3.93/1.84	YES
3.93/1.87	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.93/1.87	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.93/1.87	
3.93/1.87	
3.93/1.87	Termination w.r.t. Q of the given QTRS could be proven:
3.93/1.87	
3.93/1.87	(0) QTRS
3.93/1.87	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.93/1.87	(2) QTRS
3.93/1.87	(3) Strip Symbols Proof [SOUND, 0 ms]
3.93/1.87	(4) QTRS
3.93/1.87	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.93/1.87	(6) YES
3.93/1.87	
3.93/1.87	
3.93/1.87	----------------------------------------
3.93/1.87	
3.93/1.87	(0)
3.93/1.87	Obligation:
3.93/1.87	Q restricted rewrite system:
3.93/1.87	The TRS R consists of the following rules:
3.93/1.87	
3.93/1.87	   a(b(b(c(a(a(a(a(a(x1))))))))) -> a(a(a(a(a(a(b(b(c(a(a(b(b(c(x1))))))))))))))
3.93/1.87	
3.93/1.87	Q is empty.
3.93/1.87	
3.93/1.87	----------------------------------------
3.93/1.87	
3.93/1.87	(1) QTRS Reverse (EQUIVALENT)
3.93/1.87	We applied the QTRS Reverse Processor [REVERSE].
3.93/1.87	----------------------------------------
3.93/1.87	
3.93/1.87	(2)
3.93/1.87	Obligation:
3.93/1.87	Q restricted rewrite system:
3.93/1.87	The TRS R consists of the following rules:
3.93/1.87	
3.93/1.87	   a(a(a(a(a(c(b(b(a(x1))))))))) -> c(b(b(a(a(c(b(b(a(a(a(a(a(a(x1))))))))))))))
3.93/1.87	
3.93/1.87	Q is empty.
3.93/1.87	
3.93/1.87	----------------------------------------
3.93/1.87	
3.93/1.87	(3) Strip Symbols Proof (SOUND)
3.93/1.87	We were given the following TRS:
3.93/1.87	
3.93/1.87	   a(a(a(a(a(c(b(b(a(x1))))))))) -> c(b(b(a(a(c(b(b(a(a(a(a(a(a(x1))))))))))))))
3.93/1.87	
3.93/1.87	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.93/1.87	
3.93/1.87	   a(a(a(a(a(c(b(b(x)))))))) -> c(b(b(a(a(c(b(b(a(a(a(a(a(x)))))))))))))
3.93/1.87	
3.93/1.87	----------------------------------------
3.93/1.87	
3.93/1.87	(4)
3.93/1.87	Obligation:
3.93/1.87	Q restricted rewrite system:
3.93/1.87	The TRS R consists of the following rules:
3.93/1.87	
3.93/1.87	   a(a(a(a(a(c(b(b(x)))))))) -> c(b(b(a(a(c(b(b(a(a(a(a(a(x)))))))))))))
3.93/1.87	
3.93/1.87	Q is empty.
3.93/1.87	
3.93/1.87	----------------------------------------
3.93/1.87	
3.93/1.87	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.93/1.87	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.93/1.87	The following rules were used to construct the certificate:
3.93/1.87	
3.93/1.87	   a(a(a(a(a(c(b(b(x)))))))) -> c(b(b(a(a(c(b(b(a(a(a(a(a(x)))))))))))))
3.93/1.87	
3.93/1.87	The certificate found is represented by the following graph.
3.93/1.87	The certificate consists of the following enumerated nodes:
3.93/1.87	500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525
3.93/1.87	
3.93/1.87	Node 500 is start node and node 501 is final node.
3.93/1.87	
3.93/1.87	Those nodes are connected through the following edges:
3.93/1.87	
3.93/1.87	* 500 to 502 labelled c_1(0)* 501 to 501 labelled #_1(0)* 502 to 503 labelled b_1(0)* 503 to 504 labelled b_1(0)* 504 to 505 labelled a_1(0)* 505 to 506 labelled a_1(0)* 506 to 507 labelled c_1(0)* 507 to 508 labelled b_1(0)* 508 to 509 labelled b_1(0)* 509 to 510 labelled a_1(0)* 509 to 514 labelled c_1(1)* 510 to 511 labelled a_1(0)* 510 to 514 labelled c_1(1)* 511 to 512 labelled a_1(0)* 511 to 514 labelled c_1(1)* 512 to 513 labelled a_1(0)* 512 to 514 labelled c_1(1)* 513 to 501 labelled a_1(0)* 513 to 514 labelled c_1(1)* 514 to 515 labelled b_1(1)* 515 to 516 labelled b_1(1)* 516 to 517 labelled a_1(1)* 517 to 518 labelled a_1(1)* 518 to 519 labelled c_1(1)* 519 to 520 labelled b_1(1)* 520 to 521 labelled b_1(1)* 521 to 522 labelled a_1(1)* 521 to 514 labelled c_1(1)* 522 to 523 labelled a_1(1)* 522 to 514 labelled c_1(1)* 523 to 524 labelled a_1(1)* 523 to 514 labelled c_1(1)* 524 to 525 labelled a_1(1)* 524 to 514 labelled c_1(1)* 525 to 501 labelled a_1(1)* 525 to 514 labelled c_1(1)
3.93/1.87	
3.93/1.87	
3.93/1.87	----------------------------------------
3.93/1.87	
3.93/1.87	(6)
3.93/1.87	YES
3.93/1.88	EOF