3.43/1.70	YES
3.43/1.73	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.43/1.73	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.43/1.73	
3.43/1.73	
3.43/1.73	Termination w.r.t. Q of the given QTRS could be proven:
3.43/1.73	
3.43/1.73	(0) QTRS
3.43/1.73	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.43/1.73	(2) QTRS
3.43/1.73	(3) Strip Symbols Proof [SOUND, 0 ms]
3.43/1.73	(4) QTRS
3.43/1.73	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.43/1.73	(6) YES
3.43/1.73	
3.43/1.73	
3.43/1.73	----------------------------------------
3.43/1.73	
3.43/1.73	(0)
3.43/1.73	Obligation:
3.43/1.73	Q restricted rewrite system:
3.43/1.73	The TRS R consists of the following rules:
3.43/1.73	
3.43/1.73	   a(b(a(a(b(a(b(a(b(a(x1)))))))))) -> a(a(b(a(b(a(b(a(b(a(a(b(x1))))))))))))
3.43/1.73	
3.43/1.73	Q is empty.
3.43/1.73	
3.43/1.73	----------------------------------------
3.43/1.73	
3.43/1.73	(1) QTRS Reverse (EQUIVALENT)
3.43/1.73	We applied the QTRS Reverse Processor [REVERSE].
3.43/1.73	----------------------------------------
3.43/1.73	
3.43/1.73	(2)
3.43/1.73	Obligation:
3.43/1.73	Q restricted rewrite system:
3.43/1.73	The TRS R consists of the following rules:
3.43/1.73	
3.43/1.73	   a(b(a(b(a(b(a(a(b(a(x1)))))))))) -> b(a(a(b(a(b(a(b(a(b(a(a(x1))))))))))))
3.43/1.73	
3.43/1.73	Q is empty.
3.43/1.73	
3.43/1.73	----------------------------------------
3.43/1.73	
3.43/1.73	(3) Strip Symbols Proof (SOUND)
3.43/1.73	We were given the following TRS:
3.43/1.73	
3.43/1.73	   a(b(a(b(a(b(a(a(b(a(x1)))))))))) -> b(a(a(b(a(b(a(b(a(b(a(a(x1))))))))))))
3.43/1.73	
3.43/1.73	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.43/1.73	
3.43/1.73	   a(b(a(b(a(b(a(a(b(x))))))))) -> b(a(a(b(a(b(a(b(a(b(a(x)))))))))))
3.43/1.73	
3.43/1.73	----------------------------------------
3.43/1.73	
3.43/1.73	(4)
3.43/1.73	Obligation:
3.43/1.73	Q restricted rewrite system:
3.43/1.73	The TRS R consists of the following rules:
3.43/1.73	
3.43/1.73	   a(b(a(b(a(b(a(a(b(x))))))))) -> b(a(a(b(a(b(a(b(a(b(a(x)))))))))))
3.43/1.73	
3.43/1.73	Q is empty.
3.43/1.73	
3.43/1.73	----------------------------------------
3.43/1.73	
3.43/1.73	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.43/1.73	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.43/1.73	The following rules were used to construct the certificate:
3.43/1.73	
3.43/1.73	   a(b(a(b(a(b(a(a(b(x))))))))) -> b(a(a(b(a(b(a(b(a(b(a(x)))))))))))
3.43/1.73	
3.43/1.73	The certificate found is represented by the following graph.
3.43/1.73	The certificate consists of the following enumerated nodes:
3.43/1.73	39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82
3.43/1.73	
3.43/1.73	Node 39 is start node and node 40 is final node.
3.43/1.73	
3.43/1.73	Those nodes are connected through the following edges:
3.43/1.73	
3.43/1.73	* 39 to 41 labelled b_1(0)* 40 to 40 labelled #_1(0)* 41 to 42 labelled a_1(0)* 42 to 43 labelled a_1(0)* 43 to 44 labelled b_1(0)* 44 to 45 labelled a_1(0)* 44 to 72 labelled b_1(1)* 45 to 46 labelled b_1(0)* 46 to 47 labelled a_1(0)* 46 to 72 labelled b_1(1)* 47 to 48 labelled b_1(0)* 48 to 49 labelled a_1(0)* 48 to 72 labelled b_1(1)* 49 to 50 labelled b_1(0)* 50 to 40 labelled a_1(0)* 50 to 72 labelled b_1(1)* 72 to 73 labelled a_1(1)* 73 to 74 labelled a_1(1)* 74 to 75 labelled b_1(1)* 75 to 76 labelled a_1(1)* 75 to 72 labelled b_1(1)* 76 to 77 labelled b_1(1)* 77 to 78 labelled a_1(1)* 77 to 72 labelled b_1(1)* 78 to 79 labelled b_1(1)* 79 to 81 labelled a_1(1)* 79 to 72 labelled b_1(1)* 81 to 82 labelled b_1(1)* 82 to 40 labelled a_1(1)* 82 to 72 labelled b_1(1)
3.43/1.73	
3.43/1.73	
3.43/1.73	----------------------------------------
3.43/1.73	
3.43/1.73	(6)
3.43/1.73	YES
3.43/1.75	EOF