3.67/1.72	YES
3.86/1.79	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.86/1.79	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.86/1.79	
3.86/1.79	
3.86/1.79	Termination w.r.t. Q of the given QTRS could be proven:
3.86/1.79	
3.86/1.79	(0) QTRS
3.86/1.79	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.86/1.79	(2) QTRS
3.86/1.79	(3) Strip Symbols Proof [SOUND, 0 ms]
3.86/1.79	(4) QTRS
3.86/1.79	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 6 ms]
3.86/1.79	(6) YES
3.86/1.79	
3.86/1.79	
3.86/1.79	----------------------------------------
3.86/1.79	
3.86/1.79	(0)
3.86/1.79	Obligation:
3.86/1.79	Q restricted rewrite system:
3.86/1.79	The TRS R consists of the following rules:
3.86/1.79	
3.86/1.79	   b(b(b(a(b(a(b(b(a(b(x1)))))))))) -> b(b(a(b(a(b(b(b(a(b(a(b(b(x1)))))))))))))
3.86/1.79	
3.86/1.79	Q is empty.
3.86/1.79	
3.86/1.79	----------------------------------------
3.86/1.79	
3.86/1.79	(1) QTRS Reverse (EQUIVALENT)
3.86/1.79	We applied the QTRS Reverse Processor [REVERSE].
3.86/1.79	----------------------------------------
3.86/1.79	
3.86/1.79	(2)
3.86/1.79	Obligation:
3.86/1.79	Q restricted rewrite system:
3.86/1.79	The TRS R consists of the following rules:
3.86/1.79	
3.86/1.79	   b(a(b(b(a(b(a(b(b(b(x1)))))))))) -> b(b(a(b(a(b(b(b(a(b(a(b(b(x1)))))))))))))
3.86/1.79	
3.86/1.79	Q is empty.
3.86/1.79	
3.86/1.79	----------------------------------------
3.86/1.79	
3.86/1.79	(3) Strip Symbols Proof (SOUND)
3.86/1.79	We were given the following TRS:
3.86/1.79	
3.86/1.79	   b(a(b(b(a(b(a(b(b(b(x1)))))))))) -> b(b(a(b(a(b(b(b(a(b(a(b(b(x1)))))))))))))
3.86/1.79	
3.86/1.79	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.86/1.79	
3.86/1.79	   a(b(b(a(b(a(b(b(b(x1))))))))) -> b(a(b(a(b(b(b(a(b(a(b(b(x1))))))))))))
3.86/1.79	
3.86/1.79	----------------------------------------
3.86/1.79	
3.86/1.79	(4)
3.86/1.79	Obligation:
3.86/1.79	Q restricted rewrite system:
3.86/1.79	The TRS R consists of the following rules:
3.86/1.79	
3.86/1.79	   a(b(b(a(b(a(b(b(b(x1))))))))) -> b(a(b(a(b(b(b(a(b(a(b(b(x1))))))))))))
3.86/1.79	
3.86/1.79	Q is empty.
3.86/1.79	
3.86/1.79	----------------------------------------
3.86/1.79	
3.86/1.79	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.86/1.79	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. This implies Q-termination of R.
3.86/1.79	The following rules were used to construct the certificate:
3.86/1.79	
3.86/1.79	   a(b(b(a(b(a(b(b(b(x1))))))))) -> b(a(b(a(b(b(b(a(b(a(b(b(x1))))))))))))
3.86/1.79	
3.86/1.79	The certificate found is represented by the following graph.
3.86/1.79	The certificate consists of the following enumerated nodes:
3.86/1.79	268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313
3.86/1.79	
3.86/1.79	Node 268 is start node and node 269 is final node.
3.86/1.79	
3.86/1.79	Those nodes are connected through the following edges:
3.86/1.79	
3.86/1.79	* 268 to 270 labelled b_1(0)* 269 to 269 labelled #_1(0)* 270 to 271 labelled a_1(0)* 271 to 272 labelled b_1(0)* 272 to 273 labelled a_1(0)* 273 to 274 labelled b_1(0)* 274 to 275 labelled b_1(0)* 275 to 276 labelled b_1(0)* 276 to 277 labelled a_1(0)* 276 to 292 labelled b_1(1)* 277 to 278 labelled b_1(0)* 278 to 279 labelled a_1(0)* 278 to 281 labelled b_1(1)* 279 to 280 labelled b_1(0)* 280 to 269 labelled b_1(0)* 281 to 282 labelled a_1(1)* 282 to 283 labelled b_1(1)* 283 to 284 labelled a_1(1)* 284 to 285 labelled b_1(1)* 285 to 286 labelled b_1(1)* 286 to 287 labelled b_1(1)* 287 to 288 labelled a_1(1)* 287 to 303 labelled b_1(2)* 288 to 289 labelled b_1(1)* 289 to 290 labelled a_1(1)* 289 to 281 labelled b_1(1)* 290 to 291 labelled b_1(1)* 291 to 269 labelled b_1(1)* 292 to 293 labelled a_1(1)* 293 to 294 labelled b_1(1)* 294 to 295 labelled a_1(1)* 295 to 296 labelled b_1(1)* 296 to 297 labelled b_1(1)* 297 to 298 labelled b_1(1)* 298 to 299 labelled a_1(1)* 298 to 303 labelled b_1(2)* 299 to 300 labelled b_1(1)* 300 to 301 labelled a_1(1)* 300 to 281 labelled b_1(1)* 301 to 302 labelled b_1(1)* 302 to 287 labelled b_1(1)* 303 to 304 labelled a_1(2)* 304 to 305 labelled b_1(2)* 305 to 306 labelled a_1(2)* 306 to 307 labelled b_1(2)* 307 to 308 labelled b_1(2)* 308 to 309 labelled b_1(2)* 309 to 310 labelled a_1(2)* 309 to 303 labelled b_1(2)* 310 to 311 labelled b_1(2)* 311 to 312 labelled a_1(2)* 311 to 281 labelled b_1(1)* 312 to 313 labelled b_1(2)* 313 to 287 labelled b_1(2)
3.86/1.79	
3.86/1.79	
3.86/1.79	----------------------------------------
3.86/1.79	
3.86/1.79	(6)
3.86/1.79	YES
3.86/1.83	EOF