3.72/1.70	YES
3.72/1.72	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.72/1.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.72/1.72	
3.72/1.72	
3.72/1.72	Termination w.r.t. Q of the given QTRS could be proven:
3.72/1.72	
3.72/1.72	(0) QTRS
3.72/1.72	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.72/1.72	(2) QTRS
3.72/1.72	(3) Strip Symbols Proof [SOUND, 0 ms]
3.72/1.72	(4) QTRS
3.72/1.72	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.72/1.72	(6) YES
3.72/1.72	
3.72/1.72	
3.72/1.72	----------------------------------------
3.72/1.72	
3.72/1.72	(0)
3.72/1.72	Obligation:
3.72/1.72	Q restricted rewrite system:
3.72/1.72	The TRS R consists of the following rules:
3.72/1.72	
3.72/1.72	   a(b(a(b(a(a(b(a(b(a(b(a(x1)))))))))))) -> a(a(b(a(b(a(b(a(a(b(a(b(a(b(x1))))))))))))))
3.72/1.72	
3.72/1.72	Q is empty.
3.72/1.72	
3.72/1.72	----------------------------------------
3.72/1.72	
3.72/1.72	(1) QTRS Reverse (EQUIVALENT)
3.72/1.72	We applied the QTRS Reverse Processor [REVERSE].
3.72/1.72	----------------------------------------
3.72/1.72	
3.72/1.72	(2)
3.72/1.72	Obligation:
3.72/1.72	Q restricted rewrite system:
3.72/1.72	The TRS R consists of the following rules:
3.72/1.72	
3.72/1.72	   a(b(a(b(a(b(a(a(b(a(b(a(x1)))))))))))) -> b(a(b(a(b(a(a(b(a(b(a(b(a(a(x1))))))))))))))
3.72/1.72	
3.72/1.72	Q is empty.
3.72/1.72	
3.72/1.72	----------------------------------------
3.72/1.72	
3.72/1.72	(3) Strip Symbols Proof (SOUND)
3.72/1.72	We were given the following TRS:
3.72/1.72	
3.72/1.72	   a(b(a(b(a(b(a(a(b(a(b(a(x1)))))))))))) -> b(a(b(a(b(a(a(b(a(b(a(b(a(a(x1))))))))))))))
3.72/1.72	
3.72/1.72	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.72/1.72	
3.72/1.72	   a(b(a(b(a(b(a(a(b(a(b(x))))))))))) -> b(a(b(a(b(a(a(b(a(b(a(b(a(x)))))))))))))
3.72/1.72	
3.72/1.72	----------------------------------------
3.72/1.72	
3.72/1.72	(4)
3.72/1.72	Obligation:
3.72/1.72	Q restricted rewrite system:
3.72/1.72	The TRS R consists of the following rules:
3.72/1.72	
3.72/1.72	   a(b(a(b(a(b(a(a(b(a(b(x))))))))))) -> b(a(b(a(b(a(a(b(a(b(a(b(a(x)))))))))))))
3.72/1.72	
3.72/1.72	Q is empty.
3.72/1.72	
3.72/1.72	----------------------------------------
3.72/1.72	
3.72/1.72	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.72/1.72	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
3.72/1.72	The following rules were used to construct the certificate:
3.72/1.72	
3.72/1.72	   a(b(a(b(a(b(a(a(b(a(b(x))))))))))) -> b(a(b(a(b(a(a(b(a(b(a(b(a(x)))))))))))))
3.72/1.72	
3.72/1.72	The certificate found is represented by the following graph.
3.72/1.72	The certificate consists of the following enumerated nodes:
3.72/1.72	344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445
3.72/1.72	
3.72/1.72	Node 344 is start node and node 345 is final node.
3.72/1.72	
3.72/1.72	Those nodes are connected through the following edges:
3.72/1.72	
3.72/1.72	* 344 to 346 labelled b_1(0)* 345 to 345 labelled #_1(0)* 346 to 347 labelled a_1(0)* 347 to 348 labelled b_1(0)* 348 to 349 labelled a_1(0)* 349 to 350 labelled b_1(0)* 350 to 351 labelled a_1(0)* 350 to 396 labelled b_1(1)* 351 to 352 labelled a_1(0)* 351 to 358 labelled b_1(1)* 352 to 353 labelled b_1(0)* 353 to 354 labelled a_1(0)* 353 to 358 labelled b_1(1)* 354 to 355 labelled b_1(0)* 355 to 356 labelled a_1(0)* 355 to 358 labelled b_1(1)* 356 to 357 labelled b_1(0)* 357 to 345 labelled a_1(0)* 357 to 358 labelled b_1(1)* 358 to 359 labelled a_1(1)* 359 to 360 labelled b_1(1)* 360 to 361 labelled a_1(1)* 361 to 362 labelled b_1(1)* 362 to 363 labelled a_1(1)* 362 to 434 labelled b_1(2)* 363 to 364 labelled a_1(1)* 363 to 358 labelled b_1(1)* 364 to 365 labelled b_1(1)* 365 to 366 labelled a_1(1)* 365 to 358 labelled b_1(1)* 366 to 367 labelled b_1(1)* 367 to 368 labelled a_1(1)* 367 to 358 labelled b_1(1)* 368 to 369 labelled b_1(1)* 369 to 345 labelled a_1(1)* 369 to 358 labelled b_1(1)* 396 to 397 labelled a_1(1)* 397 to 398 labelled b_1(1)* 398 to 399 labelled a_1(1)* 399 to 400 labelled b_1(1)* 400 to 401 labelled a_1(1)* 400 to 434 labelled b_1(2)* 401 to 402 labelled a_1(1)* 401 to 358 labelled b_1(1)* 402 to 403 labelled b_1(1)* 403 to 404 labelled a_1(1)* 404 to 405 labelled b_1(1)* 405 to 406 labelled a_1(1)* 406 to 407 labelled b_1(1)* 407 to 367 labelled a_1(1)* 407 to 434 labelled b_1(2)* 434 to 435 labelled a_1(2)* 435 to 436 labelled b_1(2)* 436 to 437 labelled a_1(2)* 437 to 438 labelled b_1(2)* 438 to 439 labelled a_1(2)* 438 to 434 labelled b_1(2)* 439 to 440 labelled a_1(2)* 439 to 358 labelled b_1(1)* 440 to 441 labelled b_1(2)* 441 to 442 labelled a_1(2)* 442 to 443 labelled b_1(2)* 443 to 444 labelled a_1(2)* 444 to 445 labelled b_1(2)* 445 to 367 labelled a_1(2)* 445 to 434 labelled b_1(2)
3.72/1.72	
3.72/1.72	
3.72/1.72	----------------------------------------
3.72/1.72	
3.72/1.72	(6)
3.72/1.72	YES
3.86/2.54	EOF