4.30/1.89	YES
4.36/1.90	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
4.36/1.90	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.36/1.90	
4.36/1.90	
4.36/1.90	Termination w.r.t. Q of the given QTRS could be proven:
4.36/1.90	
4.36/1.90	(0) QTRS
4.36/1.90	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.36/1.90	(2) QTRS
4.36/1.90	(3) Strip Symbols Proof [SOUND, 0 ms]
4.36/1.90	(4) QTRS
4.36/1.90	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 2 ms]
4.36/1.90	(6) YES
4.36/1.90	
4.36/1.90	
4.36/1.90	----------------------------------------
4.36/1.90	
4.36/1.90	(0)
4.36/1.90	Obligation:
4.36/1.90	Q restricted rewrite system:
4.36/1.90	The TRS R consists of the following rules:
4.36/1.90	
4.36/1.90	   a(b(a(a(a(a(a(x1))))))) -> a(a(a(a(a(a(b(a(a(a(a(b(a(b(x1))))))))))))))
4.36/1.90	
4.36/1.90	Q is empty.
4.36/1.90	
4.36/1.90	----------------------------------------
4.36/1.90	
4.36/1.90	(1) QTRS Reverse (EQUIVALENT)
4.36/1.90	We applied the QTRS Reverse Processor [REVERSE].
4.36/1.90	----------------------------------------
4.36/1.90	
4.36/1.90	(2)
4.36/1.90	Obligation:
4.36/1.90	Q restricted rewrite system:
4.36/1.90	The TRS R consists of the following rules:
4.36/1.90	
4.36/1.90	   a(a(a(a(a(b(a(x1))))))) -> b(a(b(a(a(a(a(b(a(a(a(a(a(a(x1))))))))))))))
4.36/1.90	
4.36/1.90	Q is empty.
4.36/1.90	
4.36/1.90	----------------------------------------
4.36/1.90	
4.36/1.90	(3) Strip Symbols Proof (SOUND)
4.36/1.90	We were given the following TRS:
4.36/1.90	
4.36/1.90	   a(a(a(a(a(b(a(x1))))))) -> b(a(b(a(a(a(a(b(a(a(a(a(a(a(x1))))))))))))))
4.36/1.90	
4.36/1.90	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.36/1.90	
4.36/1.90	   a(a(a(a(a(b(x)))))) -> b(a(b(a(a(a(a(b(a(a(a(a(a(x)))))))))))))
4.36/1.90	
4.36/1.90	----------------------------------------
4.36/1.90	
4.36/1.90	(4)
4.36/1.90	Obligation:
4.36/1.90	Q restricted rewrite system:
4.36/1.90	The TRS R consists of the following rules:
4.36/1.90	
4.36/1.90	   a(a(a(a(a(b(x)))))) -> b(a(b(a(a(a(a(b(a(a(a(a(a(x)))))))))))))
4.36/1.90	
4.36/1.90	Q is empty.
4.36/1.90	
4.36/1.90	----------------------------------------
4.36/1.90	
4.36/1.90	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.36/1.90	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.36/1.90	The following rules were used to construct the certificate:
4.36/1.90	
4.36/1.90	   a(a(a(a(a(b(x)))))) -> b(a(b(a(a(a(a(b(a(a(a(a(a(x)))))))))))))
4.36/1.90	
4.36/1.90	The certificate found is represented by the following graph.
4.36/1.90	The certificate consists of the following enumerated nodes:
4.36/1.90	436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461
4.36/1.90	
4.36/1.90	Node 436 is start node and node 437 is final node.
4.36/1.90	
4.36/1.90	Those nodes are connected through the following edges:
4.36/1.90	
4.36/1.90	* 436 to 438 labelled b_1(0)* 437 to 437 labelled #_1(0)* 438 to 439 labelled a_1(0)* 439 to 440 labelled b_1(0)* 440 to 441 labelled a_1(0)* 441 to 442 labelled a_1(0)* 442 to 443 labelled a_1(0)* 443 to 444 labelled a_1(0)* 444 to 445 labelled b_1(0)* 445 to 446 labelled a_1(0)* 445 to 450 labelled b_1(1)* 446 to 447 labelled a_1(0)* 446 to 450 labelled b_1(1)* 447 to 448 labelled a_1(0)* 447 to 450 labelled b_1(1)* 448 to 449 labelled a_1(0)* 448 to 450 labelled b_1(1)* 449 to 437 labelled a_1(0)* 449 to 450 labelled b_1(1)* 450 to 451 labelled a_1(1)* 451 to 452 labelled b_1(1)* 452 to 453 labelled a_1(1)* 453 to 454 labelled a_1(1)* 454 to 455 labelled a_1(1)* 455 to 456 labelled a_1(1)* 456 to 457 labelled b_1(1)* 457 to 458 labelled a_1(1)* 457 to 450 labelled b_1(1)* 458 to 459 labelled a_1(1)* 458 to 450 labelled b_1(1)* 459 to 460 labelled a_1(1)* 459 to 450 labelled b_1(1)* 460 to 461 labelled a_1(1)* 460 to 450 labelled b_1(1)* 461 to 437 labelled a_1(1)* 461 to 450 labelled b_1(1)
4.36/1.90	
4.36/1.90	
4.36/1.90	----------------------------------------
4.36/1.90	
4.36/1.90	(6)
4.36/1.90	YES
4.38/1.93	EOF