3.29/1.76	YES
3.29/1.77	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.29/1.77	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.29/1.77	
3.29/1.77	
3.29/1.77	Termination w.r.t. Q of the given QTRS could be proven:
3.29/1.77	
3.29/1.77	(0) QTRS
3.29/1.77	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.29/1.77	(2) QTRS
3.29/1.77	(3) Strip Symbols Proof [SOUND, 0 ms]
3.29/1.77	(4) QTRS
3.29/1.77	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.29/1.77	(6) YES
3.29/1.77	
3.29/1.77	
3.29/1.77	----------------------------------------
3.29/1.77	
3.29/1.77	(0)
3.29/1.77	Obligation:
3.29/1.77	Q restricted rewrite system:
3.29/1.77	The TRS R consists of the following rules:
3.29/1.77	
3.29/1.77	   a(b(a(a(b(a(x1)))))) -> a(a(b(a(b(a(b(a(b(a(a(b(x1))))))))))))
3.29/1.77	
3.29/1.77	Q is empty.
3.29/1.77	
3.29/1.77	----------------------------------------
3.29/1.77	
3.29/1.77	(1) QTRS Reverse (EQUIVALENT)
3.29/1.77	We applied the QTRS Reverse Processor [REVERSE].
3.29/1.77	----------------------------------------
3.29/1.77	
3.29/1.77	(2)
3.29/1.77	Obligation:
3.29/1.77	Q restricted rewrite system:
3.29/1.77	The TRS R consists of the following rules:
3.29/1.77	
3.29/1.77	   a(b(a(a(b(a(x1)))))) -> b(a(a(b(a(b(a(b(a(b(a(a(x1))))))))))))
3.29/1.77	
3.29/1.77	Q is empty.
3.29/1.77	
3.29/1.77	----------------------------------------
3.29/1.77	
3.29/1.77	(3) Strip Symbols Proof (SOUND)
3.29/1.77	We were given the following TRS:
3.29/1.77	
3.29/1.77	   a(b(a(a(b(a(x1)))))) -> b(a(a(b(a(b(a(b(a(b(a(a(x1))))))))))))
3.29/1.77	
3.29/1.77	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.29/1.77	
3.29/1.77	   a(b(a(a(b(x))))) -> b(a(a(b(a(b(a(b(a(b(a(x)))))))))))
3.29/1.77	
3.29/1.77	----------------------------------------
3.29/1.77	
3.29/1.77	(4)
3.29/1.77	Obligation:
3.29/1.77	Q restricted rewrite system:
3.29/1.77	The TRS R consists of the following rules:
3.29/1.77	
3.29/1.77	   a(b(a(a(b(x))))) -> b(a(a(b(a(b(a(b(a(b(a(x)))))))))))
3.29/1.77	
3.29/1.77	Q is empty.
3.29/1.77	
3.29/1.77	----------------------------------------
3.29/1.77	
3.29/1.77	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.29/1.77	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.29/1.77	The following rules were used to construct the certificate:
3.29/1.77	
3.29/1.77	   a(b(a(a(b(x))))) -> b(a(a(b(a(b(a(b(a(b(a(x)))))))))))
3.29/1.77	
3.29/1.77	The certificate found is represented by the following graph.
3.29/1.77	The certificate consists of the following enumerated nodes:
3.29/1.77	528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549
3.29/1.77	
3.29/1.77	Node 528 is start node and node 529 is final node.
3.29/1.77	
3.29/1.77	Those nodes are connected through the following edges:
3.29/1.77	
3.29/1.77	* 528 to 530 labelled b_1(0)* 529 to 529 labelled #_1(0)* 530 to 531 labelled a_1(0)* 531 to 532 labelled a_1(0)* 532 to 533 labelled b_1(0)* 533 to 534 labelled a_1(0)* 534 to 535 labelled b_1(0)* 535 to 536 labelled a_1(0)* 536 to 537 labelled b_1(0)* 537 to 538 labelled a_1(0)* 537 to 540 labelled b_1(1)* 538 to 539 labelled b_1(0)* 539 to 529 labelled a_1(0)* 539 to 540 labelled b_1(1)* 540 to 541 labelled a_1(1)* 541 to 542 labelled a_1(1)* 542 to 543 labelled b_1(1)* 543 to 544 labelled a_1(1)* 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)* 547 to 540 labelled b_1(1)* 548 to 549 labelled b_1(1)* 549 to 529 labelled a_1(1)* 549 to 540 labelled b_1(1)
3.29/1.77	
3.29/1.77	
3.29/1.77	----------------------------------------
3.29/1.77	
3.29/1.77	(6)
3.29/1.77	YES
3.65/1.81	EOF