3.38/1.67	YES
3.38/1.69	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.38/1.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.38/1.69	
3.38/1.69	
3.38/1.69	Termination w.r.t. Q of the given QTRS could be proven:
3.38/1.69	
3.38/1.69	(0) QTRS
3.38/1.69	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.38/1.69	(2) QTRS
3.38/1.69	(3) Strip Symbols Proof [SOUND, 0 ms]
3.38/1.69	(4) QTRS
3.38/1.69	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.38/1.69	(6) YES
3.38/1.69	
3.38/1.69	
3.38/1.69	----------------------------------------
3.38/1.69	
3.38/1.69	(0)
3.38/1.69	Obligation:
3.38/1.69	Q restricted rewrite system:
3.38/1.69	The TRS R consists of the following rules:
3.38/1.69	
3.38/1.69	   a(b(a(a(a(a(a(x1))))))) -> a(a(a(a(a(a(b(a(a(a(b(a(a(b(x1))))))))))))))
3.38/1.69	
3.38/1.69	Q is empty.
3.38/1.69	
3.38/1.69	----------------------------------------
3.38/1.69	
3.38/1.69	(1) QTRS Reverse (EQUIVALENT)
3.38/1.69	We applied the QTRS Reverse Processor [REVERSE].
3.38/1.69	----------------------------------------
3.38/1.69	
3.38/1.69	(2)
3.38/1.69	Obligation:
3.38/1.69	Q restricted rewrite system:
3.38/1.69	The TRS R consists of the following rules:
3.38/1.69	
3.38/1.69	   a(a(a(a(a(b(a(x1))))))) -> b(a(a(b(a(a(a(b(a(a(a(a(a(a(x1))))))))))))))
3.38/1.69	
3.38/1.69	Q is empty.
3.38/1.69	
3.38/1.69	----------------------------------------
3.38/1.69	
3.38/1.69	(3) Strip Symbols Proof (SOUND)
3.38/1.69	We were given the following TRS:
3.38/1.69	
3.38/1.69	   a(a(a(a(a(b(a(x1))))))) -> b(a(a(b(a(a(a(b(a(a(a(a(a(a(x1))))))))))))))
3.38/1.69	
3.38/1.69	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.38/1.69	
3.38/1.69	   a(a(a(a(a(b(x)))))) -> b(a(a(b(a(a(a(b(a(a(a(a(a(x)))))))))))))
3.38/1.69	
3.38/1.69	----------------------------------------
3.38/1.69	
3.38/1.69	(4)
3.38/1.69	Obligation:
3.38/1.69	Q restricted rewrite system:
3.38/1.69	The TRS R consists of the following rules:
3.38/1.69	
3.38/1.69	   a(a(a(a(a(b(x)))))) -> b(a(a(b(a(a(a(b(a(a(a(a(a(x)))))))))))))
3.38/1.69	
3.38/1.69	Q is empty.
3.38/1.69	
3.38/1.69	----------------------------------------
3.38/1.69	
3.38/1.69	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.38/1.69	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.38/1.69	The following rules were used to construct the certificate:
3.38/1.69	
3.38/1.69	   a(a(a(a(a(b(x)))))) -> b(a(a(b(a(a(a(b(a(a(a(a(a(x)))))))))))))
3.38/1.69	
3.38/1.69	The certificate found is represented by the following graph.
3.38/1.69	The certificate consists of the following enumerated nodes:
3.38/1.69	7, 8, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359
3.38/1.69	
3.38/1.69	Node 7 is start node and node 8 is final node.
3.38/1.69	
3.38/1.69	Those nodes are connected through the following edges:
3.38/1.69	
3.38/1.69	* 7 to 141 labelled b_1(0)* 8 to 8 labelled #_1(0)* 141 to 142 labelled a_1(0)* 142 to 143 labelled a_1(0)* 143 to 144 labelled b_1(0)* 144 to 145 labelled a_1(0)* 145 to 146 labelled a_1(0)* 146 to 147 labelled a_1(0)* 147 to 148 labelled b_1(0)* 148 to 149 labelled a_1(0)* 148 to 348 labelled b_1(1)* 149 to 150 labelled a_1(0)* 149 to 348 labelled b_1(1)* 150 to 151 labelled a_1(0)* 150 to 348 labelled b_1(1)* 151 to 152 labelled a_1(0)* 151 to 348 labelled b_1(1)* 152 to 8 labelled a_1(0)* 152 to 348 labelled b_1(1)* 348 to 349 labelled a_1(1)* 349 to 350 labelled a_1(1)* 350 to 351 labelled b_1(1)* 351 to 352 labelled a_1(1)* 352 to 353 labelled a_1(1)* 353 to 354 labelled a_1(1)* 354 to 355 labelled b_1(1)* 355 to 356 labelled a_1(1)* 355 to 348 labelled b_1(1)* 356 to 357 labelled a_1(1)* 356 to 348 labelled b_1(1)* 357 to 358 labelled a_1(1)* 357 to 348 labelled b_1(1)* 358 to 359 labelled a_1(1)* 358 to 348 labelled b_1(1)* 359 to 8 labelled a_1(1)* 359 to 348 labelled b_1(1)
3.38/1.69	
3.38/1.69	
3.38/1.69	----------------------------------------
3.38/1.69	
3.38/1.69	(6)
3.38/1.69	YES
3.38/1.72	EOF