3.72/1.68	YES
3.90/1.73	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.90/1.73	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.90/1.73	
3.90/1.73	
3.90/1.73	Termination w.r.t. Q of the given QTRS could be proven:
3.90/1.73	
3.90/1.73	(0) QTRS
3.90/1.73	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.90/1.73	(2) QTRS
3.90/1.73	(3) Strip Symbols Proof [SOUND, 0 ms]
3.90/1.73	(4) QTRS
3.90/1.73	(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.90/1.73	(6) YES
3.90/1.73	
3.90/1.73	
3.90/1.73	----------------------------------------
3.90/1.73	
3.90/1.73	(0)
3.90/1.73	Obligation:
3.90/1.73	Q restricted rewrite system:
3.90/1.73	The TRS R consists of the following rules:
3.90/1.73	
3.90/1.73	   a(b(c(c(a(a(a(a(x1)))))))) -> a(a(a(a(a(b(c(c(a(a(b(c(c(x1)))))))))))))
3.90/1.73	
3.90/1.73	Q is empty.
3.90/1.73	
3.90/1.73	----------------------------------------
3.90/1.73	
3.90/1.73	(1) QTRS Reverse (EQUIVALENT)
3.90/1.73	We applied the QTRS Reverse Processor [REVERSE].
3.90/1.73	----------------------------------------
3.90/1.73	
3.90/1.73	(2)
3.90/1.73	Obligation:
3.90/1.73	Q restricted rewrite system:
3.90/1.73	The TRS R consists of the following rules:
3.90/1.73	
3.90/1.73	   a(a(a(a(c(c(b(a(x1)))))))) -> c(c(b(a(a(c(c(b(a(a(a(a(a(x1)))))))))))))
3.90/1.73	
3.90/1.73	Q is empty.
3.90/1.73	
3.90/1.73	----------------------------------------
3.90/1.73	
3.90/1.73	(3) Strip Symbols Proof (SOUND)
3.90/1.73	We were given the following TRS:
3.90/1.73	
3.90/1.73	   a(a(a(a(c(c(b(a(x1)))))))) -> c(c(b(a(a(c(c(b(a(a(a(a(a(x1)))))))))))))
3.90/1.73	
3.90/1.73	By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 
3.90/1.73	
3.90/1.73	   a(a(a(a(c(c(b(x))))))) -> c(c(b(a(a(c(c(b(a(a(a(a(x))))))))))))
3.90/1.73	
3.90/1.73	----------------------------------------
3.90/1.73	
3.90/1.73	(4)
3.90/1.73	Obligation:
3.90/1.73	Q restricted rewrite system:
3.90/1.73	The TRS R consists of the following rules:
3.90/1.73	
3.90/1.73	   a(a(a(a(c(c(b(x))))))) -> c(c(b(a(a(c(c(b(a(a(a(a(x))))))))))))
3.90/1.73	
3.90/1.73	Q is empty.
3.90/1.73	
3.90/1.73	----------------------------------------
3.90/1.73	
3.90/1.73	(5) RFCMatchBoundsTRSProof (EQUIVALENT)
3.90/1.73	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.90/1.73	The following rules were used to construct the certificate:
3.90/1.73	
3.90/1.73	   a(a(a(a(c(c(b(x))))))) -> c(c(b(a(a(c(c(b(a(a(a(a(x))))))))))))
3.90/1.73	
3.90/1.73	The certificate found is represented by the following graph.
3.90/1.73	The certificate consists of the following enumerated nodes:
3.90/1.73	424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447
3.90/1.73	
3.90/1.73	Node 424 is start node and node 425 is final node.
3.90/1.73	
3.90/1.73	Those nodes are connected through the following edges:
3.90/1.73	
3.90/1.73	* 424 to 426 labelled c_1(0)* 425 to 425 labelled #_1(0)* 426 to 427 labelled c_1(0)* 427 to 428 labelled b_1(0)* 428 to 429 labelled a_1(0)* 429 to 430 labelled a_1(0)* 430 to 431 labelled c_1(0)* 431 to 432 labelled c_1(0)* 432 to 433 labelled b_1(0)* 433 to 434 labelled a_1(0)* 433 to 437 labelled c_1(1)* 434 to 435 labelled a_1(0)* 434 to 437 labelled c_1(1)* 435 to 436 labelled a_1(0)* 435 to 437 labelled c_1(1)* 436 to 425 labelled a_1(0)* 436 to 437 labelled c_1(1)* 437 to 438 labelled c_1(1)* 438 to 439 labelled b_1(1)* 439 to 440 labelled a_1(1)* 440 to 441 labelled a_1(1)* 441 to 442 labelled c_1(1)* 442 to 443 labelled c_1(1)* 443 to 444 labelled b_1(1)* 444 to 445 labelled a_1(1)* 444 to 437 labelled c_1(1)* 445 to 446 labelled a_1(1)* 445 to 437 labelled c_1(1)* 446 to 447 labelled a_1(1)* 446 to 437 labelled c_1(1)* 447 to 425 labelled a_1(1)* 447 to 437 labelled c_1(1)
3.90/1.73	
3.90/1.73	
3.90/1.73	----------------------------------------
3.90/1.73	
3.90/1.73	(6)
3.90/1.73	YES
3.93/1.77	EOF