a(a(a(a(a(a(a(a(b(a(b(a(b(x1)))))))))))))
3.70/1.80	
3.70/1.80	Q is empty.
3.70/1.80	
3.70/1.80	----------------------------------------
3.70/1.80	
3.70/1.80	(1) QTRS Reverse (EQUIVALENT)
3.70/1.80	We applied the QTRS Reverse Processor [REVERSE].
3.70/1.80	----------------------------------------
3.70/1.80	
3.70/1.80	(2)
3.70/1.80	Obligation:
3.70/1.80	Q restricted rewrite system:
3.70/1.80	The TRS R consists of the following rules:
3.70/1.80	
3.70/1.80	   a(a(a(a(a(a(a(b(a(b(a(x1))))))))))) -> b(a(b(a(b(a(a(a(a(a(a(a(a(x1)))))))))))))
3.70/1.80	
3.70/1.80	Q is empty.
3.70/1.80	
3.70/1.80	----------------------------------------
3.70/1.80	
3.70/1.80	(3) Strip Symbols Proof (SOUND)
3.70/1.80	We were given the following TRS:
3.70/1.80	
3.70/1.80	   a(a(a(a(a(a(a(b(a(b(a(x1))))))))))) -> b(a(b(a(b(a(a(a(a(a(a(a(a(x1)))))))))))))
3.70/1.80	
3.70/1.80	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.70/1.80	
3.70/1.80	   a(a(a(a(a(a(a(b(a(b(x)))))))))) -> b(a(b(a(b(a(a(a(a(a(a(a(x))))))))))))
3.70/1.80	
3.70/1.80	----------------------------------------
3.70/1.80	
3.70/1.80	(4)
3.70/1.80	Obligation:
3.70/1.80	Q restricted rewrite system:
3.70/1.80	The TRS R consists of the following rules:
3.70/1.80	
3.70/1.80	   a(a(a(a(a(a(a(b(a(b(x)))))))))) -> b(a(b(a(b(a(a(a(a(a(a(a(x))))))))))))
3.70/1.80	
3.70/1.80	Q is empty.
3.70/1.80	
3.70/1.80	----------------------------------------
3.70/1.80	
3.70/1.80	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.70/1.80	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.70/1.80	The following rules were used to construct the certificate:
3.70/1.80	
3.70/1.80	   a(a(a(a(a(a(a(b(a(b(x)))))))))) -> b(a(b(a(b(a(a(a(a(a(a(a(x))))))))))))
3.70/1.80	
3.70/1.80	The certificate found is represented by the following graph.
3.70/1.80	The certificate consists of the following enumerated nodes:
3.70/1.80	326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349
3.70/1.80	
3.70/1.80	Node 326 is start node and node 327 is final node.
3.70/1.80	
3.70/1.80	Those nodes are connected through the following edges:
3.70/1.80	
3.70/1.80	* 326 to 328 labelled b_1(0)* 327 to 327 labelled #_1(0)* 328 to 329 labelled a_1(0)* 329 to 330 labelled b_1(0)* 330 to 331 labelled a_1(0)* 331 to 332 labelled b_1(0)* 332 to 333 labelled a_1(0)* 332 to 339 labelled b_1(1)* 333 to 334 labelled a_1(0)* 333 to 339 labelled b_1(1)* 334 to 335 labelled a_1(0)* 334 to 339 labelled b_1(1)* 335 to 336 labelled a_1(0)* 335 to 339 labelled b_1(1)* 336 to 337 labelled a_1(0)* 336 to 339 labelled b_1(1)* 337 to 338 labelled a_1(0)* 337 to 339 labelled b_1(1)* 338 to 327 labelled a_1(0)* 338 to 339 labelled b_1(1)* 339 to 340 labelled a_1(1)* 340 to 341 labelled b_1(1)* 341 to 342 labelled a_1(1)* 342 to 343 labelled b_1(1)* 343 to 344 labelled a_1(1)* 343 to 339 labelled b_1(1)* 344 to 345 labelled a_1(1)* 344 to 339 labelled b_1(1)* 345 to 346 labelled a_1(1)* 345 to 339 labelled b_1(1)* 346 to 347 labelled a_1(1)* 346 to 339 labelled b_1(1)* 347 to 348 labelled a_1(1)* 347 to 339 labelled b_1(1)* 348 to 349 labelled a_1(1)* 348 to 339 labelled b_1(1)* 349 to 327 labelled a_1(1)* 349 to 339 labelled b_1(1)
3.70/1.80	
3.70/1.80	
3.70/1.80	----------------------------------------
3.70/1.80	
3.70/1.80	(6)
3.70/1.80	YES
3.84/1.83	EOF