0.00/0.05	YES
0.00/0.05	
0.00/0.05	Problem 1: 
0.00/0.05	
0.00/0.05	(VAR x)
0.00/0.05	(STRATEGY CONTEXTSENSITIVE
0.00/0.05	(f_1)
0.00/0.05	(g_1)
0.00/0.05	(a_0)
0.00/0.05	)
0.00/0.05	(RULES
0.00/0.05	f_1(x) -> g_1(f_1(x))
0.00/0.05	g_1(f_1(x)) -> x
0.00/0.05	g_1(x) -> a_0
0.00/0.05	)
0.00/0.05	
0.00/0.05	Problem 1: 
0.00/0.05	
0.00/0.05	Dependency Pairs Processor:
0.00/0.05	-> Pairs:
0.00/0.05	 F_1(x) -> G_1(f_1(x))
0.00/0.05	 G_1(f_1(x)) -> x
0.00/0.05	-> Rules:
0.00/0.05	 f_1(x) -> g_1(f_1(x))
0.00/0.05	 g_1(f_1(x)) -> x
0.00/0.05	 g_1(x) -> a_0
0.00/0.05	-> Unhiding Rules:
0.00/0.05	 f_1(x) -> F_1(x)
0.00/0.05	
0.00/0.05	Problem 1: 
0.00/0.05	
0.00/0.05	SCC Processor:
0.00/0.05	-> Pairs:
0.00/0.05	 F_1(x) -> G_1(f_1(x))
0.00/0.05	 G_1(f_1(x)) -> x
0.00/0.05	-> Rules:
0.00/0.05	 f_1(x) -> g_1(f_1(x))
0.00/0.05	 g_1(f_1(x)) -> x
0.00/0.05	 g_1(x) -> a_0
0.00/0.05	-> Unhiding rules:
0.00/0.05	 f_1(x) -> F_1(x)
0.00/0.05	->Strongly Connected Components:
0.00/0.05	->->Cycle:
0.00/0.05	->->-> Pairs:
0.00/0.05	 F_1(x) -> G_1(f_1(x))
0.00/0.05	 G_1(f_1(x)) -> x
0.00/0.05	->->-> Rules:
0.00/0.05	 f_1(x) -> g_1(f_1(x))
0.00/0.05	 g_1(f_1(x)) -> x
0.00/0.05	 g_1(x) -> a_0
0.00/0.05	->->-> Unhiding rules:
0.00/0.05	 f_1(x) -> F_1(x)
0.00/0.05	
0.00/0.05	Problem 1: 
0.00/0.05	
0.00/0.05	Reduction Pairs Processor:
0.00/0.05	-> Pairs:
0.00/0.05	 F_1(x) -> G_1(f_1(x))
0.00/0.05	 G_1(f_1(x)) -> x
0.00/0.05	-> Rules:
0.00/0.05	 f_1(x) -> g_1(f_1(x))
0.00/0.05	 g_1(f_1(x)) -> x
0.00/0.05	 g_1(x) -> a_0
0.00/0.05	-> Unhiding rules:
0.00/0.05	 f_1(x) -> F_1(x)
0.00/0.05	-> Usable rules:
0.00/0.05	 f_1(x) -> g_1(f_1(x))
0.00/0.05	 g_1(f_1(x)) -> x
0.00/0.05	 g_1(x) -> a_0
0.00/0.05	->Interpretation type:
0.00/0.05	 Linear
0.00/0.05	->Coefficients:
0.00/0.05	 Natural Numbers
0.00/0.05	->Dimension:
0.00/0.05	 1
0.00/0.05	->Bound:
0.00/0.05	 2
0.00/0.05	->Interpretation:
0.00/0.05	 
0.00/0.05	[f_1](X) = X + 2
0.00/0.05	[g_1](X) = X
0.00/0.05	[a_0] = 0
0.00/0.05	[F_1](X) = X + 2
0.00/0.05	[G_1](X) = X
0.00/0.05	
0.00/0.05	Problem 1: 
0.00/0.05	
0.00/0.05	SCC Processor:
0.00/0.05	-> Pairs:
0.00/0.05	 F_1(x) -> G_1(f_1(x))
0.00/0.05	-> Rules:
0.00/0.05	 f_1(x) -> g_1(f_1(x))
0.00/0.05	 g_1(f_1(x)) -> x
0.00/0.05	 g_1(x) -> a_0
0.00/0.05	-> Unhiding rules:
0.00/0.05	 f_1(x) -> F_1(x)
0.00/0.05	->Strongly Connected Components:
0.00/0.05	 There is no strongly connected component
0.00/0.05	
0.00/0.05	The problem is finite.
0.00/0.05	EOF