4.07/1.91	YES
4.07/1.92	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.07/1.92	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.07/1.92	
4.07/1.92	
4.07/1.92	Termination w.r.t. Q of the given QTRS could be proven:
4.07/1.92	
4.07/1.92	(0) QTRS
4.07/1.92	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.07/1.92	(2) QTRS
4.07/1.92	(3) Strip Symbols Proof [SOUND, 0 ms]
4.07/1.92	(4) QTRS
4.07/1.92	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 5 ms]
4.07/1.92	(6) YES
4.07/1.92	
4.07/1.92	
4.07/1.92	----------------------------------------
4.07/1.92	
4.07/1.92	(0)
4.07/1.92	Obligation:
4.07/1.92	Q restricted rewrite system:
4.07/1.92	The TRS R consists of the following rules:
4.07/1.92	
4.07/1.92	   a(b(a(a(a(a(x1)))))) -> a(a(a(a(a(b(a(a(b(a(b(x1)))))))))))
4.07/1.92	
4.07/1.92	Q is empty.
4.07/1.92	
4.07/1.92	----------------------------------------
4.07/1.92	
4.07/1.92	(1) QTRS Reverse (EQUIVALENT)
4.07/1.92	We applied the QTRS Reverse Processor [REVERSE].
4.07/1.92	----------------------------------------
4.07/1.92	
4.07/1.92	(2)
4.07/1.92	Obligation:
4.07/1.92	Q restricted rewrite system:
4.07/1.92	The TRS R consists of the following rules:
4.07/1.92	
4.07/1.92	   a(a(a(a(b(a(x1)))))) -> b(a(b(a(a(b(a(a(a(a(a(x1)))))))))))
4.07/1.92	
4.07/1.92	Q is empty.
4.07/1.92	
4.07/1.92	----------------------------------------
4.07/1.92	
4.07/1.92	(3) Strip Symbols Proof (SOUND)
4.07/1.92	We were given the following TRS:
4.07/1.92	
4.07/1.92	   a(a(a(a(b(a(x1)))))) -> b(a(b(a(a(b(a(a(a(a(a(x1)))))))))))
4.07/1.92	
4.07/1.92	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.07/1.92	
4.07/1.92	   a(a(a(a(b(x))))) -> b(a(b(a(a(b(a(a(a(a(x))))))))))
4.07/1.92	
4.07/1.92	----------------------------------------
4.07/1.92	
4.07/1.92	(4)
4.07/1.92	Obligation:
4.07/1.92	Q restricted rewrite system:
4.07/1.92	The TRS R consists of the following rules:
4.07/1.92	
4.07/1.92	   a(a(a(a(b(x))))) -> b(a(b(a(a(b(a(a(a(a(x))))))))))
4.07/1.92	
4.07/1.92	Q is empty.
4.07/1.92	
4.07/1.92	----------------------------------------
4.07/1.92	
4.07/1.92	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.07/1.92	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.07/1.92	The following rules were used to construct the certificate:
4.07/1.92	
4.07/1.92	   a(a(a(a(b(x))))) -> b(a(b(a(a(b(a(a(a(a(x))))))))))
4.07/1.92	
4.07/1.92	The certificate found is represented by the following graph.
4.07/1.92	The certificate consists of the following enumerated nodes:
4.07/1.92	459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 480, 481, 482, 483, 484, 485, 486, 487, 488
4.07/1.92	
4.07/1.92	Node 459 is start node and node 460 is final node.
4.07/1.92	
4.07/1.92	Those nodes are connected through the following edges:
4.07/1.92	
4.07/1.92	* 459 to 461 labelled b_1(0)* 460 to 460 labelled #_1(0)* 461 to 462 labelled a_1(0)* 462 to 463 labelled b_1(0)* 463 to 464 labelled a_1(0)* 464 to 465 labelled a_1(0)* 465 to 466 labelled b_1(0)* 466 to 467 labelled a_1(0)* 466 to 480 labelled b_1(1)* 467 to 468 labelled a_1(0)* 467 to 480 labelled b_1(1)* 468 to 469 labelled a_1(0)* 468 to 480 labelled b_1(1)* 469 to 460 labelled a_1(0)* 469 to 480 labelled b_1(1)* 480 to 481 labelled a_1(1)* 481 to 482 labelled b_1(1)* 482 to 483 labelled a_1(1)* 483 to 484 labelled a_1(1)* 484 to 485 labelled b_1(1)* 485 to 486 labelled a_1(1)* 485 to 480 labelled b_1(1)* 486 to 487 labelled a_1(1)* 486 to 480 labelled b_1(1)* 487 to 488 labelled a_1(1)* 487 to 480 labelled b_1(1)* 488 to 460 labelled a_1(1)* 488 to 480 labelled b_1(1)
4.07/1.92	
4.07/1.92	
4.07/1.92	----------------------------------------
4.07/1.92	
4.07/1.92	(6)
4.07/1.92	YES
4.34/1.96	EOF