0.00/0.39	YES
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	(VAR v_NonEmpty:S x1:S)
0.00/0.39	(RULES
0.00/0.39	a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	)
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	Dependency Pairs Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(a(a(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	SCC Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(a(a(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Strongly Connected Components:
0.00/0.39	->->Cycle:
0.00/0.39	->->-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(a(a(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	->->-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	Reduction Pair Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(a(a(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	-> Usable rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Interpretation type:
0.00/0.39	 Linear
0.00/0.39	->Coefficients:
0.00/0.39	 Natural Numbers
0.00/0.39	->Dimension:
0.00/0.39	 1
0.00/0.39	->Bound:
0.00/0.39	 2
0.00/0.39	->Interpretation:
0.00/0.39	 
0.00/0.39	[a](X) = 2.X + 2
0.00/0.39	[b](X) = 2.X + 2
0.00/0.39	[A](X) = 2.X + 2
0.00/0.39	[B](X) = 2.X + 2
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	SCC Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Strongly Connected Components:
0.00/0.39	->->Cycle:
0.00/0.39	->->-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	->->-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	Reduction Pair Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	-> Usable rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Interpretation type:
0.00/0.39	 Linear
0.00/0.39	->Coefficients:
0.00/0.39	 Natural Numbers
0.00/0.39	->Dimension:
0.00/0.39	 1
0.00/0.39	->Bound:
0.00/0.39	 2
0.00/0.39	->Interpretation:
0.00/0.39	 
0.00/0.39	[a](X) = 2.X + 2
0.00/0.39	[b](X) = 2.X + 2
0.00/0.39	[A](X) = 2.X
0.00/0.39	[B](X) = 2.X
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	SCC Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Strongly Connected Components:
0.00/0.39	->->Cycle:
0.00/0.39	->->-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	->->-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	Reduction Pair Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	-> Usable rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Interpretation type:
0.00/0.39	 Linear
0.00/0.39	->Coefficients:
0.00/0.39	 Natural Numbers
0.00/0.39	->Dimension:
0.00/0.39	 1
0.00/0.39	->Bound:
0.00/0.39	 2
0.00/0.39	->Interpretation:
0.00/0.39	 
0.00/0.39	[a](X) = X + 2
0.00/0.39	[b](X) = X + 2
0.00/0.39	[A](X) = 2.X + 2
0.00/0.39	[B](X) = 2.X + 2
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	SCC Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Strongly Connected Components:
0.00/0.39	->->Cycle:
0.00/0.39	->->-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	->->-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	Reduction Pair Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	-> Usable rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Interpretation type:
0.00/0.39	 Linear
0.00/0.39	->Coefficients:
0.00/0.39	 Natural Numbers
0.00/0.39	->Dimension:
0.00/0.39	 1
0.00/0.39	->Bound:
0.00/0.39	 2
0.00/0.39	->Interpretation:
0.00/0.39	 
0.00/0.39	[a](X) = 2.X + 2
0.00/0.39	[b](X) = 2.X + 2
0.00/0.39	[A](X) = 2.X + 2
0.00/0.39	[B](X) = 2.X
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	SCC Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Strongly Connected Components:
0.00/0.39	->->Cycle:
0.00/0.39	->->-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	->->-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	Reduction Pair Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	-> Usable rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Interpretation type:
0.00/0.39	 Linear
0.00/0.39	->Coefficients:
0.00/0.39	 Natural Numbers
0.00/0.39	->Dimension:
0.00/0.39	 1
0.00/0.39	->Bound:
0.00/0.39	 2
0.00/0.39	->Interpretation:
0.00/0.39	 
0.00/0.39	[a](X) = 2.X + 2
0.00/0.39	[b](X) = 2.X + 2
0.00/0.39	[A](X) = 2.X + 2
0.00/0.39	[B](X) = 2.X + 2
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	SCC Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Strongly Connected Components:
0.00/0.39	->->Cycle:
0.00/0.39	->->-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	->->-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	Reduction Pair Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(a(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	-> Usable rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Interpretation type:
0.00/0.39	 Linear
0.00/0.39	->Coefficients:
0.00/0.39	 Natural Numbers
0.00/0.39	->Dimension:
0.00/0.39	 1
0.00/0.39	->Bound:
0.00/0.39	 2
0.00/0.39	->Interpretation:
0.00/0.39	 
0.00/0.39	[a](X) = 2.X + 2
0.00/0.39	[b](X) = 2
0.00/0.39	[A](X) = X
0.00/0.39	[B](X) = 2
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	SCC Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Strongly Connected Components:
0.00/0.39	->->Cycle:
0.00/0.39	->->-> Pairs:
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	->->-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	Reduction Pair Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(b(b(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	-> Usable rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Interpretation type:
0.00/0.39	 Linear
0.00/0.39	->Coefficients:
0.00/0.39	 Natural Numbers
0.00/0.39	->Dimension:
0.00/0.39	 1
0.00/0.39	->Bound:
0.00/0.39	 2
0.00/0.39	->Interpretation:
0.00/0.39	 
0.00/0.39	[a](X) = 2.X + 2
0.00/0.39	[b](X) = 2.X + 2
0.00/0.39	[A](X) = 2.X + 2
0.00/0.39	[B](X) = X + 1
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	SCC Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Strongly Connected Components:
0.00/0.39	->->Cycle:
0.00/0.39	->->-> Pairs:
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	->->-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	Reduction Pair Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 A(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	-> Usable rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Interpretation type:
0.00/0.39	 Linear
0.00/0.39	->Coefficients:
0.00/0.39	 Natural Numbers
0.00/0.39	->Dimension:
0.00/0.39	 1
0.00/0.39	->Bound:
0.00/0.39	 2
0.00/0.39	->Interpretation:
0.00/0.39	 
0.00/0.39	[a](X) = 2.X + 2
0.00/0.39	[b](X) = 2.X + 2
0.00/0.39	[A](X) = 2.X + 2
0.00/0.39	[B](X) = 2.X
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	SCC Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Strongly Connected Components:
0.00/0.39	->->Cycle:
0.00/0.39	->->-> Pairs:
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	->->-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	Reduction Pair Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	-> Usable rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Interpretation type:
0.00/0.39	 Linear
0.00/0.39	->Coefficients:
0.00/0.39	 Natural Numbers
0.00/0.39	->Dimension:
0.00/0.39	 1
0.00/0.39	->Bound:
0.00/0.39	 2
0.00/0.39	->Interpretation:
0.00/0.39	 
0.00/0.39	[a](X) = 2.X + 2
0.00/0.39	[b](X) = 0
0.00/0.39	[B](X) = 2.X
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	SCC Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Strongly Connected Components:
0.00/0.39	->->Cycle:
0.00/0.39	->->-> Pairs:
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	->->-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.39	
0.00/0.39	Subterm Processor:
0.00/0.39	-> Pairs:
0.00/0.39	 B(a(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.39	-> Rules:
0.00/0.39	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.39	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.39	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.39	->Projection:
0.00/0.39	 pi(B) = 1
0.00/0.39	
0.00/0.39	Problem 1: 
0.00/0.40	
0.00/0.40	SCC Processor:
0.00/0.40	-> Pairs:
0.00/0.40	 Empty
0.00/0.40	-> Rules:
0.00/0.40	 a(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.40	 a(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.40	 b(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.40	->Strongly Connected Components:
0.00/0.40	 There is no strongly connected component
0.00/0.40	
0.00/0.40	The problem is finite.
0.00/0.40	EOF