4.10/1.77	YES
4.10/1.79	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.10/1.79	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.10/1.79	
4.10/1.79	
4.10/1.79	Termination w.r.t. Q of the given QTRS could be proven:
4.10/1.79	
4.10/1.79	(0) QTRS
4.10/1.79	(1) Strip Symbols Proof [SOUND, 0 ms]
4.10/1.79	(2) QTRS
4.10/1.79	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
4.10/1.79	(4) YES
4.10/1.79	
4.10/1.79	
4.10/1.79	----------------------------------------
4.10/1.79	
4.10/1.79	(0)
4.10/1.79	Obligation:
4.10/1.79	Q restricted rewrite system:
4.10/1.79	The TRS R consists of the following rules:
4.10/1.79	
4.10/1.79	   c(a(a(b(c(c(a(a(b(c(x1)))))))))) -> a(a(b(c(c(a(a(b(c(a(a(b(c(c(x1))))))))))))))
4.10/1.79	
4.10/1.79	Q is empty.
4.10/1.79	
4.10/1.79	----------------------------------------
4.10/1.79	
4.10/1.79	(1) Strip Symbols Proof (SOUND)
4.10/1.79	We were given the following TRS:
4.10/1.79	
4.10/1.79	   c(a(a(b(c(c(a(a(b(c(x1)))))))))) -> a(a(b(c(c(a(a(b(c(a(a(b(c(c(x1))))))))))))))
4.10/1.79	
4.10/1.79	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
4.10/1.79	
4.10/1.79	   c(a(a(b(c(c(a(a(b(x))))))))) -> a(a(b(c(c(a(a(b(c(a(a(b(c(x)))))))))))))
4.10/1.79	
4.10/1.79	----------------------------------------
4.10/1.79	
4.10/1.79	(2)
4.10/1.79	Obligation:
4.10/1.79	Q restricted rewrite system:
4.10/1.79	The TRS R consists of the following rules:
4.10/1.79	
4.10/1.79	   c(a(a(b(c(c(a(a(b(x))))))))) -> a(a(b(c(c(a(a(b(c(a(a(b(c(x)))))))))))))
4.10/1.79	
4.10/1.79	Q is empty.
4.10/1.79	
4.10/1.79	----------------------------------------
4.10/1.79	
4.10/1.79	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
4.10/1.79	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
4.10/1.79	The following rules were used to construct the certificate:
4.10/1.79	
4.10/1.79	   c(a(a(b(c(c(a(a(b(x))))))))) -> a(a(b(c(c(a(a(b(c(a(a(b(c(x)))))))))))))
4.10/1.79	
4.10/1.79	The certificate found is represented by the following graph.
4.10/1.79	The certificate consists of the following enumerated nodes:
4.10/1.79	187, 188, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446
4.10/1.79	
4.10/1.79	Node 187 is start node and node 188 is final node.
4.10/1.79	
4.10/1.79	Those nodes are connected through the following edges:
4.10/1.79	
4.10/1.79	* 187 to 423 labelled a_1(0)* 188 to 188 labelled #_1(0)* 423 to 424 labelled a_1(0)* 424 to 425 labelled b_1(0)* 425 to 426 labelled c_1(0)* 426 to 427 labelled c_1(0)* 427 to 428 labelled a_1(0)* 428 to 429 labelled a_1(0)* 429 to 430 labelled b_1(0)* 430 to 431 labelled c_1(0)* 430 to 435 labelled a_1(1)* 431 to 432 labelled a_1(0)* 432 to 433 labelled a_1(0)* 433 to 434 labelled b_1(0)* 434 to 188 labelled c_1(0)* 434 to 435 labelled a_1(1)* 435 to 436 labelled a_1(1)* 436 to 437 labelled b_1(1)* 437 to 438 labelled c_1(1)* 438 to 439 labelled c_1(1)* 439 to 440 labelled a_1(1)* 440 to 441 labelled a_1(1)* 441 to 442 labelled b_1(1)* 442 to 443 labelled c_1(1)* 442 to 435 labelled a_1(1)* 443 to 444 labelled a_1(1)* 444 to 445 labelled a_1(1)* 445 to 446 labelled b_1(1)* 446 to 188 labelled c_1(1)* 446 to 435 labelled a_1(1)
4.10/1.79	
4.10/1.79	
4.10/1.79	----------------------------------------
4.10/1.79	
4.10/1.79	(4)
4.10/1.79	YES
4.33/1.83	EOF