3.91/1.82	YES
3.91/1.84	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.91/1.84	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.91/1.84	
3.91/1.84	
3.91/1.84	Termination w.r.t. Q of the given QTRS could be proven:
3.91/1.84	
3.91/1.84	(0) QTRS
3.91/1.84	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.91/1.84	(2) QTRS
3.91/1.84	(3) Strip Symbols Proof [SOUND, 0 ms]
3.91/1.84	(4) QTRS
3.91/1.84	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.91/1.84	(6) YES
3.91/1.84	
3.91/1.84	
3.91/1.84	----------------------------------------
3.91/1.84	
3.91/1.84	(0)
3.91/1.84	Obligation:
3.91/1.84	Q restricted rewrite system:
3.91/1.84	The TRS R consists of the following rules:
3.91/1.84	
3.91/1.84	   a(b(b(c(a(a(b(b(c(a(x1)))))))))) -> a(a(b(b(c(a(b(b(c(a(a(b(b(c(x1))))))))))))))
3.91/1.84	
3.91/1.84	Q is empty.
3.91/1.84	
3.91/1.84	----------------------------------------
3.91/1.84	
3.91/1.84	(1) QTRS Reverse (EQUIVALENT)
3.91/1.84	We applied the QTRS Reverse Processor [REVERSE].
3.91/1.84	----------------------------------------
3.91/1.84	
3.91/1.84	(2)
3.91/1.84	Obligation:
3.91/1.84	Q restricted rewrite system:
3.91/1.84	The TRS R consists of the following rules:
3.91/1.84	
3.91/1.84	   a(c(b(b(a(a(c(b(b(a(x1)))))))))) -> c(b(b(a(a(c(b(b(a(c(b(b(a(a(x1))))))))))))))
3.91/1.84	
3.91/1.84	Q is empty.
3.91/1.84	
3.91/1.84	----------------------------------------
3.91/1.84	
3.91/1.84	(3) Strip Symbols Proof (SOUND)
3.91/1.84	We were given the following TRS:
3.91/1.84	
3.91/1.84	   a(c(b(b(a(a(c(b(b(a(x1)))))))))) -> c(b(b(a(a(c(b(b(a(c(b(b(a(a(x1))))))))))))))
3.91/1.84	
3.91/1.84	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.91/1.84	
3.91/1.84	   a(c(b(b(a(a(c(b(b(x))))))))) -> c(b(b(a(a(c(b(b(a(c(b(b(a(x)))))))))))))
3.91/1.84	
3.91/1.84	----------------------------------------
3.91/1.84	
3.91/1.84	(4)
3.91/1.84	Obligation:
3.91/1.84	Q restricted rewrite system:
3.91/1.84	The TRS R consists of the following rules:
3.91/1.84	
3.91/1.84	   a(c(b(b(a(a(c(b(b(x))))))))) -> c(b(b(a(a(c(b(b(a(c(b(b(a(x)))))))))))))
3.91/1.84	
3.91/1.84	Q is empty.
3.91/1.84	
3.91/1.84	----------------------------------------
3.91/1.84	
3.91/1.84	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.91/1.84	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.91/1.84	The following rules were used to construct the certificate:
3.91/1.84	
3.91/1.84	   a(c(b(b(a(a(c(b(b(x))))))))) -> c(b(b(a(a(c(b(b(a(c(b(b(a(x)))))))))))))
3.91/1.84	
3.91/1.84	The certificate found is represented by the following graph.
3.91/1.84	The certificate consists of the following enumerated nodes:
3.91/1.84	586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611
3.91/1.84	
3.91/1.84	Node 586 is start node and node 587 is final node.
3.91/1.84	
3.91/1.84	Those nodes are connected through the following edges:
3.91/1.84	
3.91/1.84	* 586 to 588 labelled c_1(0)* 587 to 587 labelled #_1(0)* 588 to 589 labelled b_1(0)* 589 to 590 labelled b_1(0)* 590 to 591 labelled a_1(0)* 591 to 592 labelled a_1(0)* 592 to 593 labelled c_1(0)* 593 to 594 labelled b_1(0)* 594 to 595 labelled b_1(0)* 595 to 596 labelled a_1(0)* 595 to 600 labelled c_1(1)* 596 to 597 labelled c_1(0)* 597 to 598 labelled b_1(0)* 598 to 599 labelled b_1(0)* 599 to 587 labelled a_1(0)* 599 to 600 labelled c_1(1)* 600 to 601 labelled b_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 c_1(1)* 605 to 606 labelled b_1(1)* 606 to 607 labelled b_1(1)* 607 to 608 labelled a_1(1)* 607 to 600 labelled c_1(1)* 608 to 609 labelled c_1(1)* 609 to 610 labelled b_1(1)* 610 to 611 labelled b_1(1)* 611 to 587 labelled a_1(1)* 611 to 600 labelled c_1(1)
3.91/1.84	
3.91/1.84	
3.91/1.84	----------------------------------------
3.91/1.84	
3.91/1.84	(6)
3.91/1.84	YES
3.91/1.87	EOF