4.04/1.86	YES
4.04/1.87	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
4.04/1.87	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.04/1.87	
4.04/1.87	
4.04/1.87	Termination w.r.t. Q of the given QTRS could be proven:
4.04/1.87	
4.04/1.87	(0) QTRS
4.04/1.87	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.04/1.87	(2) QTRS
4.04/1.87	(3) Strip Symbols Proof [SOUND, 0 ms]
4.04/1.87	(4) QTRS
4.04/1.87	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 4 ms]
4.04/1.87	(6) YES
4.04/1.87	
4.04/1.87	
4.04/1.87	----------------------------------------
4.04/1.87	
4.04/1.87	(0)
4.04/1.87	Obligation:
4.04/1.87	Q restricted rewrite system:
4.04/1.87	The TRS R consists of the following rules:
4.04/1.87	
4.04/1.87	   a(b(a(a(b(a(x1)))))) -> a(a(b(a(b(a(b(a(a(b(x1))))))))))
4.04/1.87	
4.04/1.87	Q is empty.
4.04/1.87	
4.04/1.87	----------------------------------------
4.04/1.87	
4.04/1.87	(1) QTRS Reverse (EQUIVALENT)
4.04/1.87	We applied the QTRS Reverse Processor [REVERSE].
4.04/1.87	----------------------------------------
4.04/1.87	
4.04/1.87	(2)
4.04/1.87	Obligation:
4.04/1.87	Q restricted rewrite system:
4.04/1.87	The TRS R consists of the following rules:
4.04/1.87	
4.04/1.87	   a(b(a(a(b(a(x1)))))) -> b(a(a(b(a(b(a(b(a(a(x1))))))))))
4.04/1.87	
4.04/1.87	Q is empty.
4.04/1.87	
4.04/1.87	----------------------------------------
4.04/1.87	
4.04/1.87	(3) Strip Symbols Proof (SOUND)
4.04/1.87	We were given the following TRS:
4.04/1.87	
4.04/1.87	   a(b(a(a(b(a(x1)))))) -> b(a(a(b(a(b(a(b(a(a(x1))))))))))
4.04/1.87	
4.04/1.87	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.04/1.87	
4.04/1.87	   a(b(a(a(b(x))))) -> b(a(a(b(a(b(a(b(a(x)))))))))
4.04/1.87	
4.04/1.87	----------------------------------------
4.04/1.87	
4.04/1.87	(4)
4.04/1.87	Obligation:
4.04/1.87	Q restricted rewrite system:
4.04/1.87	The TRS R consists of the following rules:
4.04/1.87	
4.04/1.87	   a(b(a(a(b(x))))) -> b(a(a(b(a(b(a(b(a(x)))))))))
4.04/1.87	
4.04/1.87	Q is empty.
4.04/1.87	
4.04/1.87	----------------------------------------
4.04/1.87	
4.04/1.87	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.04/1.87	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.04/1.87	The following rules were used to construct the certificate:
4.04/1.87	
4.04/1.87	   a(b(a(a(b(x))))) -> b(a(a(b(a(b(a(b(a(x)))))))))
4.04/1.87	
4.04/1.87	The certificate found is represented by the following graph.
4.04/1.87	The certificate consists of the following enumerated nodes:
4.04/1.87	509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526
4.04/1.87	
4.04/1.87	Node 509 is start node and node 510 is final node.
4.04/1.87	
4.04/1.87	Those nodes are connected through the following edges:
4.04/1.87	
4.04/1.87	* 509 to 511 labelled b_1(0)* 510 to 510 labelled #_1(0)* 511 to 512 labelled a_1(0)* 512 to 513 labelled a_1(0)* 513 to 514 labelled b_1(0)* 514 to 515 labelled a_1(0)* 515 to 516 labelled b_1(0)* 516 to 517 labelled a_1(0)* 516 to 519 labelled b_1(1)* 517 to 518 labelled b_1(0)* 518 to 510 labelled a_1(0)* 518 to 519 labelled b_1(1)* 519 to 520 labelled a_1(1)* 520 to 521 labelled a_1(1)* 521 to 522 labelled b_1(1)* 522 to 523 labelled a_1(1)* 523 to 524 labelled b_1(1)* 524 to 525 labelled a_1(1)* 524 to 519 labelled b_1(1)* 525 to 526 labelled b_1(1)* 526 to 510 labelled a_1(1)* 526 to 519 labelled b_1(1)
4.04/1.87	
4.04/1.87	
4.04/1.87	----------------------------------------
4.04/1.87	
4.04/1.87	(6)
4.04/1.87	YES
4.18/1.90	EOF