0.00/0.14	YES
0.00/0.14	
0.00/0.14	Problem 1: 
0.00/0.14	
0.00/0.14	(VAR v_NonEmpty:S x1:S)
0.00/0.14	(RULES
0.00/0.14	a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	)
0.00/0.14	
0.00/0.14	Problem 1: 
0.00/0.14	
0.00/0.14	Dependency Pairs Processor:
0.00/0.14	-> Pairs:
0.00/0.14	 A(a(b(b(x1:S)))) -> A(b(b(a(x1:S))))
0.00/0.14	 A(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.14	 A(b(a(b(x1:S)))) -> A(a(b(a(x1:S))))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.14	-> Rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	
0.00/0.14	Problem 1: 
0.00/0.14	
0.00/0.14	SCC Processor:
0.00/0.14	-> Pairs:
0.00/0.14	 A(a(b(b(x1:S)))) -> A(b(b(a(x1:S))))
0.00/0.14	 A(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.14	 A(b(a(b(x1:S)))) -> A(a(b(a(x1:S))))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.14	-> Rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	->Strongly Connected Components:
0.00/0.14	->->Cycle:
0.00/0.14	->->-> Pairs:
0.00/0.14	 A(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.14	 A(b(a(b(x1:S)))) -> A(a(b(a(x1:S))))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.14	->->-> Rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	
0.00/0.14	Problem 1: 
0.00/0.14	
0.00/0.14	Reduction Pair Processor:
0.00/0.14	-> Pairs:
0.00/0.14	 A(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.14	 A(b(a(b(x1:S)))) -> A(a(b(a(x1:S))))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.14	-> Rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	-> Usable rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	->Interpretation type:
0.00/0.14	 Linear
0.00/0.14	->Coefficients:
0.00/0.14	 Natural Numbers
0.00/0.14	->Dimension:
0.00/0.14	 1
0.00/0.14	->Bound:
0.00/0.14	 2
0.00/0.14	->Interpretation:
0.00/0.14	 
0.00/0.14	[a](X) = 2.X + 1
0.00/0.14	[b](X) = 2.X + 1
0.00/0.14	[A](X) = 2.X
0.00/0.14	
0.00/0.14	Problem 1: 
0.00/0.14	
0.00/0.14	SCC Processor:
0.00/0.14	-> Pairs:
0.00/0.14	 A(b(a(b(x1:S)))) -> A(a(b(a(x1:S))))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.14	-> Rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	->Strongly Connected Components:
0.00/0.14	->->Cycle:
0.00/0.14	->->-> Pairs:
0.00/0.14	 A(b(a(b(x1:S)))) -> A(a(b(a(x1:S))))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.14	->->-> Rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	
0.00/0.14	Problem 1: 
0.00/0.14	
0.00/0.14	Reduction Pair Processor:
0.00/0.14	-> Pairs:
0.00/0.14	 A(b(a(b(x1:S)))) -> A(a(b(a(x1:S))))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.14	-> Rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	-> Usable rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	->Interpretation type:
0.00/0.14	 Linear
0.00/0.14	->Coefficients:
0.00/0.14	 Natural Numbers
0.00/0.14	->Dimension:
0.00/0.14	 1
0.00/0.14	->Bound:
0.00/0.14	 2
0.00/0.14	->Interpretation:
0.00/0.14	 
0.00/0.14	[a](X) = 2.X + 2
0.00/0.14	[b](X) = 2.X + 2
0.00/0.14	[A](X) = 2.X
0.00/0.14	
0.00/0.14	Problem 1: 
0.00/0.14	
0.00/0.14	SCC Processor:
0.00/0.14	-> Pairs:
0.00/0.14	 A(b(a(b(x1:S)))) -> A(a(b(a(x1:S))))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.14	-> Rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	->Strongly Connected Components:
0.00/0.14	->->Cycle:
0.00/0.14	->->-> Pairs:
0.00/0.14	 A(b(a(b(x1:S)))) -> A(a(b(a(x1:S))))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.14	->->-> Rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	
0.00/0.14	Problem 1: 
0.00/0.14	
0.00/0.14	Reduction Pair Processor:
0.00/0.14	-> Pairs:
0.00/0.14	 A(b(a(b(x1:S)))) -> A(a(b(a(x1:S))))
0.00/0.14	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.14	-> Rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	-> Usable rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	->Interpretation type:
0.00/0.14	 Linear
0.00/0.14	->Coefficients:
0.00/0.14	 Natural Numbers
0.00/0.14	->Dimension:
0.00/0.14	 1
0.00/0.14	->Bound:
0.00/0.14	 2
0.00/0.14	->Interpretation:
0.00/0.14	 
0.00/0.14	[a](X) = 2.X + 2
0.00/0.14	[b](X) = 2.X + 2
0.00/0.14	[A](X) = 2.X
0.00/0.14	
0.00/0.14	Problem 1: 
0.00/0.14	
0.00/0.14	SCC Processor:
0.00/0.14	-> Pairs:
0.00/0.14	 A(b(a(b(x1:S)))) -> A(a(b(a(x1:S))))
0.00/0.14	-> Rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	->Strongly Connected Components:
0.00/0.14	->->Cycle:
0.00/0.14	->->-> Pairs:
0.00/0.14	 A(b(a(b(x1:S)))) -> A(a(b(a(x1:S))))
0.00/0.14	->->-> Rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	
0.00/0.14	Problem 1: 
0.00/0.14	
0.00/0.14	Reduction Pair Processor:
0.00/0.14	-> Pairs:
0.00/0.14	 A(b(a(b(x1:S)))) -> A(a(b(a(x1:S))))
0.00/0.14	-> Rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	-> Usable rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	->Interpretation type:
0.00/0.14	 Linear
0.00/0.14	->Coefficients:
0.00/0.14	 Natural Numbers
0.00/0.14	->Dimension:
0.00/0.14	 1
0.00/0.14	->Bound:
0.00/0.14	 2
0.00/0.14	->Interpretation:
0.00/0.14	 
0.00/0.14	[a](X) = 0
0.00/0.14	[b](X) = 2
0.00/0.14	[A](X) = 2.X
0.00/0.14	
0.00/0.14	Problem 1: 
0.00/0.14	
0.00/0.14	SCC Processor:
0.00/0.14	-> Pairs:
0.00/0.14	 Empty
0.00/0.14	-> Rules:
0.00/0.14	 a(a(a(b(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.14	 a(a(b(b(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.14	 a(b(a(b(x1:S)))) -> a(a(b(a(x1:S))))
0.00/0.14	->Strongly Connected Components:
0.00/0.14	 There is no strongly connected component
0.00/0.14	
0.00/0.14	The problem is finite.
0.00/0.14	EOF