3.99/1.83	YES
3.99/1.84	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.99/1.84	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.99/1.84	
3.99/1.84	
3.99/1.84	Termination w.r.t. Q of the given QTRS could be proven:
3.99/1.84	
3.99/1.84	(0) QTRS
3.99/1.84	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.99/1.84	(2) QTRS
3.99/1.84	(3) Strip Symbols Proof [SOUND, 0 ms]
3.99/1.84	(4) QTRS
3.99/1.84	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.99/1.84	(6) YES
3.99/1.84	
3.99/1.84	
3.99/1.84	----------------------------------------
3.99/1.84	
3.99/1.84	(0)
3.99/1.84	Obligation:
3.99/1.84	Q restricted rewrite system:
3.99/1.84	The TRS R consists of the following rules:
3.99/1.84	
3.99/1.84	   a(a(b(b(a(b(x1)))))) -> a(b(b(a(a(b(b(a(x1))))))))
3.99/1.84	
3.99/1.84	Q is empty.
3.99/1.84	
3.99/1.84	----------------------------------------
3.99/1.84	
3.99/1.84	(1) QTRS Reverse (EQUIVALENT)
3.99/1.84	We applied the QTRS Reverse Processor [REVERSE].
3.99/1.84	----------------------------------------
3.99/1.84	
3.99/1.84	(2)
3.99/1.84	Obligation:
3.99/1.84	Q restricted rewrite system:
3.99/1.84	The TRS R consists of the following rules:
3.99/1.84	
3.99/1.84	   b(a(b(b(a(a(x1)))))) -> a(b(b(a(a(b(b(a(x1))))))))
3.99/1.84	
3.99/1.84	Q is empty.
3.99/1.84	
3.99/1.84	----------------------------------------
3.99/1.84	
3.99/1.84	(3) Strip Symbols Proof (SOUND)
3.99/1.84	We were given the following TRS:
3.99/1.84	
3.99/1.84	   b(a(b(b(a(a(x1)))))) -> a(b(b(a(a(b(b(a(x1))))))))
3.99/1.84	
3.99/1.84	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.99/1.84	
3.99/1.84	   b(a(b(b(a(x))))) -> a(b(b(a(a(b(b(x)))))))
3.99/1.84	
3.99/1.84	----------------------------------------
3.99/1.84	
3.99/1.84	(4)
3.99/1.84	Obligation:
3.99/1.84	Q restricted rewrite system:
3.99/1.84	The TRS R consists of the following rules:
3.99/1.84	
3.99/1.84	   b(a(b(b(a(x))))) -> a(b(b(a(a(b(b(x)))))))
3.99/1.84	
3.99/1.84	Q is empty.
3.99/1.84	
3.99/1.84	----------------------------------------
3.99/1.84	
3.99/1.84	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.99/1.84	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
3.99/1.84	The following rules were used to construct the certificate:
3.99/1.84	
3.99/1.84	   b(a(b(b(a(x))))) -> a(b(b(a(a(b(b(x)))))))
3.99/1.84	
3.99/1.84	The certificate found is represented by the following graph.
3.99/1.84	The certificate consists of the following enumerated nodes:
3.99/1.84	343, 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
3.99/1.84	
3.99/1.84	Node 343 is start node and node 344 is final node.
3.99/1.84	
3.99/1.84	Those nodes are connected through the following edges:
3.99/1.84	
3.99/1.84	* 343 to 345 labelled a_1(0)* 344 to 344 labelled #_1(0)* 345 to 346 labelled b_1(0)* 346 to 347 labelled b_1(0)* 347 to 348 labelled a_1(0)* 348 to 349 labelled a_1(0)* 349 to 350 labelled b_1(0)* 349 to 357 labelled a_1(1)* 350 to 344 labelled b_1(0)* 350 to 351 labelled a_1(1)* 351 to 352 labelled b_1(1)* 352 to 353 labelled b_1(1)* 353 to 354 labelled a_1(1)* 354 to 355 labelled a_1(1)* 355 to 356 labelled b_1(1)* 355 to 363 labelled a_1(2)* 356 to 344 labelled b_1(1)* 356 to 351 labelled a_1(1)* 357 to 358 labelled b_1(1)* 358 to 359 labelled b_1(1)* 359 to 360 labelled a_1(1)* 360 to 361 labelled a_1(1)* 361 to 362 labelled b_1(1)* 361 to 363 labelled a_1(2)* 362 to 354 labelled b_1(1)* 362 to 351 labelled a_1(1)* 363 to 364 labelled b_1(2)* 364 to 365 labelled b_1(2)* 365 to 366 labelled a_1(2)* 366 to 367 labelled a_1(2)* 367 to 368 labelled b_1(2)* 367 to 363 labelled a_1(2)* 368 to 354 labelled b_1(2)* 368 to 351 labelled a_1(1)
3.99/1.84	
3.99/1.84	
3.99/1.84	----------------------------------------
3.99/1.84	
3.99/1.84	(6)
3.99/1.84	YES
4.14/2.38	EOF