3.45/2.32	YES
3.62/2.37	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.62/2.37	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.62/2.37	
3.62/2.37	
3.62/2.37	Termination w.r.t. Q of the given QTRS could be proven:
3.62/2.37	
3.62/2.37	(0) QTRS
3.62/2.37	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.62/2.37	(2) QTRS
3.62/2.37	(3) Strip Symbols Proof [SOUND, 0 ms]
3.62/2.37	(4) QTRS
3.62/2.37	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.62/2.37	(6) YES
3.62/2.37	
3.62/2.37	
3.62/2.37	----------------------------------------
3.62/2.37	
3.62/2.37	(0)
3.62/2.37	Obligation:
3.62/2.37	Q restricted rewrite system:
3.62/2.37	The TRS R consists of the following rules:
3.62/2.37	
3.62/2.37	   a(b(b(c(a(a(a(a(x1)))))))) -> a(a(a(a(a(b(b(c(a(a(b(b(c(x1)))))))))))))
3.62/2.37	
3.62/2.37	Q is empty.
3.62/2.37	
3.62/2.37	----------------------------------------
3.62/2.37	
3.62/2.37	(1) QTRS Reverse (EQUIVALENT)
3.62/2.37	We applied the QTRS Reverse Processor [REVERSE].
3.62/2.37	----------------------------------------
3.62/2.37	
3.62/2.37	(2)
3.62/2.37	Obligation:
3.62/2.37	Q restricted rewrite system:
3.62/2.37	The TRS R consists of the following rules:
3.62/2.37	
3.62/2.37	   a(a(a(a(c(b(b(a(x1)))))))) -> c(b(b(a(a(c(b(b(a(a(a(a(a(x1)))))))))))))
3.62/2.37	
3.62/2.37	Q is empty.
3.62/2.37	
3.62/2.37	----------------------------------------
3.62/2.37	
3.62/2.37	(3) Strip Symbols Proof (SOUND)
3.62/2.37	We were given the following TRS:
3.62/2.37	
3.62/2.37	   a(a(a(a(c(b(b(a(x1)))))))) -> c(b(b(a(a(c(b(b(a(a(a(a(a(x1)))))))))))))
3.62/2.37	
3.62/2.37	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.62/2.37	
3.62/2.37	   a(a(a(a(c(b(b(x))))))) -> c(b(b(a(a(c(b(b(a(a(a(a(x))))))))))))
3.62/2.37	
3.62/2.37	----------------------------------------
3.62/2.37	
3.62/2.37	(4)
3.62/2.37	Obligation:
3.62/2.37	Q restricted rewrite system:
3.62/2.37	The TRS R consists of the following rules:
3.62/2.37	
3.62/2.37	   a(a(a(a(c(b(b(x))))))) -> c(b(b(a(a(c(b(b(a(a(a(a(x))))))))))))
3.62/2.37	
3.62/2.37	Q is empty.
3.62/2.37	
3.62/2.37	----------------------------------------
3.62/2.37	
3.62/2.37	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.62/2.37	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.62/2.37	The following rules were used to construct the certificate:
3.62/2.37	
3.62/2.37	   a(a(a(a(c(b(b(x))))))) -> c(b(b(a(a(c(b(b(a(a(a(a(x))))))))))))
3.62/2.37	
3.62/2.37	The certificate found is represented by the following graph.
3.62/2.37	The certificate consists of the following enumerated nodes:
3.62/2.37	400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423
3.62/2.37	
3.62/2.37	Node 400 is start node and node 401 is final node.
3.62/2.37	
3.62/2.37	Those nodes are connected through the following edges:
3.62/2.37	
3.62/2.37	* 400 to 402 labelled c_1(0)* 401 to 401 labelled #_1(0)* 402 to 403 labelled b_1(0)* 403 to 404 labelled b_1(0)* 404 to 405 labelled a_1(0)* 405 to 406 labelled a_1(0)* 406 to 407 labelled c_1(0)* 407 to 408 labelled b_1(0)* 408 to 409 labelled b_1(0)* 409 to 410 labelled a_1(0)* 409 to 413 labelled c_1(1)* 410 to 411 labelled a_1(0)* 410 to 413 labelled c_1(1)* 411 to 412 labelled a_1(0)* 411 to 413 labelled c_1(1)* 412 to 401 labelled a_1(0)* 412 to 413 labelled c_1(1)* 413 to 414 labelled b_1(1)* 414 to 415 labelled b_1(1)* 415 to 416 labelled a_1(1)* 416 to 417 labelled a_1(1)* 417 to 418 labelled c_1(1)* 418 to 419 labelled b_1(1)* 419 to 420 labelled b_1(1)* 420 to 421 labelled a_1(1)* 420 to 413 labelled c_1(1)* 421 to 422 labelled a_1(1)* 421 to 413 labelled c_1(1)* 422 to 423 labelled a_1(1)* 422 to 413 labelled c_1(1)* 423 to 401 labelled a_1(1)* 423 to 413 labelled c_1(1)
3.62/2.37	
3.62/2.37	
3.62/2.37	----------------------------------------
3.62/2.37	
3.62/2.37	(6)
3.62/2.37	YES
3.62/2.39	EOF