3.59/1.69	YES
3.59/1.71	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.59/1.71	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.59/1.71	
3.59/1.71	
3.59/1.71	Termination w.r.t. Q of the given QTRS could be proven:
3.59/1.71	
3.59/1.71	(0) QTRS
3.59/1.71	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.59/1.71	(2) QTRS
3.59/1.71	(3) Strip Symbols Proof [SOUND, 0 ms]
3.59/1.71	(4) QTRS
3.59/1.71	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.59/1.71	(6) YES
3.59/1.71	
3.59/1.71	
3.59/1.71	----------------------------------------
3.59/1.71	
3.59/1.71	(0)
3.59/1.71	Obligation:
3.59/1.71	Q restricted rewrite system:
3.59/1.71	The TRS R consists of the following rules:
3.59/1.71	
3.59/1.71	   a(b(c(b(a(a(b(c(b(a(x1)))))))))) -> a(a(b(c(b(a(b(c(b(a(a(b(c(b(x1))))))))))))))
3.59/1.71	
3.59/1.71	Q is empty.
3.59/1.71	
3.59/1.71	----------------------------------------
3.59/1.71	
3.59/1.71	(1) QTRS Reverse (EQUIVALENT)
3.59/1.71	We applied the QTRS Reverse Processor [REVERSE].
3.59/1.71	----------------------------------------
3.59/1.71	
3.59/1.71	(2)
3.59/1.71	Obligation:
3.59/1.71	Q restricted rewrite system:
3.59/1.71	The TRS R consists of the following rules:
3.59/1.71	
3.59/1.71	   a(b(c(b(a(a(b(c(b(a(x1)))))))))) -> b(c(b(a(a(b(c(b(a(b(c(b(a(a(x1))))))))))))))
3.59/1.71	
3.59/1.71	Q is empty.
3.59/1.71	
3.59/1.71	----------------------------------------
3.59/1.71	
3.59/1.71	(3) Strip Symbols Proof (SOUND)
3.59/1.71	We were given the following TRS:
3.59/1.71	
3.59/1.71	   a(b(c(b(a(a(b(c(b(a(x1)))))))))) -> b(c(b(a(a(b(c(b(a(b(c(b(a(a(x1))))))))))))))
3.59/1.71	
3.59/1.71	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.59/1.71	
3.59/1.71	   a(b(c(b(a(a(b(c(b(x))))))))) -> b(c(b(a(a(b(c(b(a(b(c(b(a(x)))))))))))))
3.59/1.71	
3.59/1.71	----------------------------------------
3.59/1.71	
3.59/1.71	(4)
3.59/1.71	Obligation:
3.59/1.71	Q restricted rewrite system:
3.59/1.71	The TRS R consists of the following rules:
3.59/1.71	
3.59/1.71	   a(b(c(b(a(a(b(c(b(x))))))))) -> b(c(b(a(a(b(c(b(a(b(c(b(a(x)))))))))))))
3.59/1.71	
3.59/1.71	Q is empty.
3.59/1.71	
3.59/1.71	----------------------------------------
3.59/1.71	
3.59/1.71	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.59/1.71	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.59/1.71	The following rules were used to construct the certificate:
3.59/1.71	
3.59/1.71	   a(b(c(b(a(a(b(c(b(x))))))))) -> b(c(b(a(a(b(c(b(a(b(c(b(a(x)))))))))))))
3.59/1.71	
3.59/1.71	The certificate found is represented by the following graph.
3.59/1.71	The certificate consists of the following enumerated nodes:
3.59/1.71	382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611
3.59/1.71	
3.59/1.71	Node 382 is start node and node 383 is final node.
3.59/1.71	
3.59/1.71	Those nodes are connected through the following edges:
3.59/1.71	
3.59/1.71	* 382 to 384 labelled b_1(0)* 383 to 383 labelled #_1(0)* 384 to 385 labelled c_1(0)* 385 to 386 labelled b_1(0)* 386 to 387 labelled a_1(0)* 387 to 388 labelled a_1(0)* 388 to 389 labelled b_1(0)* 389 to 390 labelled c_1(0)* 390 to 391 labelled b_1(0)* 391 to 392 labelled a_1(0)* 391 to 600 labelled b_1(1)* 392 to 393 labelled b_1(0)* 393 to 394 labelled c_1(0)* 394 to 395 labelled b_1(0)* 395 to 383 labelled a_1(0)* 395 to 600 labelled b_1(1)* 600 to 601 labelled c_1(1)* 601 to 602 labelled b_1(1)* 602 to 603 labelled a_1(1)* 603 to 604 labelled a_1(1)* 604 to 605 labelled b_1(1)* 605 to 606 labelled c_1(1)* 606 to 607 labelled b_1(1)* 607 to 608 labelled a_1(1)* 607 to 600 labelled b_1(1)* 608 to 609 labelled b_1(1)* 609 to 610 labelled c_1(1)* 610 to 611 labelled b_1(1)* 611 to 383 labelled a_1(1)* 611 to 600 labelled b_1(1)
3.59/1.71	
3.59/1.71	
3.59/1.71	----------------------------------------
3.59/1.71	
3.59/1.71	(6)
3.59/1.71	YES
3.59/1.75	EOF