0.00/0.25	YES
0.00/0.25	
0.00/0.25	Problem 1: 
0.00/0.25	
0.00/0.25	(VAR v_NonEmpty:S x1:S)
0.00/0.25	(RULES
0.00/0.25	a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	)
0.00/0.25	
0.00/0.25	Problem 1: 
0.00/0.25	
0.00/0.25	Dependency Pairs Processor:
0.00/0.25	-> Pairs:
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(a(x1:S)))
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.25	 B(b(a(a(x1:S)))) -> A(a(a(x1:S)))
0.00/0.25	 B(b(a(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(a(a(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.25	-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	
0.00/0.25	Problem 1: 
0.00/0.25	
0.00/0.25	SCC Processor:
0.00/0.25	-> Pairs:
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(a(x1:S)))
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.25	 B(b(a(a(x1:S)))) -> A(a(a(x1:S)))
0.00/0.25	 B(b(a(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(a(a(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.25	-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	->Strongly Connected Components:
0.00/0.25	->->Cycle:
0.00/0.25	->->-> Pairs:
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(a(x1:S)))
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.25	->->-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	->->Cycle:
0.00/0.25	->->-> Pairs:
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(a(a(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.25	->->-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	
0.00/0.25	
0.00/0.25	The problem is decomposed in 2 subproblems.
0.00/0.25	
0.00/0.25	Problem 1.1: 
0.00/0.25	
0.00/0.25	Reduction Pair Processor:
0.00/0.25	-> Pairs:
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(a(x1:S)))
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.25	-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	-> Usable rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	->Interpretation type:
0.00/0.25	 Linear
0.00/0.25	->Coefficients:
0.00/0.25	 Natural Numbers
0.00/0.25	->Dimension:
0.00/0.25	 1
0.00/0.25	->Bound:
0.00/0.25	 2
0.00/0.25	->Interpretation:
0.00/0.25	 
0.00/0.25	[a](X) = 2.X
0.00/0.25	[b](X) = 2.X + 2
0.00/0.25	[A](X) = 2.X
0.00/0.25	
0.00/0.25	Problem 1.1: 
0.00/0.25	
0.00/0.25	SCC Processor:
0.00/0.25	-> Pairs:
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(a(x1:S)))
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.25	-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	->Strongly Connected Components:
0.00/0.25	->->Cycle:
0.00/0.25	->->-> Pairs:
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(a(x1:S)))
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.25	->->-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	
0.00/0.25	Problem 1.1: 
0.00/0.25	
0.00/0.25	Reduction Pair Processor:
0.00/0.25	-> Pairs:
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(a(x1:S)))
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.25	-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	-> Usable rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	->Interpretation type:
0.00/0.25	 Linear
0.00/0.25	->Coefficients:
0.00/0.25	 Natural Numbers
0.00/0.25	->Dimension:
0.00/0.25	 1
0.00/0.25	->Bound:
0.00/0.25	 2
0.00/0.25	->Interpretation:
0.00/0.25	 
0.00/0.25	[a](X) = X + 2
0.00/0.25	[b](X) = 2.X
0.00/0.25	[A](X) = 2.X
0.00/0.25	
0.00/0.25	Problem 1.1: 
0.00/0.25	
0.00/0.25	SCC Processor:
0.00/0.25	-> Pairs:
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.25	-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	->Strongly Connected Components:
0.00/0.25	->->Cycle:
0.00/0.25	->->-> Pairs:
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.25	->->-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	
0.00/0.25	Problem 1.1: 
0.00/0.25	
0.00/0.25	Subterm Processor:
0.00/0.25	-> Pairs:
0.00/0.25	 A(b(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.25	-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	->Projection:
0.00/0.25	 pi(A) = 1
0.00/0.25	
0.00/0.25	Problem 1.1: 
0.00/0.25	
0.00/0.25	SCC Processor:
0.00/0.25	-> Pairs:
0.00/0.25	 Empty
0.00/0.25	-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	->Strongly Connected Components:
0.00/0.25	 There is no strongly connected component
0.00/0.25	
0.00/0.25	The problem is finite.
0.00/0.25	
0.00/0.25	Problem 1.2: 
0.00/0.25	
0.00/0.25	Reduction Pair Processor:
0.00/0.25	-> Pairs:
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(a(a(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.25	-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	-> Usable rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	->Interpretation type:
0.00/0.25	 Linear
0.00/0.25	->Coefficients:
0.00/0.25	 Natural Numbers
0.00/0.25	->Dimension:
0.00/0.25	 1
0.00/0.25	->Bound:
0.00/0.25	 2
0.00/0.25	->Interpretation:
0.00/0.25	 
0.00/0.25	[a](X) = 2.X + 2
0.00/0.25	[b](X) = 2.X + 2
0.00/0.25	[B](X) = 2.X
0.00/0.25	
0.00/0.25	Problem 1.2: 
0.00/0.25	
0.00/0.25	SCC Processor:
0.00/0.25	-> Pairs:
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(a(a(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.25	-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	->Strongly Connected Components:
0.00/0.25	->->Cycle:
0.00/0.25	->->-> Pairs:
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(a(a(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.25	->->-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	
0.00/0.25	Problem 1.2: 
0.00/0.25	
0.00/0.25	Reduction Pair Processor:
0.00/0.25	-> Pairs:
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(a(a(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.25	-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	-> Usable rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	->Interpretation type:
0.00/0.25	 Linear
0.00/0.25	->Coefficients:
0.00/0.25	 Natural Numbers
0.00/0.25	->Dimension:
0.00/0.25	 1
0.00/0.25	->Bound:
0.00/0.25	 2
0.00/0.25	->Interpretation:
0.00/0.25	 
0.00/0.25	[a](X) = 2.X + 2
0.00/0.25	[b](X) = 2.X + 2
0.00/0.25	[B](X) = 2.X
0.00/0.25	
0.00/0.25	Problem 1.2: 
0.00/0.25	
0.00/0.25	SCC Processor:
0.00/0.25	-> Pairs:
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(a(a(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.25	-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	->Strongly Connected Components:
0.00/0.25	->->Cycle:
0.00/0.25	->->-> Pairs:
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(a(a(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.25	->->-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	
0.00/0.25	Problem 1.2: 
0.00/0.25	
0.00/0.25	Reduction Pair Processor:
0.00/0.25	-> Pairs:
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(a(a(x1:S))))
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.25	-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	-> Usable rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	->Interpretation type:
0.00/0.25	 Linear
0.00/0.25	->Coefficients:
0.00/0.25	 Natural Numbers
0.00/0.25	->Dimension:
0.00/0.25	 1
0.00/0.25	->Bound:
0.00/0.25	 2
0.00/0.25	->Interpretation:
0.00/0.25	 
0.00/0.25	[a](X) = 1
0.00/0.25	[b](X) = 2
0.00/0.25	[B](X) = 2.X
0.00/0.25	
0.00/0.25	Problem 1.2: 
0.00/0.25	
0.00/0.25	SCC Processor:
0.00/0.25	-> Pairs:
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.25	-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	->Strongly Connected Components:
0.00/0.25	->->Cycle:
0.00/0.25	->->-> Pairs:
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.25	->->-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	
0.00/0.25	Problem 1.2: 
0.00/0.25	
0.00/0.25	Reduction Pair Processor:
0.00/0.25	-> Pairs:
0.00/0.25	 B(b(a(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.25	-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	-> Usable rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	->Interpretation type:
0.00/0.25	 Linear
0.00/0.25	->Coefficients:
0.00/0.25	 Natural Numbers
0.00/0.25	->Dimension:
0.00/0.25	 1
0.00/0.25	->Bound:
0.00/0.25	 2
0.00/0.25	->Interpretation:
0.00/0.25	 
0.00/0.25	[a](X) = 2
0.00/0.25	[b](X) = 2.X + 2
0.00/0.25	[B](X) = 2.X
0.00/0.25	
0.00/0.25	Problem 1.2: 
0.00/0.25	
0.00/0.25	SCC Processor:
0.00/0.25	-> Pairs:
0.00/0.25	 Empty
0.00/0.25	-> Rules:
0.00/0.25	 a(b(b(a(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.25	 b(b(a(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.25	->Strongly Connected Components:
0.00/0.25	 There is no strongly connected component
0.00/0.25	
0.00/0.25	The problem is finite.
0.00/0.25	EOF