3.60/1.65	YES
3.60/1.69	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.60/1.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.60/1.69	
3.60/1.69	
3.60/1.69	Termination w.r.t. Q of the given QTRS could be proven:
3.60/1.69	
3.60/1.69	(0) QTRS
3.60/1.69	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.60/1.69	(2) QTRS
3.60/1.69	(3) Strip Symbols Proof [SOUND, 0 ms]
3.60/1.69	(4) QTRS
3.60/1.69	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.60/1.69	(6) YES
3.60/1.69	
3.60/1.69	
3.60/1.69	----------------------------------------
3.60/1.69	
3.60/1.69	(0)
3.60/1.69	Obligation:
3.60/1.69	Q restricted rewrite system:
3.60/1.69	The TRS R consists of the following rules:
3.60/1.69	
3.60/1.69	   a(b(a(b(a(a(a(a(a(x1))))))))) -> a(a(a(a(a(a(b(a(b(a(b(x1)))))))))))
3.60/1.69	
3.60/1.69	Q is empty.
3.60/1.69	
3.60/1.69	----------------------------------------
3.60/1.69	
3.60/1.69	(1) QTRS Reverse (EQUIVALENT)
3.60/1.69	We applied the QTRS Reverse Processor [REVERSE].
3.60/1.69	----------------------------------------
3.60/1.69	
3.60/1.69	(2)
3.60/1.69	Obligation:
3.60/1.69	Q restricted rewrite system:
3.60/1.69	The TRS R consists of the following rules:
3.60/1.69	
3.60/1.69	   a(a(a(a(a(b(a(b(a(x1))))))))) -> b(a(b(a(b(a(a(a(a(a(a(x1)))))))))))
3.60/1.69	
3.60/1.69	Q is empty.
3.60/1.69	
3.60/1.69	----------------------------------------
3.60/1.69	
3.60/1.69	(3) Strip Symbols Proof (SOUND)
3.60/1.69	We were given the following TRS:
3.60/1.69	
3.60/1.69	   a(a(a(a(a(b(a(b(a(x1))))))))) -> b(a(b(a(b(a(a(a(a(a(a(x1)))))))))))
3.60/1.69	
3.60/1.69	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.60/1.69	
3.60/1.69	   a(a(a(a(a(b(a(b(x)))))))) -> b(a(b(a(b(a(a(a(a(a(x))))))))))
3.60/1.69	
3.60/1.69	----------------------------------------
3.60/1.69	
3.60/1.69	(4)
3.60/1.69	Obligation:
3.60/1.69	Q restricted rewrite system:
3.60/1.69	The TRS R consists of the following rules:
3.60/1.69	
3.60/1.69	   a(a(a(a(a(b(a(b(x)))))))) -> b(a(b(a(b(a(a(a(a(a(x))))))))))
3.60/1.69	
3.60/1.69	Q is empty.
3.60/1.69	
3.60/1.69	----------------------------------------
3.60/1.69	
3.60/1.69	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.60/1.69	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.60/1.69	The following rules were used to construct the certificate:
3.60/1.69	
3.60/1.69	   a(a(a(a(a(b(a(b(x)))))))) -> b(a(b(a(b(a(a(a(a(a(x))))))))))
3.60/1.69	
3.60/1.69	The certificate found is represented by the following graph.
3.60/1.69	The certificate consists of the following enumerated nodes:
3.60/1.69	218, 219, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344
3.60/1.69	
3.60/1.69	Node 218 is start node and node 219 is final node.
3.60/1.69	
3.60/1.69	Those nodes are connected through the following edges:
3.60/1.69	
3.60/1.69	* 218 to 327 labelled b_1(0)* 219 to 219 labelled #_1(0)* 327 to 328 labelled a_1(0)* 328 to 329 labelled b_1(0)* 329 to 330 labelled a_1(0)* 330 to 331 labelled b_1(0)* 331 to 332 labelled a_1(0)* 331 to 336 labelled b_1(1)* 332 to 333 labelled a_1(0)* 332 to 336 labelled b_1(1)* 333 to 334 labelled a_1(0)* 333 to 336 labelled b_1(1)* 334 to 335 labelled a_1(0)* 334 to 336 labelled b_1(1)* 335 to 219 labelled a_1(0)* 335 to 336 labelled b_1(1)* 336 to 337 labelled a_1(1)* 337 to 338 labelled b_1(1)* 338 to 339 labelled a_1(1)* 339 to 340 labelled b_1(1)* 340 to 341 labelled a_1(1)* 340 to 336 labelled b_1(1)* 341 to 342 labelled a_1(1)* 341 to 336 labelled b_1(1)* 342 to 343 labelled a_1(1)* 342 to 336 labelled b_1(1)* 343 to 344 labelled a_1(1)* 343 to 336 labelled b_1(1)* 344 to 219 labelled a_1(1)* 344 to 336 labelled b_1(1)
3.60/1.69	
3.60/1.69	
3.60/1.69	----------------------------------------
3.60/1.69	
3.60/1.69	(6)
3.60/1.69	YES
3.80/1.72	EOF