0.64/0.75	YES
0.64/0.75	
0.64/0.75	Problem 1: 
0.64/0.75	
0.64/0.75	(VAR v_NonEmpty:S x1:S)
0.64/0.75	(RULES
0.64/0.75	a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	)
0.64/0.75	
0.64/0.75	Problem 1: 
0.64/0.75	
0.64/0.75	Dependency Pairs Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 A(b(x1:S)) -> A(x1:S)
0.64/0.75	 A(b(x1:S)) -> B(c(a(x1:S)))
0.64/0.75	 B(a(x1:S)) -> A(c(b(x1:S)))
0.64/0.75	 B(a(x1:S)) -> B(x1:S)
0.64/0.75	 B(c(x1:S)) -> B(b(x1:S))
0.64/0.75	 B(c(x1:S)) -> B(x1:S)
0.64/0.75	-> Rules:
0.64/0.75	 a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	 b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	 b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	
0.64/0.75	Problem 1: 
0.64/0.75	
0.64/0.75	SCC Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 A(b(x1:S)) -> A(x1:S)
0.64/0.75	 A(b(x1:S)) -> B(c(a(x1:S)))
0.64/0.75	 B(a(x1:S)) -> A(c(b(x1:S)))
0.64/0.75	 B(a(x1:S)) -> B(x1:S)
0.64/0.75	 B(c(x1:S)) -> B(b(x1:S))
0.64/0.75	 B(c(x1:S)) -> B(x1:S)
0.64/0.75	-> Rules:
0.64/0.75	 a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	 b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	 b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	->Strongly Connected Components:
0.64/0.75	->->Cycle:
0.64/0.75	->->-> Pairs:
0.64/0.75	 B(a(x1:S)) -> B(x1:S)
0.64/0.75	 B(c(x1:S)) -> B(b(x1:S))
0.64/0.75	 B(c(x1:S)) -> B(x1:S)
0.64/0.75	->->-> Rules:
0.64/0.75	 a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	 b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	 b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	->->Cycle:
0.64/0.75	->->-> Pairs:
0.64/0.75	 A(b(x1:S)) -> A(x1:S)
0.64/0.75	->->-> Rules:
0.64/0.75	 a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	 b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	 b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	
0.64/0.75	
0.64/0.75	The problem is decomposed in 2 subproblems.
0.64/0.75	
0.64/0.75	Problem 1.1: 
0.64/0.75	
0.64/0.75	Reduction Pair Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 B(a(x1:S)) -> B(x1:S)
0.64/0.75	 B(c(x1:S)) -> B(b(x1:S))
0.64/0.75	 B(c(x1:S)) -> B(x1:S)
0.64/0.75	-> Rules:
0.64/0.75	 a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	 b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	 b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	-> Usable rules:
0.64/0.75	 a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	 b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	 b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	->Interpretation type:
0.64/0.75	 Linear
0.64/0.75	->Coefficients:
0.64/0.75	 Natural Numbers
0.64/0.75	->Dimension:
0.64/0.75	 1
0.64/0.75	->Bound:
0.64/0.75	 2
0.64/0.75	->Interpretation:
0.64/0.75	 
0.64/0.75	[a](X) = 2.X + 1
0.64/0.75	[b](X) = X
0.64/0.75	[c](X) = X
0.64/0.75	[B](X) = 2.X
0.64/0.75	
0.64/0.75	Problem 1.1: 
0.64/0.75	
0.64/0.75	SCC Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 B(c(x1:S)) -> B(b(x1:S))
0.64/0.75	 B(c(x1:S)) -> B(x1:S)
0.64/0.75	-> Rules:
0.64/0.75	 a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	 b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	 b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	->Strongly Connected Components:
0.64/0.75	->->Cycle:
0.64/0.75	->->-> Pairs:
0.64/0.75	 B(c(x1:S)) -> B(b(x1:S))
0.64/0.75	 B(c(x1:S)) -> B(x1:S)
0.64/0.75	->->-> Rules:
0.64/0.75	 a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	 b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	 b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	
0.64/0.75	Problem 1.1: 
0.64/0.75	
0.64/0.75	Reduction Pair Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 B(c(x1:S)) -> B(b(x1:S))
0.64/0.75	 B(c(x1:S)) -> B(x1:S)
0.64/0.75	-> Rules:
0.64/0.75	 a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	 b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	 b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	-> Usable rules:
0.64/0.75	 a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	 b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	 b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	->Interpretation type:
0.64/0.75	 Linear
0.64/0.75	->Coefficients:
0.64/0.75	 Natural Numbers
0.64/0.75	->Dimension:
0.64/0.75	 2
0.64/0.75	->Bound:
0.64/0.75	 1
0.64/0.75	->Interpretation:
0.64/0.75	 
0.64/0.75	[a](X) = [1 1;1 0].X + [1;0]
0.64/0.75	[b](X) = [1 1;0 1].X + [1;0]
0.64/0.75	[c](X) = [0 0;0 1].X + [0;1]
0.64/0.75	[B](X) = [0 1;0 1].X
0.64/0.75	
0.64/0.75	Problem 1.1: 
0.64/0.75	
0.64/0.75	SCC Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 B(c(x1:S)) -> B(x1:S)
0.64/0.75	-> Rules:
0.64/0.75	 a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	 b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	 b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	->Strongly Connected Components:
0.64/0.75	->->Cycle:
0.64/0.75	->->-> Pairs:
0.64/0.75	 B(c(x1:S)) -> B(x1:S)
0.64/0.75	->->-> Rules:
0.64/0.75	 a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	 b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	 b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	
0.64/0.75	Problem 1.1: 
0.64/0.75	
0.64/0.75	Subterm Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 B(c(x1:S)) -> B(x1:S)
0.64/0.75	-> Rules:
0.64/0.75	 a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	 b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	 b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	->Projection:
0.64/0.75	 pi(B) = 1
0.64/0.75	
0.64/0.75	Problem 1.1: 
0.64/0.75	
0.64/0.75	SCC Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 Empty
0.64/0.75	-> Rules:
0.64/0.75	 a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	 b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	 b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	->Strongly Connected Components:
0.64/0.75	 There is no strongly connected component
0.64/0.75	
0.64/0.75	The problem is finite.
0.64/0.75	
0.64/0.75	Problem 1.2: 
0.64/0.75	
0.64/0.75	Subterm Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 A(b(x1:S)) -> A(x1:S)
0.64/0.75	-> Rules:
0.64/0.75	 a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	 b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	 b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	->Projection:
0.64/0.75	 pi(A) = 1
0.64/0.75	
0.64/0.75	Problem 1.2: 
0.64/0.75	
0.64/0.75	SCC Processor:
0.64/0.75	-> Pairs:
0.64/0.75	 Empty
0.64/0.75	-> Rules:
0.64/0.75	 a(b(x1:S)) -> b(c(a(x1:S)))
0.64/0.75	 b(a(x1:S)) -> a(c(b(x1:S)))
0.64/0.75	 b(c(x1:S)) -> c(b(b(x1:S)))
0.64/0.75	->Strongly Connected Components:
0.64/0.75	 There is no strongly connected component
0.64/0.75	
0.64/0.75	The problem is finite.
0.64/0.76	EOF