3.27/1.57	YES
3.27/1.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.27/1.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.27/1.61	
3.27/1.61	
3.27/1.61	Termination w.r.t. Q of the given QTRS could be proven:
3.27/1.61	
3.27/1.61	(0) QTRS
3.27/1.61	(1) Strip Symbols Proof [SOUND, 0 ms]
3.27/1.61	(2) QTRS
3.27/1.61	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.27/1.61	(4) YES
3.27/1.61	
3.27/1.61	
3.27/1.61	----------------------------------------
3.27/1.61	
3.27/1.61	(0)
3.27/1.61	Obligation:
3.27/1.61	Q restricted rewrite system:
3.27/1.61	The TRS R consists of the following rules:
3.27/1.61	
3.27/1.61	   b(a(a(b(a(b(a(a(a(b(x1)))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(b(x1)))))))))))))
3.27/1.61	
3.27/1.61	Q is empty.
3.27/1.61	
3.27/1.61	----------------------------------------
3.27/1.61	
3.27/1.61	(1) Strip Symbols Proof (SOUND)
3.27/1.61	We were given the following TRS:
3.27/1.61	
3.27/1.61	   b(a(a(b(a(b(a(a(a(b(x1)))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(b(x1)))))))))))))
3.27/1.61	
3.27/1.61	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.27/1.61	
3.27/1.61	   b(a(a(b(a(b(a(a(a(x))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(x))))))))))))
3.27/1.61	
3.27/1.61	----------------------------------------
3.27/1.61	
3.27/1.61	(2)
3.27/1.61	Obligation:
3.27/1.61	Q restricted rewrite system:
3.27/1.61	The TRS R consists of the following rules:
3.27/1.61	
3.27/1.61	   b(a(a(b(a(b(a(a(a(x))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(x))))))))))))
3.27/1.61	
3.27/1.61	Q is empty.
3.27/1.61	
3.27/1.61	----------------------------------------
3.27/1.61	
3.27/1.61	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
3.27/1.61	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
3.27/1.61	The following rules were used to construct the certificate:
3.27/1.61	
3.27/1.61	   b(a(a(b(a(b(a(a(a(x))))))))) -> a(b(a(b(a(a(a(b(a(b(a(a(x))))))))))))
3.27/1.61	
3.27/1.61	The certificate found is represented by the following graph.
3.27/1.61	The certificate consists of the following enumerated nodes:
3.27/1.61	27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72
3.27/1.61	
3.27/1.61	Node 27 is start node and node 28 is final node.
3.27/1.61	
3.27/1.61	Those nodes are connected through the following edges:
3.27/1.61	
3.27/1.61	* 27 to 29 labelled a_1(0)* 28 to 28 labelled #_1(0)* 29 to 30 labelled b_1(0)* 30 to 31 labelled a_1(0)* 31 to 32 labelled b_1(0)* 32 to 33 labelled a_1(0)* 33 to 34 labelled a_1(0)* 34 to 35 labelled a_1(0)* 35 to 36 labelled b_1(0)* 35 to 51 labelled a_1(1)* 36 to 37 labelled a_1(0)* 37 to 38 labelled b_1(0)* 37 to 40 labelled a_1(1)* 38 to 39 labelled a_1(0)* 39 to 28 labelled a_1(0)* 40 to 41 labelled b_1(1)* 41 to 42 labelled a_1(1)* 42 to 43 labelled b_1(1)* 43 to 44 labelled a_1(1)* 44 to 45 labelled a_1(1)* 45 to 46 labelled a_1(1)* 46 to 47 labelled b_1(1)* 46 to 62 labelled a_1(2)* 47 to 48 labelled a_1(1)* 48 to 49 labelled b_1(1)* 48 to 40 labelled a_1(1)* 49 to 50 labelled a_1(1)* 50 to 28 labelled a_1(1)* 51 to 52 labelled b_1(1)* 52 to 53 labelled a_1(1)* 53 to 54 labelled b_1(1)* 54 to 55 labelled a_1(1)* 55 to 56 labelled a_1(1)* 56 to 57 labelled a_1(1)* 57 to 58 labelled b_1(1)* 57 to 62 labelled a_1(2)* 58 to 59 labelled a_1(1)* 59 to 60 labelled b_1(1)* 59 to 40 labelled a_1(1)* 60 to 61 labelled a_1(1)* 61 to 46 labelled a_1(1)* 62 to 63 labelled b_1(2)* 63 to 64 labelled a_1(2)* 64 to 65 labelled b_1(2)* 65 to 66 labelled a_1(2)* 66 to 67 labelled a_1(2)* 67 to 68 labelled a_1(2)* 68 to 69 labelled b_1(2)* 68 to 62 labelled a_1(2)* 69 to 70 labelled a_1(2)* 70 to 71 labelled b_1(2)* 70 to 40 labelled a_1(1)* 71 to 72 labelled a_1(2)* 72 to 46 labelled a_1(2)
3.27/1.61	
3.27/1.61	
3.27/1.61	----------------------------------------
3.27/1.61	
3.27/1.61	(4)
3.27/1.61	YES
3.27/1.64	EOF