4.47/1.90	YES
4.58/1.94	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
4.58/1.94	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.58/1.94	
4.58/1.94	
4.58/1.94	Termination w.r.t. Q of the given QTRS could be proven:
4.58/1.94	
4.58/1.94	(0) QTRS
4.58/1.94	(1) Strip Symbols Proof [SOUND, 0 ms]
4.58/1.94	(2) QTRS
4.58/1.94	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
4.58/1.94	(4) YES
4.58/1.94	
4.58/1.94	
4.58/1.94	----------------------------------------
4.58/1.94	
4.58/1.94	(0)
4.58/1.94	Obligation:
4.58/1.94	Q restricted rewrite system:
4.58/1.94	The TRS R consists of the following rules:
4.58/1.94	
4.58/1.94	   b(a(a(b(a(b(a(a(b(x1))))))))) -> a(b(a(b(a(a(b(a(a(b(a(b(x1))))))))))))
4.58/1.94	
4.58/1.94	Q is empty.
4.58/1.94	
4.58/1.94	----------------------------------------
4.58/1.94	
4.58/1.94	(1) Strip Symbols Proof (SOUND)
4.58/1.94	We were given the following TRS:
4.58/1.94	
4.58/1.94	   b(a(a(b(a(b(a(a(b(x1))))))))) -> a(b(a(b(a(a(b(a(a(b(a(b(x1))))))))))))
4.58/1.94	
4.58/1.94	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.58/1.94	
4.58/1.94	   b(a(a(b(a(b(a(a(x)))))))) -> a(b(a(b(a(a(b(a(a(b(a(x)))))))))))
4.58/1.94	
4.58/1.94	----------------------------------------
4.58/1.94	
4.58/1.94	(2)
4.58/1.94	Obligation:
4.58/1.94	Q restricted rewrite system:
4.58/1.94	The TRS R consists of the following rules:
4.58/1.94	
4.58/1.94	   b(a(a(b(a(b(a(a(x)))))))) -> a(b(a(b(a(a(b(a(a(b(a(x)))))))))))
4.58/1.94	
4.58/1.94	Q is empty.
4.58/1.94	
4.58/1.94	----------------------------------------
4.58/1.94	
4.58/1.94	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
4.58/1.94	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.58/1.94	The following rules were used to construct the certificate:
4.58/1.94	
4.58/1.94	   b(a(a(b(a(b(a(a(x)))))))) -> a(b(a(b(a(a(b(a(a(b(a(x)))))))))))
4.58/1.94	
4.58/1.94	The certificate found is represented by the following graph.
4.58/1.94	The certificate consists of the following enumerated nodes:
4.58/1.94	137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158
4.58/1.94	
4.58/1.94	Node 137 is start node and node 138 is final node.
4.58/1.94	
4.58/1.94	Those nodes are connected through the following edges:
4.58/1.94	
4.58/1.94	* 137 to 139 labelled a_1(0)* 138 to 138 labelled #_1(0)* 139 to 140 labelled b_1(0)* 140 to 141 labelled a_1(0)* 141 to 142 labelled b_1(0)* 142 to 143 labelled a_1(0)* 143 to 144 labelled a_1(0)* 144 to 145 labelled b_1(0)* 144 to 149 labelled a_1(1)* 145 to 146 labelled a_1(0)* 146 to 147 labelled a_1(0)* 147 to 148 labelled b_1(0)* 147 to 149 labelled a_1(1)* 148 to 138 labelled a_1(0)* 149 to 150 labelled b_1(1)* 150 to 151 labelled a_1(1)* 151 to 152 labelled b_1(1)* 152 to 153 labelled a_1(1)* 153 to 154 labelled a_1(1)* 154 to 155 labelled b_1(1)* 154 to 149 labelled a_1(1)* 155 to 156 labelled a_1(1)* 156 to 157 labelled a_1(1)* 157 to 158 labelled b_1(1)* 157 to 149 labelled a_1(1)* 158 to 138 labelled a_1(1)
4.58/1.94	
4.58/1.94	
4.58/1.94	----------------------------------------
4.58/1.94	
4.58/1.94	(4)
4.58/1.94	YES
4.58/1.98	EOF