0.00/0.41	YES
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	(VAR v_NonEmpty:S x1:S)
0.00/0.41	(RULES
0.00/0.41	a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	)
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	Dependency Pairs Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(x1:S))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.41	 A(a(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(x1:S))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.41	 A(a(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(x1:S))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.41	 A(a(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	->->-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(x1:S))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.41	 A(a(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	-> Usable rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[a](X) = 2.X + 2
0.00/0.41	[b](X) = 2.X + 2
0.00/0.41	[A](X) = 2.X + 1
0.00/0.41	[B](X) = 2.X + 2
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.41	 A(a(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.41	 A(a(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	->->-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.41	 A(a(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	-> Usable rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[a](X) = 2.X + 2
0.00/0.41	[b](X) = 2.X + 2
0.00/0.41	[A](X) = X + 1
0.00/0.41	[B](X) = X
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.41	 A(a(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.41	 A(a(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	->->-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.41	 A(a(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	-> Usable rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[a](X) = 2.X + 2
0.00/0.41	[b](X) = 2.X + 2
0.00/0.41	[A](X) = X
0.00/0.41	[B](X) = 2.X + 2
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	->->-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(a(x1:S))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	-> Usable rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[a](X) = X + 2
0.00/0.41	[b](X) = X + 2
0.00/0.41	[A](X) = 2.X + 1
0.00/0.41	[B](X) = 2.X + 2
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	->->-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	-> Usable rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[a](X) = X + 1
0.00/0.41	[b](X) = X + 1
0.00/0.41	[A](X) = 2.X
0.00/0.41	[B](X) = 2.X
0.00/0.41	
0.00/0.41	Problem 1: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.41	 B(a(b(b(x1:S)))) -> A(x1:S)
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	->->-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	->->-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	
0.00/0.41	
0.00/0.41	The problem is decomposed in 2 subproblems.
0.00/0.41	
0.00/0.41	Problem 1.1: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A(a(a(a(x1:S)))) -> A(b(a(b(x1:S))))
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	-> Usable rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[a](X) = 2.X + 2
0.00/0.41	[b](X) = 2
0.00/0.41	[A](X) = 2.X
0.00/0.41	
0.00/0.41	Problem 1.1: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	->->-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	
0.00/0.41	Problem 1.1: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 A(a(b(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	-> Usable rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[a](X) = 2.X + 1
0.00/0.41	[b](X) = 0
0.00/0.41	[A](X) = 2.X
0.00/0.41	
0.00/0.41	Problem 1.1: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 Empty
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Strongly Connected Components:
0.00/0.41	 There is no strongly connected component
0.00/0.41	
0.00/0.41	The problem is finite.
0.00/0.41	
0.00/0.41	Problem 1.2: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 B(a(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	-> Usable rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[a](X) = 2.X + 2
0.00/0.41	[b](X) = 2.X + 2
0.00/0.41	[B](X) = 2.X
0.00/0.41	
0.00/0.41	Problem 1.2: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Strongly Connected Components:
0.00/0.41	->->Cycle:
0.00/0.41	->->-> Pairs:
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	->->-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	
0.00/0.41	Problem 1.2: 
0.00/0.41	
0.00/0.41	Reduction Pair Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 B(a(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	-> Usable rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Interpretation type:
0.00/0.41	 Linear
0.00/0.41	->Coefficients:
0.00/0.41	 Natural Numbers
0.00/0.41	->Dimension:
0.00/0.41	 1
0.00/0.41	->Bound:
0.00/0.41	 2
0.00/0.41	->Interpretation:
0.00/0.41	 
0.00/0.41	[a](X) = 2
0.00/0.41	[b](X) = 1
0.00/0.41	[B](X) = 2.X
0.00/0.41	
0.00/0.41	Problem 1.2: 
0.00/0.41	
0.00/0.41	SCC Processor:
0.00/0.41	-> Pairs:
0.00/0.41	 Empty
0.00/0.41	-> Rules:
0.00/0.41	 a(a(a(a(x1:S)))) -> a(b(a(b(x1:S))))
0.00/0.41	 a(a(b(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.41	 b(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.41	->Strongly Connected Components:
0.00/0.41	 There is no strongly connected component
0.00/0.41	
0.00/0.41	The problem is finite.
0.00/0.41	EOF