3.43/1.85	YES
3.79/1.93	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.79/1.93	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.79/1.93	
3.79/1.93	
3.79/1.93	Termination w.r.t. Q of the given QTRS could be proven:
3.79/1.93	
3.79/1.93	(0) QTRS
3.79/1.93	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.79/1.93	(2) QTRS
3.79/1.93	(3) Strip Symbols Proof [SOUND, 0 ms]
3.79/1.93	(4) QTRS
3.79/1.93	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.79/1.93	(6) YES
3.79/1.93	
3.79/1.93	
3.79/1.93	----------------------------------------
3.79/1.93	
3.79/1.93	(0)
3.79/1.93	Obligation:
3.79/1.93	Q restricted rewrite system:
3.79/1.93	The TRS R consists of the following rules:
3.79/1.93	
3.79/1.93	   a(b(a(a(a(a(x1)))))) -> a(a(a(a(a(b(a(b(a(a(b(a(b(x1)))))))))))))
3.79/1.93	
3.79/1.93	Q is empty.
3.79/1.93	
3.79/1.93	----------------------------------------
3.79/1.93	
3.79/1.93	(1) QTRS Reverse (EQUIVALENT)
3.79/1.93	We applied the QTRS Reverse Processor [REVERSE].
3.79/1.93	----------------------------------------
3.79/1.93	
3.79/1.93	(2)
3.79/1.93	Obligation:
3.79/1.93	Q restricted rewrite system:
3.79/1.93	The TRS R consists of the following rules:
3.79/1.93	
3.79/1.93	   a(a(a(a(b(a(x1)))))) -> b(a(b(a(a(b(a(b(a(a(a(a(a(x1)))))))))))))
3.79/1.93	
3.79/1.93	Q is empty.
3.79/1.93	
3.79/1.93	----------------------------------------
3.79/1.93	
3.79/1.93	(3) Strip Symbols Proof (SOUND)
3.79/1.93	We were given the following TRS:
3.79/1.93	
3.79/1.93	   a(a(a(a(b(a(x1)))))) -> b(a(b(a(a(b(a(b(a(a(a(a(a(x1)))))))))))))
3.79/1.93	
3.79/1.93	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.79/1.93	
3.79/1.93	   a(a(a(a(b(x))))) -> b(a(b(a(a(b(a(b(a(a(a(a(x))))))))))))
3.79/1.93	
3.79/1.93	----------------------------------------
3.79/1.93	
3.79/1.93	(4)
3.79/1.93	Obligation:
3.79/1.93	Q restricted rewrite system:
3.79/1.93	The TRS R consists of the following rules:
3.79/1.93	
3.79/1.93	   a(a(a(a(b(x))))) -> b(a(b(a(a(b(a(b(a(a(a(a(x))))))))))))
3.79/1.93	
3.79/1.93	Q is empty.
3.79/1.93	
3.79/1.93	----------------------------------------
3.79/1.93	
3.79/1.93	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.79/1.93	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.79/1.93	The following rules were used to construct the certificate:
3.79/1.93	
3.79/1.93	   a(a(a(a(b(x))))) -> b(a(b(a(a(b(a(b(a(a(a(a(x))))))))))))
3.79/1.93	
3.79/1.93	The certificate found is represented by the following graph.
3.79/1.93	The certificate consists of the following enumerated nodes:
3.79/1.93	484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507
3.79/1.93	
3.79/1.93	Node 484 is start node and node 485 is final node.
3.79/1.93	
3.79/1.93	Those nodes are connected through the following edges:
3.79/1.93	
3.79/1.93	* 484 to 486 labelled b_1(0)* 485 to 485 labelled #_1(0)* 486 to 487 labelled a_1(0)* 487 to 488 labelled b_1(0)* 488 to 489 labelled a_1(0)* 489 to 490 labelled a_1(0)* 490 to 491 labelled b_1(0)* 491 to 492 labelled a_1(0)* 492 to 493 labelled b_1(0)* 493 to 494 labelled a_1(0)* 493 to 497 labelled b_1(1)* 494 to 495 labelled a_1(0)* 494 to 497 labelled b_1(1)* 495 to 496 labelled a_1(0)* 495 to 497 labelled b_1(1)* 496 to 485 labelled a_1(0)* 496 to 497 labelled b_1(1)* 497 to 498 labelled a_1(1)* 498 to 499 labelled b_1(1)* 499 to 500 labelled a_1(1)* 500 to 501 labelled a_1(1)* 501 to 502 labelled b_1(1)* 502 to 503 labelled a_1(1)* 503 to 504 labelled b_1(1)* 504 to 505 labelled a_1(1)* 504 to 497 labelled b_1(1)* 505 to 506 labelled a_1(1)* 505 to 497 labelled b_1(1)* 506 to 507 labelled a_1(1)* 506 to 497 labelled b_1(1)* 507 to 485 labelled a_1(1)* 507 to 497 labelled b_1(1)
3.79/1.93	
3.79/1.93	
3.79/1.93	----------------------------------------
3.79/1.93	
3.79/1.93	(6)
3.79/1.93	YES
3.79/1.95	EOF