3.93/1.83	YES
4.05/1.86	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.05/1.86	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.05/1.86	
4.05/1.86	
4.05/1.86	Termination w.r.t. Q of the given QTRS could be proven:
4.05/1.86	
4.05/1.86	(0) QTRS
4.05/1.86	(1) QTRS Reverse [EQUIVALENT, 0 ms]
4.05/1.86	(2) QTRS
4.05/1.86	(3) Strip Symbols Proof [SOUND, 0 ms]
4.05/1.86	(4) QTRS
4.05/1.86	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
4.05/1.86	(6) YES
4.05/1.86	
4.05/1.86	
4.05/1.86	----------------------------------------
4.05/1.86	
4.05/1.86	(0)
4.05/1.86	Obligation:
4.05/1.86	Q restricted rewrite system:
4.05/1.86	The TRS R consists of the following rules:
4.05/1.86	
4.05/1.86	   a(b(b(c(a(a(a(a(x1)))))))) -> a(a(a(a(a(b(b(c(a(a(a(b(b(c(x1))))))))))))))
4.05/1.86	
4.05/1.86	Q is empty.
4.05/1.86	
4.05/1.86	----------------------------------------
4.05/1.86	
4.05/1.86	(1) QTRS Reverse (EQUIVALENT)
4.05/1.86	We applied the QTRS Reverse Processor [REVERSE].
4.05/1.86	----------------------------------------
4.05/1.86	
4.05/1.86	(2)
4.05/1.86	Obligation:
4.05/1.86	Q restricted rewrite system:
4.05/1.86	The TRS R consists of the following rules:
4.05/1.86	
4.05/1.86	   a(a(a(a(c(b(b(a(x1)))))))) -> c(b(b(a(a(a(c(b(b(a(a(a(a(a(x1))))))))))))))
4.05/1.86	
4.05/1.86	Q is empty.
4.05/1.86	
4.05/1.86	----------------------------------------
4.05/1.86	
4.05/1.86	(3) Strip Symbols Proof (SOUND)
4.05/1.86	We were given the following TRS:
4.05/1.86	
4.05/1.86	   a(a(a(a(c(b(b(a(x1)))))))) -> c(b(b(a(a(a(c(b(b(a(a(a(a(a(x1))))))))))))))
4.05/1.86	
4.05/1.86	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.05/1.86	
4.05/1.86	   a(a(a(a(c(b(b(x))))))) -> c(b(b(a(a(a(c(b(b(a(a(a(a(x)))))))))))))
4.05/1.86	
4.05/1.86	----------------------------------------
4.05/1.86	
4.05/1.86	(4)
4.05/1.86	Obligation:
4.05/1.86	Q restricted rewrite system:
4.05/1.86	The TRS R consists of the following rules:
4.05/1.86	
4.05/1.86	   a(a(a(a(c(b(b(x))))))) -> c(b(b(a(a(a(c(b(b(a(a(a(a(x)))))))))))))
4.05/1.86	
4.05/1.86	Q is empty.
4.05/1.86	
4.05/1.86	----------------------------------------
4.05/1.86	
4.05/1.86	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
4.05/1.86	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.05/1.86	The following rules were used to construct the certificate:
4.05/1.86	
4.05/1.86	   a(a(a(a(c(b(b(x))))))) -> c(b(b(a(a(a(c(b(b(a(a(a(a(x)))))))))))))
4.05/1.86	
4.05/1.86	The certificate found is represented by the following graph.
4.05/1.86	The certificate consists of the following enumerated nodes:
4.05/1.86	409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434
4.05/1.86	
4.05/1.86	Node 409 is start node and node 410 is final node.
4.05/1.86	
4.05/1.86	Those nodes are connected through the following edges:
4.05/1.86	
4.05/1.86	* 409 to 411 labelled c_1(0)* 410 to 410 labelled #_1(0)* 411 to 412 labelled b_1(0)* 412 to 413 labelled b_1(0)* 413 to 414 labelled a_1(0)* 414 to 415 labelled a_1(0)* 415 to 416 labelled a_1(0)* 416 to 417 labelled c_1(0)* 417 to 418 labelled b_1(0)* 418 to 419 labelled b_1(0)* 419 to 420 labelled a_1(0)* 419 to 423 labelled c_1(1)* 420 to 421 labelled a_1(0)* 420 to 423 labelled c_1(1)* 421 to 422 labelled a_1(0)* 421 to 423 labelled c_1(1)* 422 to 410 labelled a_1(0)* 422 to 423 labelled c_1(1)* 423 to 424 labelled b_1(1)* 424 to 425 labelled b_1(1)* 425 to 426 labelled a_1(1)* 426 to 427 labelled a_1(1)* 427 to 428 labelled a_1(1)* 428 to 429 labelled c_1(1)* 429 to 430 labelled b_1(1)* 430 to 431 labelled b_1(1)* 431 to 432 labelled a_1(1)* 431 to 423 labelled c_1(1)* 432 to 433 labelled a_1(1)* 432 to 423 labelled c_1(1)* 433 to 434 labelled a_1(1)* 433 to 423 labelled c_1(1)* 434 to 410 labelled a_1(1)* 434 to 423 labelled c_1(1)
4.05/1.86	
4.05/1.86	
4.05/1.86	----------------------------------------
4.05/1.86	
4.05/1.86	(6)
4.05/1.86	YES
4.05/1.88	EOF