3.46/1.64	YES
3.46/1.68	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.46/1.68	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.46/1.68	
3.46/1.68	
3.46/1.68	Termination w.r.t. Q of the given QTRS could be proven:
3.46/1.68	
3.46/1.68	(0) QTRS
3.46/1.68	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.46/1.68	(2) QTRS
3.46/1.68	(3) Strip Symbols Proof [SOUND, 0 ms]
3.46/1.68	(4) QTRS
3.46/1.68	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.46/1.68	(6) YES
3.46/1.68	
3.46/1.68	
3.46/1.68	----------------------------------------
3.46/1.68	
3.46/1.68	(0)
3.46/1.68	Obligation:
3.46/1.68	Q restricted rewrite system:
3.46/1.68	The TRS R consists of the following rules:
3.46/1.68	
3.46/1.68	   a(b(b(a(a(a(a(a(x1)))))))) -> a(a(a(a(a(a(b(b(a(a(a(b(b(x1)))))))))))))
3.46/1.68	
3.46/1.68	Q is empty.
3.46/1.68	
3.46/1.68	----------------------------------------
3.46/1.68	
3.46/1.68	(1) QTRS Reverse (EQUIVALENT)
3.46/1.68	We applied the QTRS Reverse Processor [REVERSE].
3.46/1.68	----------------------------------------
3.46/1.68	
3.46/1.68	(2)
3.46/1.68	Obligation:
3.46/1.68	Q restricted rewrite system:
3.46/1.68	The TRS R consists of the following rules:
3.46/1.68	
3.46/1.68	   a(a(a(a(a(b(b(a(x1)))))))) -> b(b(a(a(a(b(b(a(a(a(a(a(a(x1)))))))))))))
3.46/1.68	
3.46/1.68	Q is empty.
3.46/1.68	
3.46/1.68	----------------------------------------
3.46/1.68	
3.46/1.68	(3) Strip Symbols Proof (SOUND)
3.46/1.68	We were given the following TRS:
3.46/1.68	
3.46/1.68	   a(a(a(a(a(b(b(a(x1)))))))) -> b(b(a(a(a(b(b(a(a(a(a(a(a(x1)))))))))))))
3.46/1.68	
3.46/1.68	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.46/1.68	
3.46/1.68	   a(a(a(a(a(b(b(x))))))) -> b(b(a(a(a(b(b(a(a(a(a(a(x))))))))))))
3.46/1.68	
3.46/1.68	----------------------------------------
3.46/1.68	
3.46/1.68	(4)
3.46/1.68	Obligation:
3.46/1.68	Q restricted rewrite system:
3.46/1.68	The TRS R consists of the following rules:
3.46/1.68	
3.46/1.68	   a(a(a(a(a(b(b(x))))))) -> b(b(a(a(a(b(b(a(a(a(a(a(x))))))))))))
3.46/1.68	
3.46/1.68	Q is empty.
3.46/1.68	
3.46/1.68	----------------------------------------
3.46/1.68	
3.46/1.68	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.46/1.68	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.46/1.68	The following rules were used to construct the certificate:
3.46/1.68	
3.46/1.68	   a(a(a(a(a(b(b(x))))))) -> b(b(a(a(a(b(b(a(a(a(a(a(x))))))))))))
3.46/1.68	
3.46/1.68	The certificate found is represented by the following graph.
3.46/1.68	The certificate consists of the following enumerated nodes:
3.46/1.68	412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435
3.46/1.68	
3.46/1.68	Node 412 is start node and node 413 is final node.
3.46/1.68	
3.46/1.68	Those nodes are connected through the following edges:
3.46/1.68	
3.46/1.68	* 412 to 414 labelled b_1(0)* 413 to 413 labelled #_1(0)* 414 to 415 labelled b_1(0)* 415 to 416 labelled a_1(0)* 416 to 417 labelled a_1(0)* 417 to 418 labelled a_1(0)* 418 to 419 labelled b_1(0)* 419 to 420 labelled b_1(0)* 420 to 421 labelled a_1(0)* 420 to 425 labelled b_1(1)* 421 to 422 labelled a_1(0)* 421 to 425 labelled b_1(1)* 422 to 423 labelled a_1(0)* 422 to 425 labelled b_1(1)* 423 to 424 labelled a_1(0)* 423 to 425 labelled b_1(1)* 424 to 413 labelled a_1(0)* 424 to 425 labelled b_1(1)* 425 to 426 labelled b_1(1)* 426 to 427 labelled a_1(1)* 427 to 428 labelled a_1(1)* 428 to 429 labelled a_1(1)* 429 to 430 labelled b_1(1)* 430 to 431 labelled b_1(1)* 431 to 432 labelled a_1(1)* 431 to 425 labelled b_1(1)* 432 to 433 labelled a_1(1)* 432 to 425 labelled b_1(1)* 433 to 434 labelled a_1(1)* 433 to 425 labelled b_1(1)* 434 to 435 labelled a_1(1)* 434 to 425 labelled b_1(1)* 435 to 413 labelled a_1(1)* 435 to 425 labelled b_1(1)
3.46/1.68	
3.46/1.68	
3.46/1.68	----------------------------------------
3.46/1.68	
3.46/1.68	(6)
3.46/1.68	YES
3.76/1.71	EOF