0.00/0.05	YES
0.00/0.05	
0.00/0.05	Problem 1: 
0.00/0.05	
0.00/0.05	(VAR v_NonEmpty:S x1:S)
0.00/0.05	(RULES
0.00/0.05	a(a(a(a(x1:S)))) -> b(c(x1:S))
0.00/0.05	b(c(x1:S)) -> c(b(x1:S))
0.00/0.05	c(b(x1:S)) -> a(a(a(x1:S)))
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	 A(a(a(a(x1:S)))) -> B(c(x1:S))
0.00/0.05	 A(a(a(a(x1:S)))) -> C(x1:S)
0.00/0.05	 B(c(x1:S)) -> B(x1:S)
0.00/0.05	 B(c(x1:S)) -> C(b(x1:S))
0.00/0.05	 C(b(x1:S)) -> A(a(a(x1:S)))
0.00/0.05	 C(b(x1:S)) -> A(a(x1:S))
0.00/0.05	 C(b(x1:S)) -> A(x1:S)
0.00/0.05	-> Rules:
0.00/0.05	 a(a(a(a(x1:S)))) -> b(c(x1:S))
0.00/0.05	 b(c(x1:S)) -> c(b(x1:S))
0.00/0.05	 c(b(x1:S)) -> a(a(a(x1:S)))
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	 A(a(a(a(x1:S)))) -> B(c(x1:S))
0.00/0.05	 A(a(a(a(x1:S)))) -> C(x1:S)
0.00/0.05	 B(c(x1:S)) -> B(x1:S)
0.00/0.05	 B(c(x1:S)) -> C(b(x1:S))
0.00/0.05	 C(b(x1:S)) -> A(a(a(x1:S)))
0.00/0.05	 C(b(x1:S)) -> A(a(x1:S))
0.00/0.05	 C(b(x1:S)) -> A(x1:S)
0.00/0.05	-> Rules:
0.00/0.05	 a(a(a(a(x1:S)))) -> b(c(x1:S))
0.00/0.05	 b(c(x1:S)) -> c(b(x1:S))
0.00/0.05	 c(b(x1:S)) -> a(a(a(x1:S)))
0.00/0.05	->Strongly Connected Components:
0.00/0.05	->->Cycle:
0.00/0.05	->->-> Pairs:
0.00/0.05	 A(a(a(a(x1:S)))) -> B(c(x1:S))
0.00/0.05	 A(a(a(a(x1:S)))) -> C(x1:S)
0.00/0.05	 B(c(x1:S)) -> B(x1:S)
0.00/0.05	 B(c(x1:S)) -> C(b(x1:S))
0.00/0.05	 C(b(x1:S)) -> A(a(a(x1:S)))
0.00/0.05	 C(b(x1:S)) -> A(a(x1:S))
0.00/0.05	 C(b(x1:S)) -> A(x1:S)
0.00/0.05	->->-> Rules:
0.00/0.05	 a(a(a(a(x1:S)))) -> b(c(x1:S))
0.00/0.05	 b(c(x1:S)) -> c(b(x1:S))
0.00/0.05	 c(b(x1:S)) -> a(a(a(x1:S)))
0.00/0.05	
0.00/0.05	Problem 1: 
0.00/0.05	
0.00/0.05	Reduction Pair Processor:
0.00/0.05	-> Pairs:
0.00/0.05	 A(a(a(a(x1:S)))) -> B(c(x1:S))
0.00/0.05	 A(a(a(a(x1:S)))) -> C(x1:S)
0.00/0.05	 B(c(x1:S)) -> B(x1:S)
0.00/0.05	 B(c(x1:S)) -> C(b(x1:S))
0.00/0.05	 C(b(x1:S)) -> A(a(a(x1:S)))
0.00/0.05	 C(b(x1:S)) -> A(a(x1:S))
0.00/0.05	 C(b(x1:S)) -> A(x1:S)
0.00/0.05	-> Rules:
0.00/0.05	 a(a(a(a(x1:S)))) -> b(c(x1:S))
0.00/0.05	 b(c(x1:S)) -> c(b(x1:S))
0.00/0.05	 c(b(x1:S)) -> a(a(a(x1:S)))
0.00/0.05	-> Usable rules:
0.00/0.05	 a(a(a(a(x1:S)))) -> b(c(x1:S))
0.00/0.05	 b(c(x1:S)) -> c(b(x1:S))
0.00/0.05	 c(b(x1:S)) -> a(a(a(x1:S)))
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	[a](X) = X + 1
0.00/0.05	[b](X) = X + 2
0.00/0.05	[c](X) = X + 2
0.00/0.05	[A](X) = 2.X + 2
0.00/0.05	[B](X) = 2.X + 2
0.00/0.05	[C](X) = 2.X + 2
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	 A(a(a(a(x1:S)))) -> C(x1:S)
0.00/0.05	 B(c(x1:S)) -> B(x1:S)
0.00/0.05	 B(c(x1:S)) -> C(b(x1:S))
0.00/0.05	 C(b(x1:S)) -> A(a(a(x1:S)))
0.00/0.05	 C(b(x1:S)) -> A(a(x1:S))
0.00/0.05	 C(b(x1:S)) -> A(x1:S)
0.00/0.05	-> Rules:
0.00/0.05	 a(a(a(a(x1:S)))) -> b(c(x1:S))
0.00/0.05	 b(c(x1:S)) -> c(b(x1:S))
0.00/0.05	 c(b(x1:S)) -> a(a(a(x1:S)))
0.00/0.05	->Strongly Connected Components:
0.00/0.05	->->Cycle:
0.00/0.05	->->-> Pairs:
0.00/0.05	 A(a(a(a(x1:S)))) -> C(x1:S)
0.00/0.05	 C(b(x1:S)) -> A(a(a(x1:S)))
0.00/0.05	 C(b(x1:S)) -> A(a(x1:S))
0.00/0.05	 C(b(x1:S)) -> A(x1:S)
0.00/0.05	->->-> Rules:
0.00/0.05	 a(a(a(a(x1:S)))) -> b(c(x1:S))
0.00/0.05	 b(c(x1:S)) -> c(b(x1:S))
0.00/0.05	 c(b(x1:S)) -> a(a(a(x1:S)))
0.00/0.05	->->Cycle:
0.00/0.05	->->-> Pairs:
0.00/0.05	 B(c(x1:S)) -> B(x1:S)
0.00/0.05	->->-> Rules:
0.00/0.05	 a(a(a(a(x1:S)))) -> b(c(x1:S))
0.00/0.05	 b(c(x1:S)) -> c(b(x1:S))
0.00/0.05	 c(b(x1:S)) -> a(a(a(x1:S)))
0.00/0.05	
0.00/0.05	
0.00/0.05	The problem is decomposed in 2 subproblems.
0.00/0.05	
0.00/0.05	Problem 1.1: 
0.00/0.05	
0.00/0.05	Reduction Pair Processor:
0.00/0.05	-> Pairs:
0.00/0.05	 A(a(a(a(x1:S)))) -> C(x1:S)
0.00/0.05	 C(b(x1:S)) -> A(a(a(x1:S)))
0.00/0.05	 C(b(x1:S)) -> A(a(x1:S))
0.00/0.05	 C(b(x1:S)) -> A(x1:S)
0.00/0.05	-> Rules:
0.00/0.05	 a(a(a(a(x1:S)))) -> b(c(x1:S))
0.00/0.05	 b(c(x1:S)) -> c(b(x1:S))
0.00/0.05	 c(b(x1:S)) -> a(a(a(x1:S)))
0.00/0.05	-> Usable rules:
0.00/0.05	 a(a(a(a(x1:S)))) -> b(c(x1:S))
0.00/0.05	 b(c(x1:S)) -> c(b(x1:S))
0.00/0.05	 c(b(x1:S)) -> a(a(a(x1:S)))
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	[a](X) = X + 1
0.00/0.05	[b](X) = X + 2
0.00/0.05	[c](X) = X + 2
0.00/0.05	[A](X) = 2.X + 2
0.00/0.05	[C](X) = 2.X + 2
0.00/0.05	
0.00/0.05	Problem 1.1: 
0.00/0.05	
0.00/0.05	SCC Processor:
0.00/0.05	-> Pairs:
0.00/0.05	 C(b(x1:S)) -> A(a(a(x1:S)))
0.00/0.05	 C(b(x1:S)) -> A(a(x1:S))
0.00/0.05	 C(b(x1:S)) -> A(x1:S)
0.00/0.05	-> Rules:
0.00/0.05	 a(a(a(a(x1:S)))) -> b(c(x1:S))
0.00/0.05	 b(c(x1:S)) -> c(b(x1:S))
0.00/0.05	 c(b(x1:S)) -> a(a(a(x1:S)))
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	
0.00/0.05	Problem 1.2: 
0.00/0.05	
0.00/0.05	Subterm Processor:
0.00/0.05	-> Pairs:
0.00/0.05	 B(c(x1:S)) -> B(x1:S)
0.00/0.05	-> Rules:
0.00/0.05	 a(a(a(a(x1:S)))) -> b(c(x1:S))
0.00/0.05	 b(c(x1:S)) -> c(b(x1:S))
0.00/0.05	 c(b(x1:S)) -> a(a(a(x1:S)))
0.00/0.05	->Projection:
0.00/0.05	 pi(B) = 1
0.00/0.05	
0.00/0.05	Problem 1.2: 
0.00/0.05	
0.00/0.05	SCC Processor:
0.00/0.05	-> Pairs:
0.00/0.05	 Empty
0.00/0.05	-> Rules:
0.00/0.05	 a(a(a(a(x1:S)))) -> b(c(x1:S))
0.00/0.05	 b(c(x1:S)) -> c(b(x1:S))
0.00/0.05	 c(b(x1:S)) -> a(a(a(x1:S)))
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