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 x1:S)
0.00/0.11	(RULES
0.00/0.11	a(b(x1:S)) -> x1:S
0.00/0.11	a(c(x1:S)) -> b(c(c(a(a(b(x1:S))))))
0.00/0.11	b(c(x1:S)) -> x1:S
0.00/0.11	)
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	 A(c(x1:S)) -> A(a(b(x1:S)))
0.00/0.11	 A(c(x1:S)) -> A(b(x1:S))
0.00/0.11	 A(c(x1:S)) -> B(c(c(a(a(b(x1:S))))))
0.00/0.11	 A(c(x1:S)) -> B(x1:S)
0.00/0.11	-> Rules:
0.00/0.11	 a(b(x1:S)) -> x1:S
0.00/0.11	 a(c(x1:S)) -> b(c(c(a(a(b(x1:S))))))
0.00/0.11	 b(c(x1:S)) -> x1: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	 A(c(x1:S)) -> A(a(b(x1:S)))
0.00/0.11	 A(c(x1:S)) -> A(b(x1:S))
0.00/0.11	 A(c(x1:S)) -> B(c(c(a(a(b(x1:S))))))
0.00/0.11	 A(c(x1:S)) -> B(x1:S)
0.00/0.11	-> Rules:
0.00/0.11	 a(b(x1:S)) -> x1:S
0.00/0.11	 a(c(x1:S)) -> b(c(c(a(a(b(x1:S))))))
0.00/0.11	 b(c(x1:S)) -> x1:S
0.00/0.11	->Strongly Connected Components:
0.00/0.11	->->Cycle:
0.00/0.11	->->-> Pairs:
0.00/0.11	 A(c(x1:S)) -> A(a(b(x1:S)))
0.00/0.11	 A(c(x1:S)) -> A(b(x1:S))
0.00/0.11	->->-> Rules:
0.00/0.11	 a(b(x1:S)) -> x1:S
0.00/0.11	 a(c(x1:S)) -> b(c(c(a(a(b(x1:S))))))
0.00/0.11	 b(c(x1:S)) -> x1:S
0.00/0.11	
0.00/0.11	Problem 1: 
0.00/0.11	
0.00/0.11	Reduction Pair Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 A(c(x1:S)) -> A(a(b(x1:S)))
0.00/0.11	 A(c(x1:S)) -> A(b(x1:S))
0.00/0.11	-> Rules:
0.00/0.11	 a(b(x1:S)) -> x1:S
0.00/0.11	 a(c(x1:S)) -> b(c(c(a(a(b(x1:S))))))
0.00/0.11	 b(c(x1:S)) -> x1:S
0.00/0.11	-> Usable rules:
0.00/0.11	 a(b(x1:S)) -> x1:S
0.00/0.11	 a(c(x1:S)) -> b(c(c(a(a(b(x1:S))))))
0.00/0.11	 b(c(x1:S)) -> x1: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	[a](X) = 2.X
0.00/0.11	[b](X) = 1/2.X
0.00/0.11	[c](X) = 2.X + 1
0.00/0.11	[A](X) = 2.X
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	 A(c(x1:S)) -> A(b(x1:S))
0.00/0.11	-> Rules:
0.00/0.11	 a(b(x1:S)) -> x1:S
0.00/0.11	 a(c(x1:S)) -> b(c(c(a(a(b(x1:S))))))
0.00/0.11	 b(c(x1:S)) -> x1:S
0.00/0.11	->Strongly Connected Components:
0.00/0.11	->->Cycle:
0.00/0.11	->->-> Pairs:
0.00/0.11	 A(c(x1:S)) -> A(b(x1:S))
0.00/0.11	->->-> Rules:
0.00/0.11	 a(b(x1:S)) -> x1:S
0.00/0.11	 a(c(x1:S)) -> b(c(c(a(a(b(x1:S))))))
0.00/0.11	 b(c(x1:S)) -> x1:S
0.00/0.11	
0.00/0.11	Problem 1: 
0.00/0.11	
0.00/0.11	Reduction Pair Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 A(c(x1:S)) -> A(b(x1:S))
0.00/0.11	-> Rules:
0.00/0.11	 a(b(x1:S)) -> x1:S
0.00/0.11	 a(c(x1:S)) -> b(c(c(a(a(b(x1:S))))))
0.00/0.11	 b(c(x1:S)) -> x1:S
0.00/0.11	-> Usable rules:
0.00/0.11	 b(c(x1:S)) -> x1:S
0.00/0.11	->Interpretation type:
0.00/0.11	 Linear
0.00/0.11	->Coefficients:
0.00/0.11	 Natural Numbers
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	[b](X) = 2.X + 1
0.00/0.11	[c](X) = 2.X + 2
0.00/0.11	[A](X) = 2.X
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	 Empty
0.00/0.11	-> Rules:
0.00/0.11	 a(b(x1:S)) -> x1:S
0.00/0.11	 a(c(x1:S)) -> b(c(c(a(a(b(x1:S))))))
0.00/0.11	 b(c(x1:S)) -> x1: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