3.73/1.81	YES
3.89/1.85	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.89/1.85	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.89/1.85	
3.89/1.85	
3.89/1.85	Termination w.r.t. Q of the given QTRS could be proven:
3.89/1.85	
3.89/1.85	(0) QTRS
3.89/1.85	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.89/1.85	(2) QTRS
3.89/1.85	(3) Strip Symbols Proof [SOUND, 0 ms]
3.89/1.85	(4) QTRS
3.89/1.85	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.89/1.85	(6) YES
3.89/1.85	
3.89/1.85	
3.89/1.85	----------------------------------------
3.89/1.85	
3.89/1.85	(0)
3.89/1.85	Obligation:
3.89/1.85	Q restricted rewrite system:
3.89/1.85	The TRS R consists of the following rules:
3.89/1.85	
3.89/1.85	   a(b(b(a(a(a(a(b(a(a(x1)))))))))) -> a(b(a(a(a(a(b(b(a(a(a(a(b(x1)))))))))))))
3.89/1.85	
3.89/1.85	Q is empty.
3.89/1.85	
3.89/1.85	----------------------------------------
3.89/1.85	
3.89/1.85	(1) QTRS Reverse (EQUIVALENT)
3.89/1.85	We applied the QTRS Reverse Processor [REVERSE].
3.89/1.85	----------------------------------------
3.89/1.85	
3.89/1.85	(2)
3.89/1.85	Obligation:
3.89/1.85	Q restricted rewrite system:
3.89/1.85	The TRS R consists of the following rules:
3.89/1.85	
3.89/1.85	   a(a(b(a(a(a(a(b(b(a(x1)))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(a(x1)))))))))))))
3.89/1.85	
3.89/1.85	Q is empty.
3.89/1.85	
3.89/1.85	----------------------------------------
3.89/1.85	
3.89/1.85	(3) Strip Symbols Proof (SOUND)
3.89/1.85	We were given the following TRS:
3.89/1.85	
3.89/1.85	   a(a(b(a(a(a(a(b(b(a(x1)))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(a(x1)))))))))))))
3.89/1.85	
3.89/1.85	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.89/1.85	
3.89/1.85	   a(a(b(a(a(a(a(b(b(x))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(x))))))))))))
3.89/1.85	
3.89/1.85	----------------------------------------
3.89/1.85	
3.89/1.85	(4)
3.89/1.85	Obligation:
3.89/1.85	Q restricted rewrite system:
3.89/1.85	The TRS R consists of the following rules:
3.89/1.85	
3.89/1.85	   a(a(b(a(a(a(a(b(b(x))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(x))))))))))))
3.89/1.85	
3.89/1.85	Q is empty.
3.89/1.85	
3.89/1.85	----------------------------------------
3.89/1.85	
3.89/1.85	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.89/1.85	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
3.89/1.85	The following rules were used to construct the certificate:
3.89/1.85	
3.89/1.85	   a(a(b(a(a(a(a(b(b(x))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(x))))))))))))
3.89/1.85	
3.89/1.85	The certificate found is represented by the following graph.
3.89/1.85	The certificate consists of the following enumerated nodes:
3.89/1.85	4, 6, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195
3.89/1.86	
3.89/1.86	Node 4 is start node and node 6 is final node.
3.89/1.86	
3.89/1.86	Those nodes are connected through the following edges:
3.89/1.86	
3.89/1.86	* 4 to 44 labelled b_1(0)* 6 to 6 labelled #_1(0)* 44 to 45 labelled a_1(0)* 45 to 46 labelled a_1(0)* 46 to 47 labelled a_1(0)* 47 to 48 labelled a_1(0)* 48 to 49 labelled b_1(0)* 49 to 50 labelled b_1(0)* 50 to 51 labelled a_1(0)* 50 to 174 labelled b_1(1)* 51 to 52 labelled a_1(0)* 52 to 53 labelled a_1(0)* 52 to 151 labelled b_1(1)* 53 to 54 labelled a_1(0)* 54 to 6 labelled b_1(0)* 151 to 152 labelled a_1(1)* 152 to 153 labelled a_1(1)* 153 to 154 labelled a_1(1)* 154 to 155 labelled a_1(1)* 155 to 156 labelled b_1(1)* 156 to 157 labelled b_1(1)* 157 to 158 labelled a_1(1)* 157 to 185 labelled b_1(2)* 158 to 159 labelled a_1(1)* 159 to 160 labelled a_1(1)* 159 to 151 labelled b_1(1)* 160 to 161 labelled a_1(1)* 161 to 6 labelled b_1(1)* 174 to 175 labelled a_1(1)* 175 to 176 labelled a_1(1)* 176 to 177 labelled a_1(1)* 177 to 178 labelled a_1(1)* 178 to 179 labelled b_1(1)* 179 to 180 labelled b_1(1)* 180 to 181 labelled a_1(1)* 180 to 185 labelled b_1(2)* 181 to 182 labelled a_1(1)* 182 to 183 labelled a_1(1)* 182 to 151 labelled b_1(1)* 183 to 184 labelled a_1(1)* 184 to 157 labelled b_1(1)* 185 to 186 labelled a_1(2)* 186 to 187 labelled a_1(2)* 187 to 188 labelled a_1(2)* 188 to 189 labelled a_1(2)* 189 to 190 labelled b_1(2)* 190 to 191 labelled b_1(2)* 191 to 192 labelled a_1(2)* 191 to 185 labelled b_1(2)* 192 to 193 labelled a_1(2)* 193 to 194 labelled a_1(2)* 193 to 151 labelled b_1(1)* 194 to 195 labelled a_1(2)* 195 to 157 labelled b_1(2)
3.89/1.86	
3.89/1.86	
3.89/1.86	----------------------------------------
3.89/1.86	
3.89/1.86	(6)
3.89/1.86	YES
3.89/1.87	EOF