4.16/1.82	YES
4.16/1.82	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
4.16/1.82	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.16/1.82	
4.16/1.82	
4.16/1.82	Termination w.r.t. Q of the given QTRS could be proven:
4.16/1.82	
4.16/1.82	(0) QTRS
4.16/1.82	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.16/1.82	(2) QTRS
4.16/1.82	(3) Strip Symbols Proof [SOUND, 0 ms]
4.16/1.82	(4) QTRS
4.16/1.82	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
4.16/1.82	(6) YES
4.16/1.82	
4.16/1.82	
4.16/1.82	----------------------------------------
4.16/1.82	
4.16/1.82	(0)
4.16/1.82	Obligation:
4.16/1.82	Q restricted rewrite system:
4.16/1.82	The TRS R consists of the following rules:
4.16/1.82	
4.16/1.82	   a(b(b(a(a(a(a(a(x1)))))))) -> a(a(a(a(a(a(b(b(a(b(b(a(b(b(x1))))))))))))))
4.16/1.82	
4.16/1.82	Q is empty.
4.16/1.82	
4.16/1.82	----------------------------------------
4.16/1.82	
4.16/1.82	(1) QTRS Reverse (EQUIVALENT)
4.16/1.82	We applied the QTRS Reverse Processor [REVERSE].
4.16/1.82	----------------------------------------
4.16/1.82	
4.16/1.82	(2)
4.16/1.82	Obligation:
4.16/1.82	Q restricted rewrite system:
4.16/1.82	The TRS R consists of the following rules:
4.16/1.82	
4.16/1.82	   a(a(a(a(a(b(b(a(x1)))))))) -> b(b(a(b(b(a(b(b(a(a(a(a(a(a(x1))))))))))))))
4.16/1.82	
4.16/1.82	Q is empty.
4.16/1.82	
4.16/1.82	----------------------------------------
4.16/1.82	
4.16/1.82	(3) Strip Symbols Proof (SOUND)
4.16/1.82	We were given the following TRS:
4.16/1.82	
4.16/1.82	   a(a(a(a(a(b(b(a(x1)))))))) -> b(b(a(b(b(a(b(b(a(a(a(a(a(a(x1))))))))))))))
4.16/1.82	
4.16/1.82	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.16/1.82	
4.16/1.82	   a(a(a(a(a(b(b(x))))))) -> b(b(a(b(b(a(b(b(a(a(a(a(a(x)))))))))))))
4.16/1.82	
4.16/1.82	----------------------------------------
4.16/1.82	
4.16/1.82	(4)
4.16/1.82	Obligation:
4.16/1.82	Q restricted rewrite system:
4.16/1.82	The TRS R consists of the following rules:
4.16/1.82	
4.16/1.82	   a(a(a(a(a(b(b(x))))))) -> b(b(a(b(b(a(b(b(a(a(a(a(a(x)))))))))))))
4.16/1.82	
4.16/1.82	Q is empty.
4.16/1.82	
4.16/1.82	----------------------------------------
4.16/1.82	
4.16/1.82	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.16/1.82	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.16/1.82	The following rules were used to construct the certificate:
4.16/1.82	
4.16/1.82	   a(a(a(a(a(b(b(x))))))) -> b(b(a(b(b(a(b(b(a(a(a(a(a(x)))))))))))))
4.16/1.82	
4.16/1.82	The certificate found is represented by the following graph.
4.16/1.82	The certificate consists of the following enumerated nodes:
4.16/1.82	538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563
4.16/1.82	
4.16/1.82	Node 538 is start node and node 539 is final node.
4.16/1.82	
4.16/1.82	Those nodes are connected through the following edges:
4.16/1.82	
4.16/1.82	* 538 to 540 labelled b_1(0)* 539 to 539 labelled #_1(0)* 540 to 541 labelled b_1(0)* 541 to 542 labelled a_1(0)* 542 to 543 labelled b_1(0)* 543 to 544 labelled b_1(0)* 544 to 545 labelled a_1(0)* 545 to 546 labelled b_1(0)* 546 to 547 labelled b_1(0)* 547 to 548 labelled a_1(0)* 547 to 552 labelled b_1(1)* 548 to 549 labelled a_1(0)* 548 to 552 labelled b_1(1)* 549 to 550 labelled a_1(0)* 549 to 552 labelled b_1(1)* 550 to 551 labelled a_1(0)* 550 to 552 labelled b_1(1)* 551 to 539 labelled a_1(0)* 551 to 552 labelled b_1(1)* 552 to 553 labelled b_1(1)* 553 to 554 labelled a_1(1)* 554 to 555 labelled b_1(1)* 555 to 556 labelled b_1(1)* 556 to 557 labelled a_1(1)* 557 to 558 labelled b_1(1)* 558 to 559 labelled b_1(1)* 559 to 560 labelled a_1(1)* 559 to 552 labelled b_1(1)* 560 to 561 labelled a_1(1)* 560 to 552 labelled b_1(1)* 561 to 562 labelled a_1(1)* 561 to 552 labelled b_1(1)* 562 to 563 labelled a_1(1)* 562 to 552 labelled b_1(1)* 563 to 539 labelled a_1(1)* 563 to 552 labelled b_1(1)
4.16/1.82	
4.16/1.82	
4.16/1.82	----------------------------------------
4.16/1.82	
4.16/1.82	(6)
4.16/1.82	YES
4.16/1.86	EOF