3.42/1.61	YES
3.77/1.65	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.77/1.65	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.77/1.65	
3.77/1.65	
3.77/1.65	Termination w.r.t. Q of the given QTRS could be proven:
3.77/1.65	
3.77/1.65	(0) QTRS
3.77/1.65	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.77/1.65	(2) QTRS
3.77/1.65	(3) Strip Symbols Proof [SOUND, 0 ms]
3.77/1.65	(4) QTRS
3.77/1.65	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.77/1.65	(6) YES
3.77/1.65	
3.77/1.65	
3.77/1.65	----------------------------------------
3.77/1.65	
3.77/1.65	(0)
3.77/1.65	Obligation:
3.77/1.65	Q restricted rewrite system:
3.77/1.65	The TRS R consists of the following rules:
3.77/1.65	
3.77/1.65	   a(b(a(a(a(a(a(a(a(x1))))))))) -> a(a(a(a(a(a(a(a(b(a(b(x1)))))))))))
3.77/1.65	
3.77/1.65	Q is empty.
3.77/1.65	
3.77/1.65	----------------------------------------
3.77/1.65	
3.77/1.65	(1) QTRS Reverse (EQUIVALENT)
3.77/1.65	We applied the QTRS Reverse Processor [REVERSE].
3.77/1.65	----------------------------------------
3.77/1.65	
3.77/1.65	(2)
3.77/1.65	Obligation:
3.77/1.65	Q restricted rewrite system:
3.77/1.65	The TRS R consists of the following rules:
3.77/1.65	
3.77/1.65	   a(a(a(a(a(a(a(b(a(x1))))))))) -> b(a(b(a(a(a(a(a(a(a(a(x1)))))))))))
3.77/1.65	
3.77/1.65	Q is empty.
3.77/1.65	
3.77/1.65	----------------------------------------
3.77/1.65	
3.77/1.65	(3) Strip Symbols Proof (SOUND)
3.77/1.65	We were given the following TRS:
3.77/1.65	
3.77/1.65	   a(a(a(a(a(a(a(b(a(x1))))))))) -> b(a(b(a(a(a(a(a(a(a(a(x1)))))))))))
3.77/1.65	
3.77/1.65	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.77/1.65	
3.77/1.65	   a(a(a(a(a(a(a(b(x)))))))) -> b(a(b(a(a(a(a(a(a(a(x))))))))))
3.77/1.65	
3.77/1.65	----------------------------------------
3.77/1.65	
3.77/1.65	(4)
3.77/1.65	Obligation:
3.77/1.65	Q restricted rewrite system:
3.77/1.65	The TRS R consists of the following rules:
3.77/1.65	
3.77/1.65	   a(a(a(a(a(a(a(b(x)))))))) -> b(a(b(a(a(a(a(a(a(a(x))))))))))
3.77/1.65	
3.77/1.65	Q is empty.
3.77/1.65	
3.77/1.65	----------------------------------------
3.77/1.65	
3.77/1.65	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.77/1.65	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.77/1.65	The following rules were used to construct the certificate:
3.77/1.65	
3.77/1.65	   a(a(a(a(a(a(a(b(x)))))))) -> b(a(b(a(a(a(a(a(a(a(x))))))))))
3.77/1.65	
3.77/1.65	The certificate found is represented by the following graph.
3.77/1.65	The certificate consists of the following enumerated nodes:
3.77/1.65	167, 168, 178, 179, 180, 181, 182, 183, 184, 185, 186, 196, 197, 198, 199, 200, 201, 202, 203, 204
3.77/1.65	
3.77/1.65	Node 167 is start node and node 168 is final node.
3.77/1.65	
3.77/1.65	Those nodes are connected through the following edges:
3.77/1.65	
3.77/1.65	* 167 to 178 labelled b_1(0)* 168 to 168 labelled #_1(0)* 178 to 179 labelled a_1(0)* 179 to 180 labelled b_1(0)* 180 to 181 labelled a_1(0)* 180 to 196 labelled b_1(1)* 181 to 182 labelled a_1(0)* 181 to 196 labelled b_1(1)* 182 to 183 labelled a_1(0)* 182 to 196 labelled b_1(1)* 183 to 184 labelled a_1(0)* 183 to 196 labelled b_1(1)* 184 to 185 labelled a_1(0)* 184 to 196 labelled b_1(1)* 185 to 186 labelled a_1(0)* 185 to 196 labelled b_1(1)* 186 to 168 labelled a_1(0)* 186 to 196 labelled b_1(1)* 196 to 197 labelled a_1(1)* 197 to 198 labelled b_1(1)* 198 to 199 labelled a_1(1)* 198 to 196 labelled b_1(1)* 199 to 200 labelled a_1(1)* 199 to 196 labelled b_1(1)* 200 to 201 labelled a_1(1)* 200 to 196 labelled b_1(1)* 201 to 202 labelled a_1(1)* 201 to 196 labelled b_1(1)* 202 to 203 labelled a_1(1)* 202 to 196 labelled b_1(1)* 203 to 204 labelled a_1(1)* 203 to 196 labelled b_1(1)* 204 to 168 labelled a_1(1)* 204 to 196 labelled b_1(1)
3.77/1.65	
3.77/1.65	
3.77/1.65	----------------------------------------
3.77/1.65	
3.77/1.65	(6)
3.77/1.65	YES
3.77/1.69	EOF