3.42/1.81	YES
3.66/1.84	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.66/1.84	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.66/1.84	
3.66/1.84	
3.66/1.84	Termination w.r.t. Q of the given QTRS could be proven:
3.66/1.84	
3.66/1.84	(0) QTRS
3.66/1.84	(1) Strip Symbols Proof [SOUND, 0 ms]
3.66/1.84	(2) QTRS
3.66/1.84	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 2 ms]
3.66/1.84	(4) YES
3.66/1.84	
3.66/1.84	
3.66/1.84	----------------------------------------
3.66/1.84	
3.66/1.84	(0)
3.66/1.84	Obligation:
3.66/1.84	Q restricted rewrite system:
3.66/1.84	The TRS R consists of the following rules:
3.66/1.84	
3.66/1.84	   b(a(a(a(b(b(a(a(a(b(x1)))))))))) -> a(a(a(b(b(a(a(a(b(a(a(a(b(b(x1))))))))))))))
3.66/1.84	
3.66/1.84	Q is empty.
3.66/1.84	
3.66/1.84	----------------------------------------
3.66/1.84	
3.66/1.84	(1) Strip Symbols Proof (SOUND)
3.66/1.84	We were given the following TRS:
3.66/1.84	
3.66/1.84	   b(a(a(a(b(b(a(a(a(b(x1)))))))))) -> a(a(a(b(b(a(a(a(b(a(a(a(b(b(x1))))))))))))))
3.66/1.84	
3.66/1.84	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.66/1.84	
3.66/1.84	   b(a(a(a(b(b(a(a(a(x))))))))) -> a(a(a(b(b(a(a(a(b(a(a(a(b(x)))))))))))))
3.66/1.84	
3.66/1.84	----------------------------------------
3.66/1.84	
3.66/1.84	(2)
3.66/1.84	Obligation:
3.66/1.84	Q restricted rewrite system:
3.66/1.84	The TRS R consists of the following rules:
3.66/1.84	
3.66/1.84	   b(a(a(a(b(b(a(a(a(x))))))))) -> a(a(a(b(b(a(a(a(b(a(a(a(b(x)))))))))))))
3.66/1.84	
3.66/1.84	Q is empty.
3.66/1.84	
3.66/1.84	----------------------------------------
3.66/1.84	
3.66/1.84	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
3.66/1.84	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.66/1.84	The following rules were used to construct the certificate:
3.66/1.84	
3.66/1.84	   b(a(a(a(b(b(a(a(a(x))))))))) -> a(a(a(b(b(a(a(a(b(a(a(a(b(x)))))))))))))
3.66/1.84	
3.66/1.84	The certificate found is represented by the following graph.
3.66/1.84	The certificate consists of the following enumerated nodes:
3.66/1.84	174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199
3.66/1.84	
3.66/1.84	Node 174 is start node and node 175 is final node.
3.66/1.84	
3.66/1.84	Those nodes are connected through the following edges:
3.66/1.84	
3.66/1.84	* 174 to 176 labelled a_1(0)* 175 to 175 labelled #_1(0)* 176 to 177 labelled a_1(0)* 177 to 178 labelled a_1(0)* 178 to 179 labelled b_1(0)* 179 to 180 labelled b_1(0)* 180 to 181 labelled a_1(0)* 181 to 182 labelled a_1(0)* 182 to 183 labelled a_1(0)* 183 to 184 labelled b_1(0)* 183 to 188 labelled a_1(1)* 184 to 185 labelled a_1(0)* 185 to 186 labelled a_1(0)* 186 to 187 labelled a_1(0)* 187 to 175 labelled b_1(0)* 187 to 188 labelled a_1(1)* 188 to 189 labelled a_1(1)* 189 to 190 labelled a_1(1)* 190 to 191 labelled b_1(1)* 191 to 192 labelled b_1(1)* 192 to 193 labelled a_1(1)* 193 to 194 labelled a_1(1)* 194 to 195 labelled a_1(1)* 195 to 196 labelled b_1(1)* 195 to 188 labelled a_1(1)* 196 to 197 labelled a_1(1)* 197 to 198 labelled a_1(1)* 198 to 199 labelled a_1(1)* 199 to 175 labelled b_1(1)* 199 to 188 labelled a_1(1)
3.66/1.84	
3.66/1.84	
3.66/1.84	----------------------------------------
3.66/1.84	
3.66/1.84	(4)
3.66/1.84	YES
3.81/1.87	EOF