4.49/1.98	YES
4.95/2.03	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.95/2.03	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.95/2.03	
4.95/2.03	
4.95/2.03	Termination w.r.t. Q of the given QTRS could be proven:
4.95/2.03	
4.95/2.03	(0) QTRS
4.95/2.03	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.95/2.03	(2) QTRS
4.95/2.03	(3) Strip Symbols Proof [SOUND, 0 ms]
4.95/2.03	(4) QTRS
4.95/2.03	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 5 ms]
4.95/2.03	(6) YES
4.95/2.03	
4.95/2.03	
4.95/2.03	----------------------------------------
4.95/2.03	
4.95/2.03	(0)
4.95/2.03	Obligation:
4.95/2.03	Q restricted rewrite system:
4.95/2.03	The TRS R consists of the following rules:
4.95/2.03	
4.95/2.03	   a(b(a(a(a(a(x1)))))) -> a(a(a(a(a(b(a(b(a(a(b(a(a(b(x1))))))))))))))
4.95/2.03	
4.95/2.03	Q is empty.
4.95/2.03	
4.95/2.03	----------------------------------------
4.95/2.03	
4.95/2.03	(1) QTRS Reverse (EQUIVALENT)
4.95/2.03	We applied the QTRS Reverse Processor [REVERSE].
4.95/2.03	----------------------------------------
4.95/2.03	
4.95/2.03	(2)
4.95/2.03	Obligation:
4.95/2.03	Q restricted rewrite system:
4.95/2.03	The TRS R consists of the following rules:
4.95/2.03	
4.95/2.03	   a(a(a(a(b(a(x1)))))) -> b(a(a(b(a(a(b(a(b(a(a(a(a(a(x1))))))))))))))
4.95/2.03	
4.95/2.03	Q is empty.
4.95/2.03	
4.95/2.03	----------------------------------------
4.95/2.03	
4.95/2.03	(3) Strip Symbols Proof (SOUND)
4.95/2.03	We were given the following TRS:
4.95/2.03	
4.95/2.03	   a(a(a(a(b(a(x1)))))) -> b(a(a(b(a(a(b(a(b(a(a(a(a(a(x1))))))))))))))
4.95/2.03	
4.95/2.03	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.95/2.03	
4.95/2.03	   a(a(a(a(b(x))))) -> b(a(a(b(a(a(b(a(b(a(a(a(a(x)))))))))))))
4.95/2.03	
4.95/2.03	----------------------------------------
4.95/2.03	
4.95/2.03	(4)
4.95/2.03	Obligation:
4.95/2.03	Q restricted rewrite system:
4.95/2.03	The TRS R consists of the following rules:
4.95/2.03	
4.95/2.03	   a(a(a(a(b(x))))) -> b(a(a(b(a(a(b(a(b(a(a(a(a(x)))))))))))))
4.95/2.03	
4.95/2.03	Q is empty.
4.95/2.03	
4.95/2.03	----------------------------------------
4.95/2.03	
4.95/2.03	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.95/2.03	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.95/2.03	The following rules were used to construct the certificate:
4.95/2.03	
4.95/2.03	   a(a(a(a(b(x))))) -> b(a(a(b(a(a(b(a(b(a(a(a(a(x)))))))))))))
4.95/2.03	
4.95/2.03	The certificate found is represented by the following graph.
4.95/2.03	The certificate consists of the following enumerated nodes:
4.95/2.03	421, 422, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555
4.95/2.03	
4.95/2.03	Node 421 is start node and node 422 is final node.
4.95/2.03	
4.95/2.03	Those nodes are connected through the following edges:
4.95/2.03	
4.95/2.03	* 421 to 527 labelled b_1(0)* 422 to 422 labelled #_1(0)* 527 to 528 labelled a_1(0)* 528 to 529 labelled a_1(0)* 529 to 530 labelled b_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)* 535 to 544 labelled b_1(1)* 536 to 537 labelled a_1(0)* 536 to 544 labelled b_1(1)* 537 to 538 labelled a_1(0)* 537 to 544 labelled b_1(1)* 538 to 422 labelled a_1(0)* 538 to 544 labelled b_1(1)* 544 to 545 labelled a_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 a_1(1)* 549 to 550 labelled b_1(1)* 550 to 551 labelled a_1(1)* 551 to 552 labelled b_1(1)* 552 to 553 labelled a_1(1)* 552 to 544 labelled b_1(1)* 553 to 554 labelled a_1(1)* 553 to 544 labelled b_1(1)* 554 to 555 labelled a_1(1)* 554 to 544 labelled b_1(1)* 555 to 422 labelled a_1(1)* 555 to 544 labelled b_1(1)
4.95/2.03	
4.95/2.03	
4.95/2.03	----------------------------------------
4.95/2.03	
4.95/2.03	(6)
4.95/2.03	YES
4.95/2.08	EOF