3.34/1.68	YES
3.87/1.77	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.87/1.77	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.87/1.77	
3.87/1.77	
3.87/1.77	Termination w.r.t. Q of the given QTRS could be proven:
3.87/1.77	
3.87/1.77	(0) QTRS
3.87/1.77	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.87/1.77	(2) QTRS
3.87/1.77	(3) Strip Symbols Proof [SOUND, 0 ms]
3.87/1.77	(4) QTRS
3.87/1.77	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.87/1.77	(6) YES
3.87/1.77	
3.87/1.77	
3.87/1.77	----------------------------------------
3.87/1.77	
3.87/1.77	(0)
3.87/1.77	Obligation:
3.87/1.77	Q restricted rewrite system:
3.87/1.77	The TRS R consists of the following rules:
3.87/1.77	
3.87/1.77	   a(b(a(a(a(a(x1)))))) -> a(a(a(a(a(b(a(a(b(a(a(b(a(b(x1))))))))))))))
3.87/1.77	
3.87/1.77	Q is empty.
3.87/1.77	
3.87/1.77	----------------------------------------
3.87/1.77	
3.87/1.77	(1) QTRS Reverse (EQUIVALENT)
3.87/1.77	We applied the QTRS Reverse Processor [REVERSE].
3.87/1.77	----------------------------------------
3.87/1.77	
3.87/1.77	(2)
3.87/1.77	Obligation:
3.87/1.77	Q restricted rewrite system:
3.87/1.77	The TRS R consists of the following rules:
3.87/1.77	
3.87/1.77	   a(a(a(a(b(a(x1)))))) -> b(a(b(a(a(b(a(a(b(a(a(a(a(a(x1))))))))))))))
3.87/1.77	
3.87/1.77	Q is empty.
3.87/1.77	
3.87/1.77	----------------------------------------
3.87/1.77	
3.87/1.77	(3) Strip Symbols Proof (SOUND)
3.87/1.77	We were given the following TRS:
3.87/1.77	
3.87/1.77	   a(a(a(a(b(a(x1)))))) -> b(a(b(a(a(b(a(a(b(a(a(a(a(a(x1))))))))))))))
3.87/1.77	
3.87/1.77	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.87/1.77	
3.87/1.77	   a(a(a(a(b(x))))) -> b(a(b(a(a(b(a(a(b(a(a(a(a(x)))))))))))))
3.87/1.77	
3.87/1.77	----------------------------------------
3.87/1.77	
3.87/1.77	(4)
3.87/1.77	Obligation:
3.87/1.77	Q restricted rewrite system:
3.87/1.77	The TRS R consists of the following rules:
3.87/1.77	
3.87/1.77	   a(a(a(a(b(x))))) -> b(a(b(a(a(b(a(a(b(a(a(a(a(x)))))))))))))
3.87/1.77	
3.87/1.77	Q is empty.
3.87/1.77	
3.87/1.77	----------------------------------------
3.87/1.77	
3.87/1.77	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.87/1.77	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.87/1.77	The following rules were used to construct the certificate:
3.87/1.77	
3.87/1.77	   a(a(a(a(b(x))))) -> b(a(b(a(a(b(a(a(b(a(a(a(a(x)))))))))))))
3.87/1.77	
3.87/1.77	The certificate found is represented by the following graph.
3.87/1.77	The certificate consists of the following enumerated nodes:
3.87/1.77	220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245
3.87/1.77	
3.87/1.77	Node 220 is start node and node 221 is final node.
3.87/1.77	
3.87/1.77	Those nodes are connected through the following edges:
3.87/1.77	
3.87/1.77	* 220 to 222 labelled b_1(0)* 221 to 221 labelled #_1(0)* 222 to 223 labelled a_1(0)* 223 to 224 labelled b_1(0)* 224 to 225 labelled a_1(0)* 225 to 226 labelled a_1(0)* 226 to 227 labelled b_1(0)* 227 to 228 labelled a_1(0)* 228 to 229 labelled a_1(0)* 229 to 230 labelled b_1(0)* 230 to 231 labelled a_1(0)* 230 to 234 labelled b_1(1)* 231 to 232 labelled a_1(0)* 231 to 234 labelled b_1(1)* 232 to 233 labelled a_1(0)* 232 to 234 labelled b_1(1)* 233 to 221 labelled a_1(0)* 233 to 234 labelled b_1(1)* 234 to 235 labelled a_1(1)* 235 to 236 labelled b_1(1)* 236 to 237 labelled a_1(1)* 237 to 238 labelled a_1(1)* 238 to 239 labelled b_1(1)* 239 to 240 labelled a_1(1)* 240 to 241 labelled a_1(1)* 241 to 242 labelled b_1(1)* 242 to 243 labelled a_1(1)* 242 to 234 labelled b_1(1)* 243 to 244 labelled a_1(1)* 243 to 234 labelled b_1(1)* 244 to 245 labelled a_1(1)* 244 to 234 labelled b_1(1)* 245 to 221 labelled a_1(1)* 245 to 234 labelled b_1(1)
3.87/1.77	
3.87/1.77	
3.87/1.77	----------------------------------------
3.87/1.77	
3.87/1.77	(6)
3.87/1.77	YES
3.90/1.80	EOF