3.50/1.69	YES
3.50/1.73	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.50/1.73	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.50/1.73	
3.50/1.73	
3.50/1.73	Termination w.r.t. Q of the given QTRS could be proven:
3.50/1.73	
3.50/1.73	(0) QTRS
3.50/1.73	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.50/1.73	(2) QTRS
3.50/1.73	(3) Strip Symbols Proof [SOUND, 0 ms]
3.50/1.73	(4) QTRS
3.50/1.73	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.50/1.73	(6) YES
3.50/1.73	
3.50/1.73	
3.50/1.73	----------------------------------------
3.50/1.73	
3.50/1.73	(0)
3.50/1.73	Obligation:
3.50/1.73	Q restricted rewrite system:
3.50/1.73	The TRS R consists of the following rules:
3.50/1.73	
3.50/1.73	   a(b(a(b(a(a(a(x1))))))) -> a(a(a(a(b(a(b(a(b(x1)))))))))
3.50/1.73	
3.50/1.73	Q is empty.
3.50/1.73	
3.50/1.73	----------------------------------------
3.50/1.73	
3.50/1.73	(1) QTRS Reverse (EQUIVALENT)
3.50/1.73	We applied the QTRS Reverse Processor [REVERSE].
3.50/1.73	----------------------------------------
3.50/1.73	
3.50/1.73	(2)
3.50/1.73	Obligation:
3.50/1.73	Q restricted rewrite system:
3.50/1.73	The TRS R consists of the following rules:
3.50/1.73	
3.50/1.73	   a(a(a(b(a(b(a(x1))))))) -> b(a(b(a(b(a(a(a(a(x1)))))))))
3.50/1.73	
3.50/1.73	Q is empty.
3.50/1.73	
3.50/1.73	----------------------------------------
3.50/1.73	
3.50/1.73	(3) Strip Symbols Proof (SOUND)
3.50/1.73	We were given the following TRS:
3.50/1.73	
3.50/1.73	   a(a(a(b(a(b(a(x1))))))) -> b(a(b(a(b(a(a(a(a(x1)))))))))
3.50/1.73	
3.50/1.73	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.50/1.73	
3.50/1.73	   a(a(a(b(a(b(x)))))) -> b(a(b(a(b(a(a(a(x))))))))
3.50/1.73	
3.50/1.73	----------------------------------------
3.50/1.73	
3.50/1.73	(4)
3.50/1.73	Obligation:
3.50/1.73	Q restricted rewrite system:
3.50/1.73	The TRS R consists of the following rules:
3.50/1.73	
3.50/1.73	   a(a(a(b(a(b(x)))))) -> b(a(b(a(b(a(a(a(x))))))))
3.50/1.73	
3.50/1.73	Q is empty.
3.50/1.73	
3.50/1.73	----------------------------------------
3.50/1.73	
3.50/1.73	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.50/1.73	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.50/1.73	The following rules were used to construct the certificate:
3.50/1.73	
3.50/1.73	   a(a(a(b(a(b(x)))))) -> b(a(b(a(b(a(a(a(x))))))))
3.50/1.73	
3.50/1.73	The certificate found is represented by the following graph.
3.50/1.73	The certificate consists of the following enumerated nodes:
3.50/1.73	553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568
3.50/1.73	
3.50/1.73	Node 553 is start node and node 554 is final node.
3.50/1.73	
3.50/1.73	Those nodes are connected through the following edges:
3.50/1.73	
3.50/1.73	* 553 to 555 labelled b_1(0)* 554 to 554 labelled #_1(0)* 555 to 556 labelled a_1(0)* 556 to 557 labelled b_1(0)* 557 to 558 labelled a_1(0)* 558 to 559 labelled b_1(0)* 559 to 560 labelled a_1(0)* 559 to 562 labelled b_1(1)* 560 to 561 labelled a_1(0)* 560 to 562 labelled b_1(1)* 561 to 554 labelled a_1(0)* 561 to 562 labelled b_1(1)* 562 to 563 labelled a_1(1)* 563 to 564 labelled b_1(1)* 564 to 565 labelled a_1(1)* 565 to 566 labelled b_1(1)* 566 to 567 labelled a_1(1)* 566 to 562 labelled b_1(1)* 567 to 568 labelled a_1(1)* 567 to 562 labelled b_1(1)* 568 to 554 labelled a_1(1)* 568 to 562 labelled b_1(1)
3.50/1.73	
3.50/1.73	
3.50/1.73	----------------------------------------
3.50/1.73	
3.50/1.73	(6)
3.50/1.73	YES
3.87/1.76	EOF