0.00/0.02	YES
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	
0.00/0.02	(VAR v_NonEmpty:S)
0.00/0.02	(RULES
0.00/0.02	a -> c | b ->* c
0.00/0.02	b -> c
0.00/0.02	f(b) -> f(a)
0.00/0.02	)
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	Valid CTRS Processor:
0.00/0.02	-> Rules:
0.00/0.02	 a -> c | b ->* c
0.00/0.02	 b -> c
0.00/0.02	 f(b) -> f(a)
0.00/0.02	-> The system is a deterministic 3-CTRS.
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	
0.00/0.02	Conditional Termination Problem 1:
0.00/0.02	-> Pairs:
0.00/0.02	 F(b) -> A
0.00/0.02	 F(b) -> F(a)
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 a -> c | b ->* c
0.00/0.02	 b -> c
0.00/0.02	 f(b) -> f(a)
0.00/0.02	
0.00/0.02	Conditional Termination Problem 2:
0.00/0.02	-> Pairs:
0.00/0.02	 A -> B
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 a -> c | b ->* c
0.00/0.02	 b -> c
0.00/0.02	 f(b) -> f(a)
0.00/0.02	
0.00/0.02	
0.00/0.02	The problem is decomposed in 2 subproblems.
0.00/0.02	
0.00/0.02	Problem 1.1: 
0.00/0.02	
0.00/0.02	SCC Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 F(b) -> A
0.00/0.02	 F(b) -> F(a)
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 a -> c | b ->* c
0.00/0.02	 b -> c
0.00/0.02	 f(b) -> f(a)
0.00/0.02	->Strongly Connected Components:
0.00/0.02	->->Cycle:
0.00/0.02	->->-> Pairs:
0.00/0.02	 F(b) -> F(a)
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	->->-> Rules:
0.00/0.02	 a -> c | b ->* c
0.00/0.02	 b -> c
0.00/0.02	 f(b) -> f(a)
0.00/0.02	
0.00/0.02	Problem 1.1: 
0.00/0.02	
0.00/0.02	Reduction Triple Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 F(b) -> F(a)
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 a -> c | b ->* c
0.00/0.02	 b -> c
0.00/0.02	 f(b) -> f(a)
0.00/0.02	-> Usable rules:
0.00/0.02	 a -> c | b ->* c
0.00/0.02	 b -> c
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	[a] = 1
0.00/0.02	[b] = 2
0.00/0.02	[f](X) = 0
0.00/0.02	[c] = 0
0.00/0.02	[fSNonEmpty] = 0
0.00/0.02	[A] = 0
0.00/0.02	[B] = 0
0.00/0.02	[F](X) = 2.X
0.00/0.02	
0.00/0.02	Problem 1.1: 
0.00/0.02	
0.00/0.02	SCC Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 Empty
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 a -> c | b ->* c
0.00/0.02	 b -> c
0.00/0.02	 f(b) -> f(a)
0.00/0.02	->Strongly Connected Components:
0.00/0.02	 There is no strongly connected component
0.00/0.02	
0.00/0.02	The problem is finite.
0.00/0.02	
0.00/0.02	Problem 1.2: 
0.00/0.02	
0.00/0.02	SCC Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 A -> B
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 a -> c | b ->* c
0.00/0.02	 b -> c
0.00/0.02	 f(b) -> f(a)
0.00/0.02	->Strongly Connected Components:
0.00/0.02	 There is no strongly connected component
0.00/0.02	
0.00/0.02	The problem is finite.
0.00/0.03	EOF