0.00/0.11	YES
0.00/0.11	
0.00/0.11	Problem 1: 
0.00/0.11	
0.00/0.11	(VAR v_NonEmpty:S x:S)
0.00/0.11	(RULES
0.00/0.11	bits(0) -> 0
0.00/0.11	bits(s(x:S)) -> s(bits(half(s(x:S))))
0.00/0.11	half(0) -> 0
0.00/0.11	half(s(0)) -> 0
0.00/0.11	half(s(s(x:S))) -> s(half(x:S))
0.00/0.11	) 
0.00/0.11	(STRATEGY INNERMOST)
0.00/0.11	
0.00/0.11	Problem 1: 
0.00/0.11	
0.00/0.11	Dependency Pairs Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 BITS(s(x:S)) -> BITS(half(s(x:S)))
0.00/0.11	 BITS(s(x:S)) -> HALF(s(x:S))
0.00/0.11	 HALF(s(s(x:S))) -> HALF(x:S)
0.00/0.11	-> Rules:
0.00/0.11	 bits(0) -> 0
0.00/0.11	 bits(s(x:S)) -> s(bits(half(s(x:S))))
0.00/0.11	 half(0) -> 0
0.00/0.11	 half(s(0)) -> 0
0.00/0.11	 half(s(s(x:S))) -> s(half(x:S))
0.00/0.11	
0.00/0.11	Problem 1: 
0.00/0.11	
0.00/0.11	SCC Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 BITS(s(x:S)) -> BITS(half(s(x:S)))
0.00/0.11	 BITS(s(x:S)) -> HALF(s(x:S))
0.00/0.11	 HALF(s(s(x:S))) -> HALF(x:S)
0.00/0.11	-> Rules:
0.00/0.11	 bits(0) -> 0
0.00/0.11	 bits(s(x:S)) -> s(bits(half(s(x:S))))
0.00/0.11	 half(0) -> 0
0.00/0.11	 half(s(0)) -> 0
0.00/0.11	 half(s(s(x:S))) -> s(half(x:S))
0.00/0.11	->Strongly Connected Components:
0.00/0.11	->->Cycle:
0.00/0.11	->->-> Pairs:
0.00/0.11	 HALF(s(s(x:S))) -> HALF(x:S)
0.00/0.11	->->-> Rules:
0.00/0.11	 bits(0) -> 0
0.00/0.11	 bits(s(x:S)) -> s(bits(half(s(x:S))))
0.00/0.11	 half(0) -> 0
0.00/0.11	 half(s(0)) -> 0
0.00/0.11	 half(s(s(x:S))) -> s(half(x:S))
0.00/0.11	->->Cycle:
0.00/0.11	->->-> Pairs:
0.00/0.11	 BITS(s(x:S)) -> BITS(half(s(x:S)))
0.00/0.11	->->-> Rules:
0.00/0.11	 bits(0) -> 0
0.00/0.11	 bits(s(x:S)) -> s(bits(half(s(x:S))))
0.00/0.11	 half(0) -> 0
0.00/0.11	 half(s(0)) -> 0
0.00/0.11	 half(s(s(x:S))) -> s(half(x:S))
0.00/0.11	
0.00/0.11	
0.00/0.11	The problem is decomposed in 2 subproblems.
0.00/0.11	
0.00/0.11	Problem 1.1: 
0.00/0.11	
0.00/0.11	Subterm Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 HALF(s(s(x:S))) -> HALF(x:S)
0.00/0.11	-> Rules:
0.00/0.11	 bits(0) -> 0
0.00/0.11	 bits(s(x:S)) -> s(bits(half(s(x:S))))
0.00/0.11	 half(0) -> 0
0.00/0.11	 half(s(0)) -> 0
0.00/0.11	 half(s(s(x:S))) -> s(half(x:S))
0.00/0.11	->Projection:
0.00/0.11	 pi(HALF) = 1
0.00/0.11	
0.00/0.11	Problem 1.1: 
0.00/0.11	
0.00/0.11	SCC Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 Empty
0.00/0.11	-> Rules:
0.00/0.11	 bits(0) -> 0
0.00/0.11	 bits(s(x:S)) -> s(bits(half(s(x:S))))
0.00/0.11	 half(0) -> 0
0.00/0.11	 half(s(0)) -> 0
0.00/0.11	 half(s(s(x:S))) -> s(half(x:S))
0.00/0.11	->Strongly Connected Components:
0.00/0.11	 There is no strongly connected component
0.00/0.11	
0.00/0.11	The problem is finite.
0.00/0.11	
0.00/0.11	Problem 1.2: 
0.00/0.11	
0.00/0.11	Reduction Pairs Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 BITS(s(x:S)) -> BITS(half(s(x:S)))
0.00/0.11	-> Rules:
0.00/0.11	 bits(0) -> 0
0.00/0.11	 bits(s(x:S)) -> s(bits(half(s(x:S))))
0.00/0.11	 half(0) -> 0
0.00/0.11	 half(s(0)) -> 0
0.00/0.11	 half(s(s(x:S))) -> s(half(x:S))
0.00/0.11	-> Usable rules:
0.00/0.11	 half(0) -> 0
0.00/0.11	 half(s(0)) -> 0
0.00/0.11	 half(s(s(x:S))) -> s(half(x:S))
0.00/0.11	->Interpretation type:
0.00/0.11	 Linear
0.00/0.11	->Coefficients:
0.00/0.11	 All rationals
0.00/0.11	->Dimension:
0.00/0.11	 1
0.00/0.11	->Bound:
0.00/0.11	 2
0.00/0.11	->Interpretation:
0.00/0.11	 
0.00/0.11	[bits](X) = 0
0.00/0.11	[half](X) = 1/2.X
0.00/0.11	[0] = 0
0.00/0.11	[fSNonEmpty] = 0
0.00/0.11	[s](X) = X + 1/2
0.00/0.11	[BITS](X) = X
0.00/0.11	[HALF](X) = 0
0.00/0.11	
0.00/0.11	Problem 1.2: 
0.00/0.11	
0.00/0.11	SCC Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 Empty
0.00/0.11	-> Rules:
0.00/0.11	 bits(0) -> 0
0.00/0.11	 bits(s(x:S)) -> s(bits(half(s(x:S))))
0.00/0.11	 half(0) -> 0
0.00/0.11	 half(s(0)) -> 0
0.00/0.11	 half(s(s(x:S))) -> s(half(x:S))
0.00/0.11	->Strongly Connected Components:
0.00/0.11	 There is no strongly connected component
0.00/0.11	
0.00/0.11	The problem is finite.
0.00/0.11	EOF