3.53/1.69	YES
3.68/1.72	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.68/1.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.68/1.72	
3.68/1.72	
3.68/1.72	Termination w.r.t. Q of the given QTRS could be proven:
3.68/1.72	
3.68/1.72	(0) QTRS
3.68/1.72	(1) Strip Symbols Proof [SOUND, 0 ms]
3.68/1.72	(2) QTRS
3.68/1.72	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.68/1.72	(4) YES
3.68/1.72	
3.68/1.72	
3.68/1.72	----------------------------------------
3.68/1.72	
3.68/1.72	(0)
3.68/1.72	Obligation:
3.68/1.72	Q restricted rewrite system:
3.68/1.72	The TRS R consists of the following rules:
3.68/1.72	
3.68/1.72	   b(a(a(b(a(a(b(b(a(a(b(x1))))))))))) -> a(a(b(b(a(a(b(a(a(b(a(a(b(b(x1))))))))))))))
3.68/1.72	
3.68/1.72	Q is empty.
3.68/1.72	
3.68/1.72	----------------------------------------
3.68/1.72	
3.68/1.72	(1) Strip Symbols Proof (SOUND)
3.68/1.72	We were given the following TRS:
3.68/1.72	
3.68/1.72	   b(a(a(b(a(a(b(b(a(a(b(x1))))))))))) -> a(a(b(b(a(a(b(a(a(b(a(a(b(b(x1))))))))))))))
3.68/1.72	
3.68/1.72	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.68/1.72	
3.68/1.72	   b(a(a(b(a(a(b(b(a(a(x)))))))))) -> a(a(b(b(a(a(b(a(a(b(a(a(b(x)))))))))))))
3.68/1.72	
3.68/1.72	----------------------------------------
3.68/1.72	
3.68/1.72	(2)
3.68/1.72	Obligation:
3.68/1.72	Q restricted rewrite system:
3.68/1.72	The TRS R consists of the following rules:
3.68/1.72	
3.68/1.72	   b(a(a(b(a(a(b(b(a(a(x)))))))))) -> a(a(b(b(a(a(b(a(a(b(a(a(b(x)))))))))))))
3.68/1.72	
3.68/1.72	Q is empty.
3.68/1.72	
3.68/1.72	----------------------------------------
3.68/1.72	
3.68/1.72	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
3.68/1.72	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.68/1.72	The following rules were used to construct the certificate:
3.68/1.72	
3.68/1.72	   b(a(a(b(a(a(b(b(a(a(x)))))))))) -> a(a(b(b(a(a(b(a(a(b(a(a(b(x)))))))))))))
3.68/1.72	
3.68/1.72	The certificate found is represented by the following graph.
3.68/1.72	The certificate consists of the following enumerated nodes:
3.68/1.72	185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210
3.68/1.72	
3.68/1.72	Node 185 is start node and node 186 is final node.
3.68/1.72	
3.68/1.72	Those nodes are connected through the following edges:
3.68/1.72	
3.68/1.72	* 185 to 187 labelled a_1(0)* 186 to 186 labelled #_1(0)* 187 to 188 labelled a_1(0)* 188 to 189 labelled b_1(0)* 189 to 190 labelled b_1(0)* 190 to 191 labelled a_1(0)* 191 to 192 labelled a_1(0)* 192 to 193 labelled b_1(0)* 192 to 199 labelled a_1(1)* 193 to 194 labelled a_1(0)* 194 to 195 labelled a_1(0)* 195 to 196 labelled b_1(0)* 195 to 199 labelled a_1(1)* 196 to 197 labelled a_1(0)* 197 to 198 labelled a_1(0)* 198 to 186 labelled b_1(0)* 198 to 199 labelled a_1(1)* 199 to 200 labelled a_1(1)* 200 to 201 labelled b_1(1)* 201 to 202 labelled b_1(1)* 202 to 203 labelled a_1(1)* 203 to 204 labelled a_1(1)* 204 to 205 labelled b_1(1)* 204 to 199 labelled a_1(1)* 205 to 206 labelled a_1(1)* 206 to 207 labelled a_1(1)* 207 to 208 labelled b_1(1)* 207 to 199 labelled a_1(1)* 208 to 209 labelled a_1(1)* 209 to 210 labelled a_1(1)* 210 to 186 labelled b_1(1)* 210 to 199 labelled a_1(1)
3.68/1.72	
3.68/1.72	
3.68/1.72	----------------------------------------
3.68/1.72	
3.68/1.72	(4)
3.68/1.72	YES
3.68/1.75	EOF