3.06/1.61	YES
3.39/1.66	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.39/1.66	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.39/1.66	
3.39/1.66	
3.39/1.66	Termination w.r.t. Q of the given QTRS could be proven:
3.39/1.66	
3.39/1.66	(0) QTRS
3.39/1.66	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.39/1.66	(2) QTRS
3.39/1.66	(3) Strip Symbols Proof [SOUND, 0 ms]
3.39/1.66	(4) QTRS
3.39/1.66	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.39/1.66	(6) YES
3.39/1.66	
3.39/1.66	
3.39/1.66	----------------------------------------
3.39/1.66	
3.39/1.66	(0)
3.39/1.66	Obligation:
3.39/1.66	Q restricted rewrite system:
3.39/1.66	The TRS R consists of the following rules:
3.39/1.66	
3.39/1.66	   a(b(a(a(a(a(x1)))))) -> a(a(a(a(a(b(a(b(a(b(a(a(b(x1)))))))))))))
3.39/1.66	
3.39/1.66	Q is empty.
3.39/1.66	
3.39/1.66	----------------------------------------
3.39/1.66	
3.39/1.66	(1) QTRS Reverse (EQUIVALENT)
3.39/1.66	We applied the QTRS Reverse Processor [REVERSE].
3.39/1.66	----------------------------------------
3.39/1.66	
3.39/1.66	(2)
3.39/1.66	Obligation:
3.39/1.66	Q restricted rewrite system:
3.39/1.66	The TRS R consists of the following rules:
3.39/1.66	
3.39/1.66	   a(a(a(a(b(a(x1)))))) -> b(a(a(b(a(b(a(b(a(a(a(a(a(x1)))))))))))))
3.39/1.66	
3.39/1.66	Q is empty.
3.39/1.66	
3.39/1.66	----------------------------------------
3.39/1.66	
3.39/1.66	(3) Strip Symbols Proof (SOUND)
3.39/1.66	We were given the following TRS:
3.39/1.66	
3.39/1.66	   a(a(a(a(b(a(x1)))))) -> b(a(a(b(a(b(a(b(a(a(a(a(a(x1)))))))))))))
3.39/1.66	
3.39/1.66	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.39/1.66	
3.39/1.66	   a(a(a(a(b(x))))) -> b(a(a(b(a(b(a(b(a(a(a(a(x))))))))))))
3.39/1.66	
3.39/1.66	----------------------------------------
3.39/1.66	
3.39/1.66	(4)
3.39/1.66	Obligation:
3.39/1.66	Q restricted rewrite system:
3.39/1.66	The TRS R consists of the following rules:
3.39/1.66	
3.39/1.66	   a(a(a(a(b(x))))) -> b(a(a(b(a(b(a(b(a(a(a(a(x))))))))))))
3.39/1.66	
3.39/1.66	Q is empty.
3.39/1.66	
3.39/1.66	----------------------------------------
3.39/1.66	
3.39/1.66	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.39/1.66	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.39/1.66	The following rules were used to construct the certificate:
3.39/1.66	
3.39/1.66	   a(a(a(a(b(x))))) -> b(a(a(b(a(b(a(b(a(a(a(a(x))))))))))))
3.39/1.66	
3.39/1.66	The certificate found is represented by the following graph.
3.39/1.66	The certificate consists of the following enumerated nodes:
3.39/1.66	5, 6, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333
3.39/1.66	
3.39/1.66	Node 5 is start node and node 6 is final node.
3.39/1.66	
3.39/1.66	Those nodes are connected through the following edges:
3.39/1.66	
3.39/1.66	* 5 to 21 labelled b_1(0)* 6 to 6 labelled #_1(0)* 21 to 22 labelled a_1(0)* 22 to 23 labelled a_1(0)* 23 to 24 labelled b_1(0)* 24 to 25 labelled a_1(0)* 25 to 26 labelled b_1(0)* 26 to 27 labelled a_1(0)* 27 to 28 labelled b_1(0)* 28 to 29 labelled a_1(0)* 28 to 323 labelled b_1(1)* 29 to 30 labelled a_1(0)* 29 to 323 labelled b_1(1)* 30 to 31 labelled a_1(0)* 30 to 323 labelled b_1(1)* 31 to 6 labelled a_1(0)* 31 to 323 labelled b_1(1)* 323 to 324 labelled a_1(1)* 324 to 325 labelled a_1(1)* 325 to 326 labelled b_1(1)* 326 to 327 labelled a_1(1)* 327 to 328 labelled b_1(1)* 328 to 329 labelled a_1(1)* 329 to 330 labelled b_1(1)* 330 to 331 labelled a_1(1)* 330 to 323 labelled b_1(1)* 331 to 332 labelled a_1(1)* 331 to 323 labelled b_1(1)* 332 to 333 labelled a_1(1)* 332 to 323 labelled b_1(1)* 333 to 6 labelled a_1(1)* 333 to 323 labelled b_1(1)
3.39/1.66	
3.39/1.66	
3.39/1.66	----------------------------------------
3.39/1.66	
3.39/1.66	(6)
3.39/1.66	YES
3.39/1.68	EOF