95.37/95.75	YES
95.37/95.75	
95.37/95.75	Problem 1: 
95.37/95.75	
95.37/95.75	(VAR v_NonEmpty:S x1:S)
95.37/95.75	(RULES
95.37/95.75	a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	)
95.37/95.75	
95.37/95.75	Problem 1: 
95.37/95.75	
95.37/95.75	Dependency Pairs Processor:
95.37/95.75	-> Pairs:
95.37/95.75	 A(a(x1:S)) -> A(b(b(b(x1:S))))
95.37/95.75	 A(a(x1:S)) -> B(b(b(x1:S)))
95.37/95.75	 A(a(x1:S)) -> B(b(x1:S))
95.37/95.75	 A(a(x1:S)) -> B(x1:S)
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(a(b(x1:S))))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(b(x1:S)))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(b(x1:S))
95.37/95.75	 A(b(b(c(x1:S)))) -> B(x1:S)
95.37/95.75	-> Rules:
95.37/95.75	 a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	 a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	
95.37/95.75	Problem 1: 
95.37/95.75	
95.37/95.75	SCC Processor:
95.37/95.75	-> Pairs:
95.37/95.75	 A(a(x1:S)) -> A(b(b(b(x1:S))))
95.37/95.75	 A(a(x1:S)) -> B(b(b(x1:S)))
95.37/95.75	 A(a(x1:S)) -> B(b(x1:S))
95.37/95.75	 A(a(x1:S)) -> B(x1:S)
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(a(b(x1:S))))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(b(x1:S)))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(b(x1:S))
95.37/95.75	 A(b(b(c(x1:S)))) -> B(x1:S)
95.37/95.75	-> Rules:
95.37/95.75	 a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	 a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	->Strongly Connected Components:
95.37/95.75	->->Cycle:
95.37/95.75	->->-> Pairs:
95.37/95.75	 A(a(x1:S)) -> A(b(b(b(x1:S))))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(a(b(x1:S))))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(b(x1:S)))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(b(x1:S))
95.37/95.75	->->-> Rules:
95.37/95.75	 a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	 a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	
95.37/95.75	Problem 1: 
95.37/95.75	
95.37/95.75	Narrowing Processor:
95.37/95.75	-> Pairs:
95.37/95.75	 A(a(x1:S)) -> A(b(b(b(x1:S))))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(a(b(x1:S))))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(b(x1:S)))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(b(x1:S))
95.37/95.75	-> Rules:
95.37/95.75	 a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	 a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	->Narrowed Pairs:
95.37/95.75	->->Original Pair:
95.37/95.75	 A(a(x1:S)) -> A(b(b(b(x1:S))))
95.37/95.75	->-> Narrowed pairs:
95.37/95.75	 A(a(a(x1:S))) -> A(b(b(b(b(c(x1:S))))))
95.37/95.75	
95.37/95.75	Problem 1: 
95.37/95.75	
95.37/95.75	SCC Processor:
95.37/95.75	-> Pairs:
95.37/95.75	 A(a(a(x1:S))) -> A(b(b(b(b(c(x1:S))))))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(a(b(x1:S))))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(b(x1:S)))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(b(x1:S))
95.37/95.75	-> Rules:
95.37/95.75	 a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	 a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	->Strongly Connected Components:
95.37/95.75	->->Cycle:
95.37/95.75	->->-> Pairs:
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(a(b(x1:S))))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(b(x1:S)))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(b(x1:S))
95.37/95.75	->->-> Rules:
95.37/95.75	 a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	 a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	
95.37/95.75	Problem 1: 
95.37/95.75	
95.37/95.75	Reduction Pair Processor:
95.37/95.75	-> Pairs:
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(a(b(x1:S))))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(b(x1:S)))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(b(x1:S))
95.37/95.75	-> Rules:
95.37/95.75	 a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	 a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	-> Usable rules:
95.37/95.75	 a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	 a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	->Interpretation type:
95.37/95.75	 Linear
95.37/95.75	->Coefficients:
95.37/95.75	 Natural Numbers
95.37/95.75	->Dimension:
95.37/95.75	 1
95.37/95.75	->Bound:
95.37/95.75	 2
95.37/95.75	->Interpretation:
95.37/95.75	 
95.37/95.75	[a](X) = 1
95.37/95.75	[b](X) = 2
95.37/95.75	[c](X) = 0
95.37/95.75	[A](X) = X
95.37/95.75	
95.37/95.75	Problem 1: 
95.37/95.75	
95.37/95.75	SCC Processor:
95.37/95.75	-> Pairs:
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(b(x1:S)))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(b(x1:S))
95.37/95.75	-> Rules:
95.37/95.75	 a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	 a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	->Strongly Connected Components:
95.37/95.75	->->Cycle:
95.37/95.75	->->-> Pairs:
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(b(x1:S)))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(b(x1:S))
95.37/95.75	->->-> Rules:
95.37/95.75	 a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	 a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	
95.37/95.75	Problem 1: 
95.37/95.75	
95.37/95.75	Reduction Pair Processor:
95.37/95.75	-> Pairs:
95.37/95.75	 A(b(b(c(x1:S)))) -> A(a(b(x1:S)))
95.37/95.75	 A(b(b(c(x1:S)))) -> A(b(x1:S))
95.37/95.75	-> Rules:
95.37/95.75	 a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	 a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	-> Usable rules:
95.37/95.75	 a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	 a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	->Interpretation type:
95.37/95.75	 Linear
95.37/95.75	->Coefficients:
95.37/95.75	 Natural Numbers
95.37/95.75	->Dimension:
95.37/95.75	 1
95.37/95.75	->Bound:
95.37/95.75	 2
95.37/95.75	->Interpretation:
95.37/95.75	 
95.37/95.75	[a](X) = 1
95.37/95.75	[b](X) = 2
95.37/95.75	[c](X) = 0
95.37/95.75	[A](X) = X
95.37/95.75	
95.37/95.75	Problem 1: 
95.37/95.75	
95.37/95.75	SCC Processor:
95.37/95.75	-> Pairs:
95.37/95.75	 A(b(b(c(x1:S)))) -> A(b(x1:S))
95.37/95.75	-> Rules:
95.37/95.75	 a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	 a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	->Strongly Connected Components:
95.37/95.75	->->Cycle:
95.37/95.75	->->-> Pairs:
95.37/95.75	 A(b(b(c(x1:S)))) -> A(b(x1:S))
95.37/95.75	->->-> Rules:
95.37/95.75	 a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	 a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	
95.37/95.75	Problem 1: 
95.37/95.75	
95.37/95.75	Reduction Pair Processor:
95.37/95.75	-> Pairs:
95.37/95.75	 A(b(b(c(x1:S)))) -> A(b(x1:S))
95.37/95.75	-> Rules:
95.37/95.75	 a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	 a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	-> Usable rules:
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	->Interpretation type:
95.37/95.75	 Linear
95.37/95.75	->Coefficients:
95.37/95.75	 Natural Numbers
95.37/95.75	->Dimension:
95.37/95.75	 1
95.37/95.75	->Bound:
95.37/95.75	 2
95.37/95.75	->Interpretation:
95.37/95.75	 
95.37/95.75	[a](X) = 2.X + 2
95.37/95.75	[b](X) = X + 1
95.37/95.75	[c](X) = 2.X + 1
95.37/95.75	[A](X) = 2.X
95.37/95.75	
95.37/95.75	Problem 1: 
95.37/95.75	
95.37/95.75	SCC Processor:
95.37/95.75	-> Pairs:
95.37/95.75	 Empty
95.37/95.75	-> Rules:
95.37/95.75	 a(a(x1:S)) -> a(b(b(b(x1:S))))
95.37/95.75	 a(b(b(c(x1:S)))) -> a(a(a(b(x1:S))))
95.37/95.75	 b(a(x1:S)) -> b(b(c(x1:S)))
95.37/95.75	->Strongly Connected Components:
95.37/95.75	 There is no strongly connected component
95.37/95.75	
95.37/95.75	The problem is finite.
95.37/95.75	EOF