4.33/1.85	YES
4.33/1.88	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
4.33/1.88	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.33/1.88	
4.33/1.88	
4.33/1.88	Termination w.r.t. Q of the given QTRS could be proven:
4.33/1.88	
4.33/1.88	(0) QTRS
4.33/1.88	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.33/1.88	(2) QTRS
4.33/1.88	(3) Strip Symbols Proof [SOUND, 0 ms]
4.33/1.88	(4) QTRS
4.33/1.88	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
4.33/1.88	(6) YES
4.33/1.88	
4.33/1.88	
4.33/1.88	----------------------------------------
4.33/1.88	
4.33/1.88	(0)
4.33/1.88	Obligation:
4.33/1.88	Q restricted rewrite system:
4.33/1.88	The TRS R consists of the following rules:
4.33/1.88	
4.33/1.88	   a(b(a(b(a(a(a(a(a(x1))))))))) -> a(a(a(a(a(a(b(a(b(a(b(a(b(x1)))))))))))))
4.33/1.88	
4.33/1.88	Q is empty.
4.33/1.88	
4.33/1.88	----------------------------------------
4.33/1.88	
4.33/1.88	(1) QTRS Reverse (EQUIVALENT)
4.33/1.88	We applied the QTRS Reverse Processor [REVERSE].
4.33/1.88	----------------------------------------
4.33/1.88	
4.33/1.88	(2)
4.33/1.88	Obligation:
4.33/1.88	Q restricted rewrite system:
4.33/1.88	The TRS R consists of the following rules:
4.33/1.88	
4.33/1.88	   a(a(a(a(a(b(a(b(a(x1))))))))) -> b(a(b(a(b(a(b(a(a(a(a(a(a(x1)))))))))))))
4.33/1.88	
4.33/1.88	Q is empty.
4.33/1.88	
4.33/1.88	----------------------------------------
4.33/1.88	
4.33/1.88	(3) Strip Symbols Proof (SOUND)
4.33/1.88	We were given the following TRS:
4.33/1.88	
4.33/1.88	   a(a(a(a(a(b(a(b(a(x1))))))))) -> b(a(b(a(b(a(b(a(a(a(a(a(a(x1)))))))))))))
4.33/1.88	
4.33/1.88	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.33/1.88	
4.33/1.88	   a(a(a(a(a(b(a(b(x)))))))) -> b(a(b(a(b(a(b(a(a(a(a(a(x))))))))))))
4.33/1.88	
4.33/1.88	----------------------------------------
4.33/1.88	
4.33/1.88	(4)
4.33/1.88	Obligation:
4.33/1.88	Q restricted rewrite system:
4.33/1.88	The TRS R consists of the following rules:
4.33/1.88	
4.33/1.88	   a(a(a(a(a(b(a(b(x)))))))) -> b(a(b(a(b(a(b(a(a(a(a(a(x))))))))))))
4.33/1.88	
4.33/1.88	Q is empty.
4.33/1.88	
4.33/1.88	----------------------------------------
4.33/1.88	
4.33/1.88	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.33/1.88	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.33/1.88	The following rules were used to construct the certificate:
4.33/1.88	
4.33/1.88	   a(a(a(a(a(b(a(b(x)))))))) -> b(a(b(a(b(a(b(a(a(a(a(a(x))))))))))))
4.33/1.88	
4.33/1.88	The certificate found is represented by the following graph.
4.33/1.88	The certificate consists of the following enumerated nodes:
4.33/1.88	532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555
4.33/1.88	
4.33/1.88	Node 532 is start node and node 533 is final node.
4.33/1.88	
4.33/1.88	Those nodes are connected through the following edges:
4.33/1.88	
4.33/1.88	* 532 to 534 labelled b_1(0)* 533 to 533 labelled #_1(0)* 534 to 535 labelled a_1(0)* 535 to 536 labelled b_1(0)* 536 to 537 labelled a_1(0)* 537 to 538 labelled b_1(0)* 538 to 539 labelled a_1(0)* 539 to 540 labelled b_1(0)* 540 to 541 labelled a_1(0)* 540 to 545 labelled b_1(1)* 541 to 542 labelled a_1(0)* 541 to 545 labelled b_1(1)* 542 to 543 labelled a_1(0)* 542 to 545 labelled b_1(1)* 543 to 544 labelled a_1(0)* 543 to 545 labelled b_1(1)* 544 to 533 labelled a_1(0)* 544 to 545 labelled b_1(1)* 545 to 546 labelled a_1(1)* 546 to 547 labelled b_1(1)* 547 to 548 labelled a_1(1)* 548 to 549 labelled b_1(1)* 549 to 550 labelled a_1(1)* 550 to 551 labelled b_1(1)* 551 to 552 labelled a_1(1)* 551 to 545 labelled b_1(1)* 552 to 553 labelled a_1(1)* 552 to 545 labelled b_1(1)* 553 to 554 labelled a_1(1)* 553 to 545 labelled b_1(1)* 554 to 555 labelled a_1(1)* 554 to 545 labelled b_1(1)* 555 to 533 labelled a_1(1)* 555 to 545 labelled b_1(1)
4.33/1.88	
4.33/1.88	
4.33/1.88	----------------------------------------
4.33/1.88	
4.33/1.88	(6)
4.33/1.88	YES
4.61/1.93	EOF