3.00/1.54	YES
3.00/1.55	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.00/1.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.00/1.55	
3.00/1.55	
3.00/1.55	Termination w.r.t. Q of the given QTRS could be proven:
3.00/1.55	
3.00/1.55	(0) QTRS
3.00/1.55	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.00/1.55	(2) YES
3.00/1.55	
3.00/1.55	
3.00/1.55	----------------------------------------
3.00/1.55	
3.00/1.55	(0)
3.00/1.55	Obligation:
3.00/1.55	Q restricted rewrite system:
3.00/1.55	The TRS R consists of the following rules:
3.00/1.55	
3.00/1.55	   f(f(x)) -> f(x)
3.00/1.55	   g(0) -> g(f(0))
3.00/1.55	
3.00/1.55	The set Q consists of the following terms:
3.00/1.55	
3.00/1.55	   f(f(x0))
3.00/1.55	   g(0)
3.00/1.55	
3.00/1.55	
3.00/1.55	----------------------------------------
3.00/1.55	
3.00/1.55	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.00/1.55	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.00/1.55	The following rules were used to construct the certificate:
3.00/1.55	
3.00/1.55	   f(f(x)) -> f(x)
3.00/1.55	   g(0) -> g(f(0))
3.00/1.55	
3.00/1.55	The certificate found is represented by the following graph.
3.00/1.55	The certificate consists of the following enumerated nodes:
3.00/1.55	1, 2, 3, 4
3.00/1.55	
3.00/1.55	Node 1 is start node and node 2 is final node.
3.00/1.55	
3.00/1.55	Those nodes are connected through the following edges:
3.00/1.55	
3.00/1.55	* 1 to 2 labelled f_1(0), f_1(1)* 1 to 3 labelled g_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled f_1(0)* 4 to 2 labelled 0(0)
3.00/1.55	
3.00/1.55	
3.00/1.55	----------------------------------------
3.00/1.55	
3.00/1.55	(2)
3.00/1.55	YES
3.00/1.57	EOF