4.07/1.79	YES
4.10/1.80	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.10/1.80	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.10/1.80	
4.10/1.80	
4.10/1.80	Termination w.r.t. Q of the given QTRS could be proven:
4.10/1.80	
4.10/1.80	(0) QTRS
4.10/1.80	(1) Strip Symbols Proof [SOUND, 0 ms]
4.10/1.80	(2) QTRS
4.10/1.80	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
4.10/1.80	(4) YES
4.10/1.80	
4.10/1.80	
4.10/1.80	----------------------------------------
4.10/1.80	
4.10/1.80	(0)
4.10/1.80	Obligation:
4.10/1.80	Q restricted rewrite system:
4.10/1.80	The TRS R consists of the following rules:
4.10/1.80	
4.10/1.80	   b(a(a(b(b(a(a(b(x1)))))))) -> a(a(b(b(a(a(b(a(a(b(b(x1)))))))))))
4.10/1.80	
4.10/1.80	Q is empty.
4.10/1.80	
4.10/1.80	----------------------------------------
4.10/1.80	
4.10/1.80	(1) Strip Symbols Proof (SOUND)
4.10/1.80	We were given the following TRS:
4.10/1.80	
4.10/1.80	   b(a(a(b(b(a(a(b(x1)))))))) -> a(a(b(b(a(a(b(a(a(b(b(x1)))))))))))
4.10/1.80	
4.10/1.80	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.10/1.80	
4.10/1.80	   b(a(a(b(b(a(a(x))))))) -> a(a(b(b(a(a(b(a(a(b(x))))))))))
4.10/1.80	
4.10/1.80	----------------------------------------
4.10/1.80	
4.10/1.80	(2)
4.10/1.80	Obligation:
4.10/1.80	Q restricted rewrite system:
4.10/1.80	The TRS R consists of the following rules:
4.10/1.80	
4.10/1.80	   b(a(a(b(b(a(a(x))))))) -> a(a(b(b(a(a(b(a(a(b(x))))))))))
4.10/1.80	
4.10/1.80	Q is empty.
4.10/1.80	
4.10/1.80	----------------------------------------
4.10/1.80	
4.10/1.80	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
4.10/1.80	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.10/1.80	The following rules were used to construct the certificate:
4.10/1.80	
4.10/1.80	   b(a(a(b(b(a(a(x))))))) -> a(a(b(b(a(a(b(a(a(b(x))))))))))
4.10/1.80	
4.10/1.80	The certificate found is represented by the following graph.
4.10/1.80	The certificate consists of the following enumerated nodes:
4.10/1.80	355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374
4.10/1.80	
4.10/1.80	Node 355 is start node and node 356 is final node.
4.10/1.80	
4.10/1.80	Those nodes are connected through the following edges:
4.10/1.80	
4.10/1.80	* 355 to 357 labelled a_1(0)* 356 to 356 labelled #_1(0)* 357 to 358 labelled a_1(0)* 358 to 359 labelled b_1(0)* 359 to 360 labelled b_1(0)* 360 to 361 labelled a_1(0)* 361 to 362 labelled a_1(0)* 362 to 363 labelled b_1(0)* 362 to 366 labelled a_1(1)* 363 to 364 labelled a_1(0)* 364 to 365 labelled a_1(0)* 365 to 356 labelled b_1(0)* 365 to 366 labelled a_1(1)* 366 to 367 labelled a_1(1)* 367 to 368 labelled b_1(1)* 368 to 369 labelled b_1(1)* 369 to 370 labelled a_1(1)* 370 to 371 labelled a_1(1)* 371 to 372 labelled b_1(1)* 371 to 366 labelled a_1(1)* 372 to 373 labelled a_1(1)* 373 to 374 labelled a_1(1)* 374 to 356 labelled b_1(1)* 374 to 366 labelled a_1(1)
4.10/1.80	
4.10/1.80	
4.10/1.80	----------------------------------------
4.10/1.80	
4.10/1.80	(4)
4.10/1.80	YES
4.14/1.83	EOF