0.00/0.08	YES
0.00/0.08	
0.00/0.08	Problem 1: 
0.00/0.08	
0.00/0.08	(VAR x)
0.00/0.08	(STRATEGY CONTEXTSENSITIVE
0.00/0.08	(*top*_0 1)
0.00/0.08	(f_0 1)
0.00/0.08	(f_1)
0.00/0.08	(h_1)
0.00/0.08	(i_1)
0.00/0.08	)
0.00/0.08	(RULES
0.00/0.08	*top*_0(f_1(i_1(x))) -> *top*_0(x)
0.00/0.08	f_0(f_1(i_1(x))) -> f_1(x)
0.00/0.08	f_1(h_1(x)) -> f_1(i_1(x))
0.00/0.08	f_1(i_1(x)) -> x
0.00/0.08	h_1(x) -> f_1(h_1(x))
0.00/0.08	i_1(x) -> h_1(x)
0.00/0.08	)
0.00/0.08	
0.00/0.08	Problem 1: 
0.00/0.08	
0.00/0.08	Dependency Pairs Processor:
0.00/0.08	-> Pairs:
0.00/0.08	 *TOP*_0(f_1(i_1(x))) -> *TOP*_0(x)
0.00/0.08	 *TOP*_0(f_1(i_1(x))) -> x
0.00/0.08	 F_0(f_1(i_1(x))) -> F_1(x)
0.00/0.08	 F_1(h_1(x)) -> F_1(i_1(x))
0.00/0.08	 F_1(i_1(x)) -> x
0.00/0.08	 H_1(x) -> F_1(h_1(x))
0.00/0.08	 I_1(x) -> H_1(x)
0.00/0.08	-> Rules:
0.00/0.08	 *top*_0(f_1(i_1(x))) -> *top*_0(x)
0.00/0.08	 f_0(f_1(i_1(x))) -> f_1(x)
0.00/0.08	 f_1(h_1(x)) -> f_1(i_1(x))
0.00/0.08	 f_1(i_1(x)) -> x
0.00/0.08	 h_1(x) -> f_1(h_1(x))
0.00/0.08	 i_1(x) -> h_1(x)
0.00/0.08	-> Unhiding Rules:
0.00/0.08	 h_1(x) -> H_1(x)
0.00/0.08	 i_1(x) -> I_1(x)
0.00/0.08	
0.00/0.08	Problem 1: 
0.00/0.08	
0.00/0.08	SCC Processor:
0.00/0.08	-> Pairs:
0.00/0.08	 *TOP*_0(f_1(i_1(x))) -> *TOP*_0(x)
0.00/0.08	 *TOP*_0(f_1(i_1(x))) -> x
0.00/0.08	 F_0(f_1(i_1(x))) -> F_1(x)
0.00/0.08	 F_1(h_1(x)) -> F_1(i_1(x))
0.00/0.08	 F_1(i_1(x)) -> x
0.00/0.08	 H_1(x) -> F_1(h_1(x))
0.00/0.08	 I_1(x) -> H_1(x)
0.00/0.08	-> Rules:
0.00/0.08	 *top*_0(f_1(i_1(x))) -> *top*_0(x)
0.00/0.08	 f_0(f_1(i_1(x))) -> f_1(x)
0.00/0.08	 f_1(h_1(x)) -> f_1(i_1(x))
0.00/0.08	 f_1(i_1(x)) -> x
0.00/0.08	 h_1(x) -> f_1(h_1(x))
0.00/0.08	 i_1(x) -> h_1(x)
0.00/0.08	-> Unhiding rules:
0.00/0.08	 h_1(x) -> H_1(x)
0.00/0.08	 i_1(x) -> I_1(x)
0.00/0.08	->Strongly Connected Components:
0.00/0.08	->->Cycle:
0.00/0.08	->->-> Pairs:
0.00/0.08	 F_1(h_1(x)) -> F_1(i_1(x))
0.00/0.08	 F_1(i_1(x)) -> x
0.00/0.08	 H_1(x) -> F_1(h_1(x))
0.00/0.08	 I_1(x) -> H_1(x)
0.00/0.08	->->-> Rules:
0.00/0.08	 *top*_0(f_1(i_1(x))) -> *top*_0(x)
0.00/0.08	 f_0(f_1(i_1(x))) -> f_1(x)
0.00/0.08	 f_1(h_1(x)) -> f_1(i_1(x))
0.00/0.08	 f_1(i_1(x)) -> x
0.00/0.08	 h_1(x) -> f_1(h_1(x))
0.00/0.08	 i_1(x) -> h_1(x)
0.00/0.08	->->-> Unhiding rules:
0.00/0.08	 h_1(x) -> H_1(x)
0.00/0.08	 i_1(x) -> I_1(x)
0.00/0.08	->->Cycle:
0.00/0.08	->->-> Pairs:
0.00/0.08	 *TOP*_0(f_1(i_1(x))) -> *TOP*_0(x)
0.00/0.08	->->-> Rules:
0.00/0.08	 *top*_0(f_1(i_1(x))) -> *top*_0(x)
0.00/0.08	 f_0(f_1(i_1(x))) -> f_1(x)
0.00/0.08	 f_1(h_1(x)) -> f_1(i_1(x))
0.00/0.08	 f_1(i_1(x)) -> x
0.00/0.08	 h_1(x) -> f_1(h_1(x))
0.00/0.08	 i_1(x) -> h_1(x)
0.00/0.08	->->-> Unhiding rules:
0.00/0.08	 Empty
0.00/0.08	
0.00/0.08	
0.00/0.08	The problem is decomposed in 2 subproblems.
0.00/0.08	
0.00/0.08	Problem 1.1: 
0.00/0.08	
0.00/0.08	Reduction Pairs Processor:
0.00/0.08	-> Pairs:
0.00/0.08	 F_1(h_1(x)) -> F_1(i_1(x))
0.00/0.08	 F_1(i_1(x)) -> x
0.00/0.08	 H_1(x) -> F_1(h_1(x))
0.00/0.08	 I_1(x) -> H_1(x)
0.00/0.08	-> Rules:
0.00/0.08	 *top*_0(f_1(i_1(x))) -> *top*_0(x)
0.00/0.08	 f_0(f_1(i_1(x))) -> f_1(x)
0.00/0.08	 f_1(h_1(x)) -> f_1(i_1(x))
0.00/0.08	 f_1(i_1(x)) -> x
0.00/0.08	 h_1(x) -> f_1(h_1(x))
0.00/0.08	 i_1(x) -> h_1(x)
0.00/0.08	-> Unhiding rules:
0.00/0.08	 h_1(x) -> H_1(x)
0.00/0.08	 i_1(x) -> I_1(x)
0.00/0.08	-> Usable rules:
0.00/0.08	 f_1(h_1(x)) -> f_1(i_1(x))
0.00/0.08	 f_1(i_1(x)) -> x
0.00/0.08	 h_1(x) -> f_1(h_1(x))
0.00/0.08	 i_1(x) -> h_1(x)
0.00/0.08	->Interpretation type:
0.00/0.08	 Linear
0.00/0.08	->Coefficients:
0.00/0.08	 Natural Numbers
0.00/0.08	->Dimension:
0.00/0.08	 1
0.00/0.08	->Bound:
0.00/0.08	 2
0.00/0.08	->Interpretation:
0.00/0.08	 
0.00/0.08	[f_1](X) = X
0.00/0.08	[h_1](X) = X + 2
0.00/0.08	[i_1](X) = X + 2
0.00/0.08	[F_1](X) = X
0.00/0.08	[H_1](X) = X + 2
0.00/0.08	[I_1](X) = X + 2
0.00/0.08	
0.00/0.08	Problem 1.1: 
0.00/0.08	
0.00/0.08	SCC Processor:
0.00/0.08	-> Pairs:
0.00/0.08	 F_1(h_1(x)) -> F_1(i_1(x))
0.00/0.08	 H_1(x) -> F_1(h_1(x))
0.00/0.08	 I_1(x) -> H_1(x)
0.00/0.08	-> Rules:
0.00/0.08	 *top*_0(f_1(i_1(x))) -> *top*_0(x)
0.00/0.08	 f_0(f_1(i_1(x))) -> f_1(x)
0.00/0.08	 f_1(h_1(x)) -> f_1(i_1(x))
0.00/0.08	 f_1(i_1(x)) -> x
0.00/0.08	 h_1(x) -> f_1(h_1(x))
0.00/0.08	 i_1(x) -> h_1(x)
0.00/0.08	-> Unhiding rules:
0.00/0.08	 h_1(x) -> H_1(x)
0.00/0.08	 i_1(x) -> I_1(x)
0.00/0.08	->Strongly Connected Components:
0.00/0.08	 There is no strongly connected component
0.00/0.08	
0.00/0.08	The problem is finite.
0.00/0.08	
0.00/0.08	Problem 1.2: 
0.00/0.08	
0.00/0.08	Reduction Pairs Processor:
0.00/0.08	-> Pairs:
0.00/0.08	 *TOP*_0(f_1(i_1(x))) -> *TOP*_0(x)
0.00/0.08	-> Rules:
0.00/0.08	 *top*_0(f_1(i_1(x))) -> *top*_0(x)
0.00/0.08	 f_0(f_1(i_1(x))) -> f_1(x)
0.00/0.08	 f_1(h_1(x)) -> f_1(i_1(x))
0.00/0.08	 f_1(i_1(x)) -> x
0.00/0.08	 h_1(x) -> f_1(h_1(x))
0.00/0.08	 i_1(x) -> h_1(x)
0.00/0.08	-> Unhiding rules:
0.00/0.08	 Empty
0.00/0.08	-> Usable rules:
0.00/0.08	 f_1(h_1(x)) -> f_1(i_1(x))
0.00/0.08	 f_1(i_1(x)) -> x
0.00/0.08	 h_1(x) -> f_1(h_1(x))
0.00/0.08	 i_1(x) -> h_1(x)
0.00/0.08	->Interpretation type:
0.00/0.08	 Linear
0.00/0.08	->Coefficients:
0.00/0.08	 Natural Numbers
0.00/0.08	->Dimension:
0.00/0.08	 1
0.00/0.08	->Bound:
0.00/0.08	 2
0.00/0.08	->Interpretation:
0.00/0.08	 
0.00/0.08	[f_1](X) = X
0.00/0.08	[h_1](X) = 2.X + 2
0.00/0.08	[i_1](X) = 2.X + 2
0.00/0.08	[*TOP*_0](X) = 2.X
0.00/0.08	
0.00/0.08	Problem 1.2: 
0.00/0.08	
0.00/0.08	Basic Processor:
0.00/0.08	-> Pairs:
0.00/0.08	 Empty
0.00/0.08	-> Rules:
0.00/0.08	 *top*_0(f_1(i_1(x))) -> *top*_0(x)
0.00/0.08	 f_0(f_1(i_1(x))) -> f_1(x)
0.00/0.08	 f_1(h_1(x)) -> f_1(i_1(x))
0.00/0.08	 f_1(i_1(x)) -> x
0.00/0.08	 h_1(x) -> f_1(h_1(x))
0.00/0.08	 i_1(x) -> h_1(x)
0.00/0.08	-> Unhiding rules:
0.00/0.08	 Empty
0.00/0.08	-> Result:
0.00/0.08	 Set P is empty
0.00/0.08	
0.00/0.08	The problem is finite.
0.00/0.08	EOF