0.00/0.37	YES
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	(VAR v_NonEmpty:S x1:S)
0.00/0.37	(RULES
0.00/0.37	a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	)
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Dependency Pairs Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(b(b(x1:S)))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(b(b(x1:S)))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(b(b(x1:S)))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	->->-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(b(b(x1:S)))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[a](X) = 2.X + 2
0.00/0.37	[b](X) = 2.X + 2
0.00/0.37	[A](X) = 2.X + 2
0.00/0.37	[B](X) = 2.X + 2
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	->->-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[a](X) = 2.X + 2
0.00/0.37	[b](X) = 2.X + 2
0.00/0.37	[A](X) = 2.X + 2
0.00/0.37	[B](X) = 2.X + 2
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	->->-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(a(a(a(x1:S)))) -> B(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[a](X) = 2.X + 2
0.00/0.37	[b](X) = 2.X + 2
0.00/0.37	[A](X) = 2.X + 2
0.00/0.37	[B](X) = 2.X + 2
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	->->-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(b(a(x1:S)))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[a](X) = 2.X + 2
0.00/0.37	[b](X) = 2.X + 2
0.00/0.37	[A](X) = 2.X + 2
0.00/0.37	[B](X) = X + 2
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	->->-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[a](X) = 2.X + 2
0.00/0.37	[b](X) = 2.X + 2
0.00/0.37	[A](X) = 2.X + 2
0.00/0.37	[B](X) = 2.X + 2
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	->->-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(a(a(a(x1:S)))) -> A(b(b(b(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[a](X) = 2
0.00/0.37	[b](X) = 1
0.00/0.37	[A](X) = 2.X + 2
0.00/0.37	[B](X) = 2.X
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	->->-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(b(a(x1:S))))
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[a](X) = 2.X + 1
0.00/0.37	[b](X) = 2.X + 1
0.00/0.37	[A](X) = 2.X + 2
0.00/0.37	[B](X) = 2.X + 1
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	->->-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 A(b(b(b(x1:S)))) -> B(a(x1:S))
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[a](X) = 2.X + 1
0.00/0.37	[b](X) = 2.X + 1
0.00/0.37	[A](X) = 2.X + 2
0.00/0.37	[B](X) = X + 2
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 B(a(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	->->-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Reduction Pair Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 B(a(a(b(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	-> Usable rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Interpretation type:
0.00/0.37	 Linear
0.00/0.37	->Coefficients:
0.00/0.37	 Natural Numbers
0.00/0.37	->Dimension:
0.00/0.37	 1
0.00/0.37	->Bound:
0.00/0.37	 2
0.00/0.37	->Interpretation:
0.00/0.37	 
0.00/0.37	[a](X) = 2.X + 1
0.00/0.37	[b](X) = 2
0.00/0.37	[B](X) = 2.X
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	->->Cycle:
0.00/0.37	->->-> Pairs:
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	->->-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	Subterm Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 B(a(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Projection:
0.00/0.37	 pi(B) = 1
0.00/0.37	
0.00/0.37	Problem 1: 
0.00/0.37	
0.00/0.37	SCC Processor:
0.00/0.37	-> Pairs:
0.00/0.37	 Empty
0.00/0.37	-> Rules:
0.00/0.37	 a(a(a(a(x1:S)))) -> a(b(b(b(x1:S))))
0.00/0.37	 a(b(b(b(x1:S)))) -> b(a(b(a(x1:S))))
0.00/0.37	 b(a(a(b(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.37	->Strongly Connected Components:
0.00/0.37	 There is no strongly connected component
0.00/0.37	
0.00/0.37	The problem is finite.
0.00/0.37	EOF