3.84/1.75	YES
3.84/1.77	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.84/1.77	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.84/1.77	
3.84/1.77	
3.84/1.77	Termination w.r.t. Q of the given QTRS could be proven:
3.84/1.77	
3.84/1.77	(0) QTRS
3.84/1.77	(1) Strip Symbols Proof [SOUND, 0 ms]
3.84/1.77	(2) QTRS
3.84/1.77	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.84/1.77	(4) YES
3.84/1.77	
3.84/1.77	
3.84/1.77	----------------------------------------
3.84/1.77	
3.84/1.77	(0)
3.84/1.77	Obligation:
3.84/1.77	Q restricted rewrite system:
3.84/1.77	The TRS R consists of the following rules:
3.84/1.77	
3.84/1.77	   b(a(a(b(b(a(a(a(a(b(x1)))))))))) -> a(a(b(b(a(a(a(a(b(b(a(a(b(x1)))))))))))))
3.84/1.77	
3.84/1.77	Q is empty.
3.84/1.77	
3.84/1.77	----------------------------------------
3.84/1.77	
3.84/1.77	(1) Strip Symbols Proof (SOUND)
3.84/1.77	We were given the following TRS:
3.84/1.77	
3.84/1.77	   b(a(a(b(b(a(a(a(a(b(x1)))))))))) -> a(a(b(b(a(a(a(a(b(b(a(a(b(x1)))))))))))))
3.84/1.77	
3.84/1.77	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.84/1.77	
3.84/1.77	   b(a(a(b(b(a(a(a(a(x))))))))) -> a(a(b(b(a(a(a(a(b(b(a(a(x))))))))))))
3.84/1.77	
3.84/1.77	----------------------------------------
3.84/1.77	
3.84/1.77	(2)
3.84/1.77	Obligation:
3.84/1.77	Q restricted rewrite system:
3.84/1.77	The TRS R consists of the following rules:
3.84/1.77	
3.84/1.77	   b(a(a(b(b(a(a(a(a(x))))))))) -> a(a(b(b(a(a(a(a(b(b(a(a(x))))))))))))
3.84/1.77	
3.84/1.77	Q is empty.
3.84/1.77	
3.84/1.77	----------------------------------------
3.84/1.77	
3.84/1.77	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
3.84/1.77	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
3.84/1.77	The following rules were used to construct the certificate:
3.84/1.77	
3.84/1.77	   b(a(a(b(b(a(a(a(a(x))))))))) -> a(a(b(b(a(a(a(a(b(b(a(a(x))))))))))))
3.84/1.77	
3.84/1.77	The certificate found is represented by the following graph.
3.84/1.77	The certificate consists of the following enumerated nodes:
3.84/1.77	125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182
3.84/1.77	
3.84/1.77	Node 125 is start node and node 126 is final node.
3.84/1.77	
3.84/1.77	Those nodes are connected through the following edges:
3.84/1.77	
3.84/1.77	* 125 to 127 labelled a_1(0)* 126 to 126 labelled #_1(0)* 127 to 128 labelled a_1(0)* 128 to 129 labelled b_1(0)* 129 to 130 labelled b_1(0)* 130 to 131 labelled a_1(0)* 131 to 132 labelled a_1(0)* 132 to 133 labelled a_1(0)* 133 to 134 labelled a_1(0)* 134 to 135 labelled b_1(0)* 134 to 161 labelled a_1(1)* 135 to 136 labelled b_1(0)* 135 to 138 labelled a_1(1)* 136 to 137 labelled a_1(0)* 137 to 126 labelled a_1(0)* 138 to 139 labelled a_1(1)* 139 to 140 labelled b_1(1)* 140 to 141 labelled b_1(1)* 141 to 142 labelled a_1(1)* 142 to 143 labelled a_1(1)* 143 to 144 labelled a_1(1)* 144 to 145 labelled a_1(1)* 145 to 146 labelled b_1(1)* 145 to 172 labelled a_1(2)* 146 to 147 labelled b_1(1)* 146 to 138 labelled a_1(1)* 147 to 148 labelled a_1(1)* 148 to 126 labelled a_1(1)* 161 to 162 labelled a_1(1)* 162 to 163 labelled b_1(1)* 163 to 164 labelled b_1(1)* 164 to 165 labelled a_1(1)* 165 to 166 labelled a_1(1)* 166 to 167 labelled a_1(1)* 167 to 168 labelled a_1(1)* 168 to 169 labelled b_1(1)* 168 to 172 labelled a_1(2)* 169 to 170 labelled b_1(1)* 169 to 138 labelled a_1(1)* 170 to 171 labelled a_1(1)* 171 to 145 labelled a_1(1)* 172 to 173 labelled a_1(2)* 173 to 174 labelled b_1(2)* 174 to 175 labelled b_1(2)* 175 to 176 labelled a_1(2)* 176 to 177 labelled a_1(2)* 177 to 178 labelled a_1(2)* 178 to 179 labelled a_1(2)* 179 to 180 labelled b_1(2)* 179 to 172 labelled a_1(2)* 180 to 181 labelled b_1(2)* 180 to 138 labelled a_1(1)* 181 to 182 labelled a_1(2)* 182 to 145 labelled a_1(2)
3.84/1.77	
3.84/1.77	
3.84/1.77	----------------------------------------
3.84/1.77	
3.84/1.77	(4)
3.84/1.77	YES
3.84/1.80	EOF