4.05/1.89	YES
4.05/1.89	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
4.05/1.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.05/1.89	
4.05/1.89	
4.05/1.89	Termination w.r.t. Q of the given QTRS could be proven:
4.05/1.89	
4.05/1.89	(0) QTRS
4.05/1.89	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.05/1.89	(2) QTRS
4.05/1.89	(3) Strip Symbols Proof [SOUND, 0 ms]
4.05/1.89	(4) QTRS
4.05/1.89	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 6 ms]
4.05/1.89	(6) YES
4.05/1.89	
4.05/1.89	
4.05/1.89	----------------------------------------
4.05/1.89	
4.05/1.89	(0)
4.05/1.89	Obligation:
4.05/1.89	Q restricted rewrite system:
4.05/1.89	The TRS R consists of the following rules:
4.05/1.89	
4.05/1.89	   a(b(a(a(a(a(x1)))))) -> a(a(a(a(a(b(a(a(a(b(a(a(a(b(x1))))))))))))))
4.05/1.89	
4.05/1.89	Q is empty.
4.05/1.89	
4.05/1.89	----------------------------------------
4.05/1.89	
4.05/1.89	(1) QTRS Reverse (EQUIVALENT)
4.05/1.89	We applied the QTRS Reverse Processor [REVERSE].
4.05/1.89	----------------------------------------
4.05/1.89	
4.05/1.89	(2)
4.05/1.89	Obligation:
4.05/1.89	Q restricted rewrite system:
4.05/1.89	The TRS R consists of the following rules:
4.05/1.89	
4.05/1.89	   a(a(a(a(b(a(x1)))))) -> b(a(a(a(b(a(a(a(b(a(a(a(a(a(x1))))))))))))))
4.05/1.89	
4.05/1.89	Q is empty.
4.05/1.89	
4.05/1.89	----------------------------------------
4.05/1.89	
4.05/1.89	(3) Strip Symbols Proof (SOUND)
4.05/1.89	We were given the following TRS:
4.05/1.89	
4.05/1.89	   a(a(a(a(b(a(x1)))))) -> b(a(a(a(b(a(a(a(b(a(a(a(a(a(x1))))))))))))))
4.05/1.89	
4.05/1.89	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.05/1.89	
4.05/1.89	   a(a(a(a(b(x))))) -> b(a(a(a(b(a(a(a(b(a(a(a(a(x)))))))))))))
4.05/1.89	
4.05/1.89	----------------------------------------
4.05/1.89	
4.05/1.89	(4)
4.05/1.89	Obligation:
4.05/1.89	Q restricted rewrite system:
4.05/1.89	The TRS R consists of the following rules:
4.05/1.89	
4.05/1.89	   a(a(a(a(b(x))))) -> b(a(a(a(b(a(a(a(b(a(a(a(a(x)))))))))))))
4.05/1.89	
4.05/1.89	Q is empty.
4.05/1.89	
4.05/1.89	----------------------------------------
4.05/1.89	
4.05/1.89	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.05/1.89	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.05/1.89	The following rules were used to construct the certificate:
4.05/1.89	
4.05/1.89	   a(a(a(a(b(x))))) -> b(a(a(a(b(a(a(a(b(a(a(a(a(x)))))))))))))
4.05/1.89	
4.05/1.89	The certificate found is represented by the following graph.
4.05/1.89	The certificate consists of the following enumerated nodes:
4.05/1.89	421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446
4.05/1.89	
4.05/1.89	Node 421 is start node and node 422 is final node.
4.05/1.89	
4.05/1.89	Those nodes are connected through the following edges:
4.05/1.89	
4.05/1.89	* 421 to 423 labelled b_1(0)* 422 to 422 labelled #_1(0)* 423 to 424 labelled a_1(0)* 424 to 425 labelled a_1(0)* 425 to 426 labelled a_1(0)* 426 to 427 labelled b_1(0)* 427 to 428 labelled a_1(0)* 428 to 429 labelled a_1(0)* 429 to 430 labelled a_1(0)* 430 to 431 labelled b_1(0)* 431 to 432 labelled a_1(0)* 431 to 435 labelled b_1(1)* 432 to 433 labelled a_1(0)* 432 to 435 labelled b_1(1)* 433 to 434 labelled a_1(0)* 433 to 435 labelled b_1(1)* 434 to 422 labelled a_1(0)* 434 to 435 labelled b_1(1)* 435 to 436 labelled a_1(1)* 436 to 437 labelled a_1(1)* 437 to 438 labelled a_1(1)* 438 to 439 labelled b_1(1)* 439 to 440 labelled a_1(1)* 440 to 441 labelled a_1(1)* 441 to 442 labelled a_1(1)* 442 to 443 labelled b_1(1)* 443 to 444 labelled a_1(1)* 443 to 435 labelled b_1(1)* 444 to 445 labelled a_1(1)* 444 to 435 labelled b_1(1)* 445 to 446 labelled a_1(1)* 445 to 435 labelled b_1(1)* 446 to 422 labelled a_1(1)* 446 to 435 labelled b_1(1)
4.05/1.89	
4.05/1.89	
4.05/1.89	----------------------------------------
4.05/1.89	
4.05/1.89	(6)
4.05/1.89	YES
4.05/1.92	EOF