3.13/1.70	YES
3.13/1.72	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.13/1.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.13/1.72	
3.13/1.72	
3.13/1.72	Termination w.r.t. Q of the given QTRS could be proven:
3.13/1.72	
3.13/1.72	(0) QTRS
3.13/1.72	(1) Strip Symbols Proof [SOUND, 0 ms]
3.13/1.72	(2) QTRS
3.13/1.72	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.13/1.72	(4) YES
3.13/1.72	
3.13/1.72	
3.13/1.72	----------------------------------------
3.13/1.72	
3.13/1.72	(0)
3.13/1.72	Obligation:
3.13/1.72	Q restricted rewrite system:
3.13/1.72	The TRS R consists of the following rules:
3.13/1.72	
3.13/1.72	   b(a(a(b(b(a(a(b(x1)))))))) -> a(a(b(b(a(a(b(a(a(b(a(a(b(b(x1))))))))))))))
3.13/1.72	
3.13/1.72	Q is empty.
3.13/1.72	
3.13/1.72	----------------------------------------
3.13/1.72	
3.13/1.72	(1) Strip Symbols Proof (SOUND)
3.13/1.72	We were given the following TRS:
3.13/1.72	
3.13/1.72	   b(a(a(b(b(a(a(b(x1)))))))) -> a(a(b(b(a(a(b(a(a(b(a(a(b(b(x1))))))))))))))
3.13/1.72	
3.13/1.72	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.13/1.72	
3.13/1.72	   b(a(a(b(b(a(a(x))))))) -> a(a(b(b(a(a(b(a(a(b(a(a(b(x)))))))))))))
3.13/1.72	
3.13/1.72	----------------------------------------
3.13/1.72	
3.13/1.72	(2)
3.13/1.72	Obligation:
3.13/1.72	Q restricted rewrite system:
3.13/1.72	The TRS R consists of the following rules:
3.13/1.72	
3.13/1.72	   b(a(a(b(b(a(a(x))))))) -> a(a(b(b(a(a(b(a(a(b(a(a(b(x)))))))))))))
3.13/1.72	
3.13/1.72	Q is empty.
3.13/1.72	
3.13/1.72	----------------------------------------
3.13/1.72	
3.13/1.72	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
3.13/1.72	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.13/1.72	The following rules were used to construct the certificate:
3.13/1.72	
3.13/1.72	   b(a(a(b(b(a(a(x))))))) -> a(a(b(b(a(a(b(a(a(b(a(a(b(x)))))))))))))
3.13/1.72	
3.13/1.72	The certificate found is represented by the following graph.
3.13/1.72	The certificate consists of the following enumerated nodes:
3.13/1.72	94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119
3.13/1.72	
3.13/1.72	Node 94 is start node and node 95 is final node.
3.13/1.72	
3.13/1.72	Those nodes are connected through the following edges:
3.13/1.72	
3.13/1.72	* 94 to 96 labelled a_1(0)* 95 to 95 labelled #_1(0)* 96 to 97 labelled a_1(0)* 97 to 98 labelled b_1(0)* 98 to 99 labelled b_1(0)* 99 to 100 labelled a_1(0)* 100 to 101 labelled a_1(0)* 101 to 102 labelled b_1(0)* 102 to 103 labelled a_1(0)* 103 to 104 labelled a_1(0)* 104 to 105 labelled b_1(0)* 104 to 108 labelled a_1(1)* 105 to 106 labelled a_1(0)* 106 to 107 labelled a_1(0)* 107 to 95 labelled b_1(0)* 107 to 108 labelled a_1(1)* 108 to 109 labelled a_1(1)* 109 to 110 labelled b_1(1)* 110 to 111 labelled b_1(1)* 111 to 112 labelled a_1(1)* 112 to 113 labelled a_1(1)* 113 to 114 labelled b_1(1)* 114 to 115 labelled a_1(1)* 115 to 116 labelled a_1(1)* 116 to 117 labelled b_1(1)* 116 to 108 labelled a_1(1)* 117 to 118 labelled a_1(1)* 118 to 119 labelled a_1(1)* 119 to 95 labelled b_1(1)* 119 to 108 labelled a_1(1)
3.13/1.72	
3.13/1.72	
3.13/1.72	----------------------------------------
3.13/1.72	
3.13/1.72	(4)
3.13/1.72	YES
3.32/1.75	EOF