4.33/1.94	YES
4.33/1.98	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.33/1.98	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.33/1.98	
4.33/1.98	
4.33/1.98	Termination w.r.t. Q of the given QTRS could be proven:
4.33/1.98	
4.33/1.98	(0) QTRS
4.33/1.98	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.33/1.98	(2) QTRS
4.33/1.98	(3) Strip Symbols Proof [SOUND, 0 ms]
4.33/1.98	(4) QTRS
4.33/1.98	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
4.33/1.98	(6) YES
4.33/1.98	
4.33/1.98	
4.33/1.98	----------------------------------------
4.33/1.98	
4.33/1.98	(0)
4.33/1.98	Obligation:
4.33/1.98	Q restricted rewrite system:
4.33/1.98	The TRS R consists of the following rules:
4.33/1.98	
4.33/1.98	   a(b(a(a(b(a(b(a(b(a(x1)))))))))) -> a(a(b(a(b(a(b(a(b(a(a(b(a(b(x1))))))))))))))
4.33/1.98	
4.33/1.98	Q is empty.
4.33/1.98	
4.33/1.98	----------------------------------------
4.33/1.98	
4.33/1.98	(1) QTRS Reverse (EQUIVALENT)
4.33/1.98	We applied the QTRS Reverse Processor [REVERSE].
4.33/1.98	----------------------------------------
4.33/1.98	
4.33/1.98	(2)
4.33/1.98	Obligation:
4.33/1.98	Q restricted rewrite system:
4.33/1.98	The TRS R consists of the following rules:
4.33/1.98	
4.33/1.98	   a(b(a(b(a(b(a(a(b(a(x1)))))))))) -> b(a(b(a(a(b(a(b(a(b(a(b(a(a(x1))))))))))))))
4.33/1.98	
4.33/1.98	Q is empty.
4.33/1.98	
4.33/1.98	----------------------------------------
4.33/1.98	
4.33/1.98	(3) Strip Symbols Proof (SOUND)
4.33/1.98	We were given the following TRS:
4.33/1.98	
4.33/1.98	   a(b(a(b(a(b(a(a(b(a(x1)))))))))) -> b(a(b(a(a(b(a(b(a(b(a(b(a(a(x1))))))))))))))
4.33/1.98	
4.33/1.98	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.33/1.98	
4.33/1.98	   a(b(a(b(a(b(a(a(b(x))))))))) -> b(a(b(a(a(b(a(b(a(b(a(b(a(x)))))))))))))
4.33/1.98	
4.33/1.98	----------------------------------------
4.33/1.98	
4.33/1.98	(4)
4.33/1.98	Obligation:
4.33/1.98	Q restricted rewrite system:
4.33/1.98	The TRS R consists of the following rules:
4.33/1.98	
4.33/1.98	   a(b(a(b(a(b(a(a(b(x))))))))) -> b(a(b(a(a(b(a(b(a(b(a(b(a(x)))))))))))))
4.33/1.98	
4.33/1.98	Q is empty.
4.33/1.98	
4.33/1.98	----------------------------------------
4.33/1.98	
4.33/1.98	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.33/1.98	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.33/1.98	The following rules were used to construct the certificate:
4.33/1.98	
4.33/1.98	   a(b(a(b(a(b(a(a(b(x))))))))) -> b(a(b(a(a(b(a(b(a(b(a(b(a(x)))))))))))))
4.33/1.98	
4.33/1.98	The certificate found is represented by the following graph.
4.33/1.98	The certificate consists of the following enumerated nodes:
4.33/1.98	614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639
4.33/1.98	
4.33/1.98	Node 614 is start node and node 615 is final node.
4.33/1.98	
4.33/1.98	Those nodes are connected through the following edges:
4.33/1.98	
4.33/1.98	* 614 to 616 labelled b_1(0)* 615 to 615 labelled #_1(0)* 616 to 617 labelled a_1(0)* 617 to 618 labelled b_1(0)* 618 to 619 labelled a_1(0)* 619 to 620 labelled a_1(0)* 620 to 621 labelled b_1(0)* 621 to 622 labelled a_1(0)* 621 to 628 labelled b_1(1)* 622 to 623 labelled b_1(0)* 623 to 624 labelled a_1(0)* 623 to 628 labelled b_1(1)* 624 to 625 labelled b_1(0)* 625 to 626 labelled a_1(0)* 625 to 628 labelled b_1(1)* 626 to 627 labelled b_1(0)* 627 to 615 labelled a_1(0)* 627 to 628 labelled b_1(1)* 628 to 629 labelled a_1(1)* 629 to 630 labelled b_1(1)* 630 to 631 labelled a_1(1)* 631 to 632 labelled a_1(1)* 632 to 633 labelled b_1(1)* 633 to 634 labelled a_1(1)* 633 to 628 labelled b_1(1)* 634 to 635 labelled b_1(1)* 635 to 636 labelled a_1(1)* 635 to 628 labelled b_1(1)* 636 to 637 labelled b_1(1)* 637 to 638 labelled a_1(1)* 637 to 628 labelled b_1(1)* 638 to 639 labelled b_1(1)* 639 to 615 labelled a_1(1)* 639 to 628 labelled b_1(1)
4.33/1.98	
4.33/1.98	
4.33/1.98	----------------------------------------
4.33/1.98	
4.33/1.98	(6)
4.33/1.98	YES
4.64/2.02	EOF