3.89/1.71	YES
3.89/1.73	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.89/1.73	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.89/1.73	
3.89/1.73	
3.89/1.73	Termination w.r.t. Q of the given QTRS could be proven:
3.89/1.73	
3.89/1.73	(0) QTRS
3.89/1.73	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.89/1.73	(2) QTRS
3.89/1.73	(3) Strip Symbols Proof [SOUND, 0 ms]
3.89/1.73	(4) QTRS
3.89/1.73	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.89/1.73	(6) YES
3.89/1.73	
3.89/1.73	
3.89/1.73	----------------------------------------
3.89/1.73	
3.89/1.73	(0)
3.89/1.73	Obligation:
3.89/1.73	Q restricted rewrite system:
3.89/1.73	The TRS R consists of the following rules:
3.89/1.73	
3.89/1.73	   a(b(c(b(a(a(a(a(a(x1))))))))) -> a(a(a(a(a(a(b(c(b(a(a(b(c(b(x1))))))))))))))
3.89/1.73	
3.89/1.73	Q is empty.
3.89/1.73	
3.89/1.73	----------------------------------------
3.89/1.73	
3.89/1.73	(1) QTRS Reverse (EQUIVALENT)
3.89/1.73	We applied the QTRS Reverse Processor [REVERSE].
3.89/1.73	----------------------------------------
3.89/1.73	
3.89/1.73	(2)
3.89/1.73	Obligation:
3.89/1.73	Q restricted rewrite system:
3.89/1.73	The TRS R consists of the following rules:
3.89/1.73	
3.89/1.73	   a(a(a(a(a(b(c(b(a(x1))))))))) -> b(c(b(a(a(b(c(b(a(a(a(a(a(a(x1))))))))))))))
3.89/1.73	
3.89/1.73	Q is empty.
3.89/1.73	
3.89/1.73	----------------------------------------
3.89/1.73	
3.89/1.73	(3) Strip Symbols Proof (SOUND)
3.89/1.73	We were given the following TRS:
3.89/1.73	
3.89/1.73	   a(a(a(a(a(b(c(b(a(x1))))))))) -> b(c(b(a(a(b(c(b(a(a(a(a(a(a(x1))))))))))))))
3.89/1.73	
3.89/1.73	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.89/1.73	
3.89/1.73	   a(a(a(a(a(b(c(b(x)))))))) -> b(c(b(a(a(b(c(b(a(a(a(a(a(x)))))))))))))
3.89/1.73	
3.89/1.73	----------------------------------------
3.89/1.73	
3.89/1.73	(4)
3.89/1.73	Obligation:
3.89/1.73	Q restricted rewrite system:
3.89/1.73	The TRS R consists of the following rules:
3.89/1.73	
3.89/1.73	   a(a(a(a(a(b(c(b(x)))))))) -> b(c(b(a(a(b(c(b(a(a(a(a(a(x)))))))))))))
3.89/1.73	
3.89/1.73	Q is empty.
3.89/1.73	
3.89/1.73	----------------------------------------
3.89/1.73	
3.89/1.73	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.89/1.73	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.89/1.73	The following rules were used to construct the certificate:
3.89/1.73	
3.89/1.73	   a(a(a(a(a(b(c(b(x)))))))) -> b(c(b(a(a(b(c(b(a(a(a(a(a(x)))))))))))))
3.89/1.73	
3.89/1.73	The certificate found is represented by the following graph.
3.89/1.73	The certificate consists of the following enumerated nodes:
3.89/1.73	248, 249, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285
3.89/1.73	
3.89/1.73	Node 248 is start node and node 249 is final node.
3.89/1.73	
3.89/1.73	Those nodes are connected through the following edges:
3.89/1.73	
3.89/1.73	* 248 to 262 labelled b_1(0)* 249 to 249 labelled #_1(0)* 262 to 263 labelled c_1(0)* 263 to 264 labelled b_1(0)* 264 to 265 labelled a_1(0)* 265 to 266 labelled a_1(0)* 266 to 267 labelled b_1(0)* 267 to 268 labelled c_1(0)* 268 to 269 labelled b_1(0)* 269 to 270 labelled a_1(0)* 269 to 274 labelled b_1(1)* 270 to 271 labelled a_1(0)* 270 to 274 labelled b_1(1)* 271 to 272 labelled a_1(0)* 271 to 274 labelled b_1(1)* 272 to 273 labelled a_1(0)* 272 to 274 labelled b_1(1)* 273 to 249 labelled a_1(0)* 273 to 274 labelled b_1(1)* 274 to 275 labelled c_1(1)* 275 to 276 labelled b_1(1)* 276 to 277 labelled a_1(1)* 277 to 278 labelled a_1(1)* 278 to 279 labelled b_1(1)* 279 to 280 labelled c_1(1)* 280 to 281 labelled b_1(1)* 281 to 282 labelled a_1(1)* 281 to 274 labelled b_1(1)* 282 to 283 labelled a_1(1)* 282 to 274 labelled b_1(1)* 283 to 284 labelled a_1(1)* 283 to 274 labelled b_1(1)* 284 to 285 labelled a_1(1)* 284 to 274 labelled b_1(1)* 285 to 249 labelled a_1(1)* 285 to 274 labelled b_1(1)
3.89/1.73	
3.89/1.73	
3.89/1.73	----------------------------------------
3.89/1.73	
3.89/1.73	(6)
3.89/1.73	YES
3.89/1.77	EOF