3.29/1.66	YES
3.29/1.66	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.29/1.66	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.29/1.66	
3.29/1.66	
3.29/1.66	Termination w.r.t. Q of the given QTRS could be proven:
3.29/1.66	
3.29/1.66	(0) QTRS
3.29/1.66	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.29/1.66	(2) YES
3.29/1.66	
3.29/1.66	
3.29/1.66	----------------------------------------
3.29/1.66	
3.29/1.66	(0)
3.29/1.66	Obligation:
3.29/1.66	Q restricted rewrite system:
3.29/1.66	The TRS R consists of the following rules:
3.29/1.66	
3.29/1.66	   f(f(a)) -> c
3.29/1.66	
3.29/1.66	The set Q consists of the following terms:
3.29/1.66	
3.29/1.66	   f(f(a))
3.29/1.66	
3.29/1.66	
3.29/1.66	----------------------------------------
3.29/1.66	
3.29/1.66	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.29/1.66	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 0. This implies Q-termination of R.
3.29/1.66	The following rules were used to construct the certificate:
3.29/1.66	
3.29/1.66	   f(f(a)) -> c
3.29/1.66	
3.29/1.66	The certificate found is represented by the following graph.
3.29/1.66	The certificate consists of the following enumerated nodes:
3.29/1.66	1, 2
3.29/1.66	
3.29/1.66	Node 1 is start node and node 2 is final node.
3.29/1.66	
3.29/1.66	Those nodes are connected through the following edges:
3.29/1.66	
3.29/1.66	* 1 to 2 labelled c(0)* 2 to 2 labelled #_1(0)
3.29/1.66	
3.29/1.66	
3.29/1.66	----------------------------------------
3.29/1.66	
3.29/1.66	(2)
3.29/1.66	YES
3.29/1.69	EOF