0.00/0.02	YES
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	
0.00/0.02	(VAR x y)
0.00/0.02	(STRATEGY CONTEXTSENSITIVE
0.00/0.02	(f_1)
0.00/0.02	(g_1)
0.00/0.02	(a_0)
0.00/0.02	(i_0 1)
0.00/0.02	)
0.00/0.02	(RULES
0.00/0.02	f_1(x,i_0(g_1(x))) -> a_0
0.00/0.02	f_1(x,i_0(x)) -> f_1(x,x)
0.00/0.02	f_1(x,x) -> f_1(i_0(x),g_1(g_1(x)))
0.00/0.02	f_1(x,y) -> x
0.00/0.02	g_1(x) -> i_0(x)
0.00/0.02	)
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	
0.00/0.02	Dependency Pairs Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 F_1(x,i_0(x)) -> F_1(x,x)
0.00/0.02	 F_1(x,x) -> F_1(i_0(x),g_1(g_1(x)))
0.00/0.02	 F_1(x,y) -> x
0.00/0.02	 G_1(x) -> x
0.00/0.02	-> Rules:
0.00/0.02	 f_1(x,i_0(g_1(x))) -> a_0
0.00/0.02	 f_1(x,i_0(x)) -> f_1(x,x)
0.00/0.02	 f_1(x,x) -> f_1(i_0(x),g_1(g_1(x)))
0.00/0.02	 f_1(x,y) -> x
0.00/0.02	 g_1(x) -> i_0(x)
0.00/0.02	-> Unhiding Rules:
0.00/0.02	 g_1(g_1(x)) -> G_1(g_1(x))
0.00/0.02	 i_0(x2) -> x2
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	
0.00/0.02	SCC Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 F_1(x,i_0(x)) -> F_1(x,x)
0.00/0.02	 F_1(x,x) -> F_1(i_0(x),g_1(g_1(x)))
0.00/0.02	 F_1(x,y) -> x
0.00/0.02	 G_1(x) -> x
0.00/0.02	-> Rules:
0.00/0.02	 f_1(x,i_0(g_1(x))) -> a_0
0.00/0.02	 f_1(x,i_0(x)) -> f_1(x,x)
0.00/0.02	 f_1(x,x) -> f_1(i_0(x),g_1(g_1(x)))
0.00/0.02	 f_1(x,y) -> x
0.00/0.02	 g_1(x) -> i_0(x)
0.00/0.02	-> Unhiding rules:
0.00/0.02	 g_1(g_1(x)) -> G_1(g_1(x))
0.00/0.02	 i_0(x2) -> x2
0.00/0.02	->Strongly Connected Components:
0.00/0.02	->->Cycle:
0.00/0.02	->->-> Pairs:
0.00/0.02	 G_1(x) -> x
0.00/0.02	->->-> Rules:
0.00/0.02	 f_1(x,i_0(g_1(x))) -> a_0
0.00/0.02	 f_1(x,i_0(x)) -> f_1(x,x)
0.00/0.02	 f_1(x,x) -> f_1(i_0(x),g_1(g_1(x)))
0.00/0.02	 f_1(x,y) -> x
0.00/0.02	 g_1(x) -> i_0(x)
0.00/0.02	->->-> Unhiding rules:
0.00/0.02	 g_1(g_1(x)) -> G_1(g_1(x))
0.00/0.02	 i_0(x2) -> x2
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	
0.00/0.02	Reduction Pairs Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 G_1(x) -> x
0.00/0.02	-> Rules:
0.00/0.02	 f_1(x,i_0(g_1(x))) -> a_0
0.00/0.02	 f_1(x,i_0(x)) -> f_1(x,x)
0.00/0.02	 f_1(x,x) -> f_1(i_0(x),g_1(g_1(x)))
0.00/0.02	 f_1(x,y) -> x
0.00/0.02	 g_1(x) -> i_0(x)
0.00/0.02	-> Unhiding rules:
0.00/0.02	 g_1(g_1(x)) -> G_1(g_1(x))
0.00/0.02	 i_0(x2) -> x2
0.00/0.02	-> Usable rules:
0.00/0.02	 g_1(x) -> i_0(x)
0.00/0.02	->Interpretation type:
0.00/0.02	 Linear
0.00/0.02	->Coefficients:
0.00/0.02	 Natural Numbers
0.00/0.02	->Dimension:
0.00/0.02	 1
0.00/0.02	->Bound:
0.00/0.02	 2
0.00/0.02	->Interpretation:
0.00/0.02	 
0.00/0.02	[g_1](X) = 2.X + 2
0.00/0.02	[i_0](X) = 2.X
0.00/0.02	[G_1](X) = 2.X + 2
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	
0.00/0.02	Basic Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 f_1(x,i_0(g_1(x))) -> a_0
0.00/0.02	 f_1(x,i_0(x)) -> f_1(x,x)
0.00/0.02	 f_1(x,x) -> f_1(i_0(x),g_1(g_1(x)))
0.00/0.02	 f_1(x,y) -> x
0.00/0.02	 g_1(x) -> i_0(x)
0.00/0.02	-> Unhiding rules:
0.00/0.02	 g_1(g_1(x)) -> G_1(g_1(x))
0.00/0.02	 i_0(x2) -> x2
0.00/0.02	-> Result:
0.00/0.02	 Set P is empty
0.00/0.02	
0.00/0.02	The problem is finite.
0.00/0.04	EOF