0.00/0.20	YES
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	(VAR v_NonEmpty:S x1:S)
0.00/0.20	(RULES
0.00/0.20	a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	)
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Dependency Pairs Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
0.00/0.20	 A(b(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.20	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
0.00/0.20	 B(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.20	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
0.00/0.20	 A(b(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.20	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
0.00/0.20	 B(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.20	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Strongly Connected Components:
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
0.00/0.20	 A(b(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.20	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
0.00/0.20	 B(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.20	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	->->-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Reduction Pair Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
0.00/0.20	 A(b(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.20	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
0.00/0.20	 B(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.20	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	-> Usable rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Interpretation type:
0.00/0.20	 Linear
0.00/0.20	->Coefficients:
0.00/0.20	 Natural Numbers
0.00/0.20	->Dimension:
0.00/0.20	 1
0.00/0.20	->Bound:
0.00/0.20	 2
0.00/0.20	->Interpretation:
0.00/0.20	 
0.00/0.20	[a](X) = 2.X + 2
0.00/0.20	[b](X) = 2.X
0.00/0.20	[A](X) = 2.X + 2
0.00/0.20	[B](X) = 2.X + 2
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A(b(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.20	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
0.00/0.20	 B(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.20	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Strongly Connected Components:
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 A(b(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.20	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
0.00/0.20	 B(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.20	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	->->-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Reduction Pair Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A(b(a(a(x1:S)))) -> B(a(x1:S))
0.00/0.20	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
0.00/0.20	 B(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.20	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	-> Usable rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Interpretation type:
0.00/0.20	 Linear
0.00/0.20	->Coefficients:
0.00/0.20	 Natural Numbers
0.00/0.20	->Dimension:
0.00/0.20	 1
0.00/0.20	->Bound:
0.00/0.20	 2
0.00/0.20	->Interpretation:
0.00/0.20	 
0.00/0.20	[a](X) = 2.X + 2
0.00/0.20	[b](X) = 2.X + 2
0.00/0.20	[A](X) = 2.X + 2
0.00/0.20	[B](X) = 2.X + 2
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
0.00/0.20	 B(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.20	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Strongly Connected Components:
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
0.00/0.20	 B(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.20	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	->->-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Reduction Pair Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
0.00/0.20	 B(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.20	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	-> Usable rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Interpretation type:
0.00/0.20	 Linear
0.00/0.20	->Coefficients:
0.00/0.20	 Natural Numbers
0.00/0.20	->Dimension:
0.00/0.20	 1
0.00/0.20	->Bound:
0.00/0.20	 2
0.00/0.20	->Interpretation:
0.00/0.20	 
0.00/0.20	[a](X) = 2.X + 2
0.00/0.20	[b](X) = 2.X + 2
0.00/0.20	[A](X) = X + 2
0.00/0.20	[B](X) = 2.X + 2
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 B(a(a(a(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.20	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Strongly Connected Components:
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	->->-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Reduction Pair Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	-> Usable rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Interpretation type:
0.00/0.20	 Linear
0.00/0.20	->Coefficients:
0.00/0.20	 Natural Numbers
0.00/0.20	->Dimension:
0.00/0.20	 1
0.00/0.20	->Bound:
0.00/0.20	 2
0.00/0.20	->Interpretation:
0.00/0.20	 
0.00/0.20	[a](X) = 2.X + 2
0.00/0.20	[b](X) = 2.X + 2
0.00/0.20	[B](X) = 2.X
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 B(a(b(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Strongly Connected Components:
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 B(a(b(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	->->-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Reduction Pair Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 B(a(b(a(x1:S)))) -> B(a(b(b(x1:S))))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	-> Usable rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Interpretation type:
0.00/0.20	 Linear
0.00/0.20	->Coefficients:
0.00/0.20	 Natural Numbers
0.00/0.20	->Dimension:
0.00/0.20	 1
0.00/0.20	->Bound:
0.00/0.20	 2
0.00/0.20	->Interpretation:
0.00/0.20	 
0.00/0.20	[a](X) = 2.X + 2
0.00/0.20	[b](X) = 2.X + 1
0.00/0.20	[B](X) = 2.X
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Strongly Connected Components:
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	->->-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Reduction Pair Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	-> Usable rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Interpretation type:
0.00/0.20	 Linear
0.00/0.20	->Coefficients:
0.00/0.20	 Natural Numbers
0.00/0.20	->Dimension:
0.00/0.20	 1
0.00/0.20	->Bound:
0.00/0.20	 2
0.00/0.20	->Interpretation:
0.00/0.20	 
0.00/0.20	[a](X) = 2.X + 2
0.00/0.20	[b](X) = 2.X + 2
0.00/0.20	[B](X) = 2.X
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Strongly Connected Components:
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	->->-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Reduction Pair Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 B(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	-> Usable rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Interpretation type:
0.00/0.20	 Linear
0.00/0.20	->Coefficients:
0.00/0.20	 Natural Numbers
0.00/0.20	->Dimension:
0.00/0.20	 1
0.00/0.20	->Bound:
0.00/0.20	 2
0.00/0.20	->Interpretation:
0.00/0.20	 
0.00/0.20	[a](X) = 2.X + 2
0.00/0.20	[b](X) = 2.X + 2
0.00/0.20	[B](X) = 2.X
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Strongly Connected Components:
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	->->-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Reduction Pair Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 B(b(b(a(x1:S)))) -> B(a(b(x1:S)))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	-> Usable rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Interpretation type:
0.00/0.20	 Linear
0.00/0.20	->Coefficients:
0.00/0.20	 Natural Numbers
0.00/0.20	->Dimension:
0.00/0.20	 1
0.00/0.20	->Bound:
0.00/0.20	 2
0.00/0.20	->Interpretation:
0.00/0.20	 
0.00/0.20	[a](X) = 2.X + 2
0.00/0.20	[b](X) = 2.X + 2
0.00/0.20	[B](X) = 2.X
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Strongly Connected Components:
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	->->-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Reduction Pair Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 B(b(b(a(x1:S)))) -> B(b(a(b(x1:S))))
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	-> Usable rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Interpretation type:
0.00/0.20	 Linear
0.00/0.20	->Coefficients:
0.00/0.20	 Natural Numbers
0.00/0.20	->Dimension:
0.00/0.20	 1
0.00/0.20	->Bound:
0.00/0.20	 2
0.00/0.20	->Interpretation:
0.00/0.20	 
0.00/0.20	[a](X) = 2.X + 2
0.00/0.20	[b](X) = 2.X + 1
0.00/0.20	[B](X) = 2.X
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Strongly Connected Components:
0.00/0.20	->->Cycle:
0.00/0.20	->->-> Pairs:
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	->->-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	Subterm Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 B(b(b(a(x1:S)))) -> B(x1:S)
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Projection:
0.00/0.20	 pi(B) = 1
0.00/0.20	
0.00/0.20	Problem 1: 
0.00/0.20	
0.00/0.20	SCC Processor:
0.00/0.20	-> Pairs:
0.00/0.20	 Empty
0.00/0.20	-> Rules:
0.00/0.20	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
0.00/0.20	 b(a(a(a(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.20	 b(a(b(a(x1:S)))) -> b(a(b(b(x1:S))))
0.00/0.20	 b(b(b(a(x1:S)))) -> b(b(a(b(x1:S))))
0.00/0.20	->Strongly Connected Components:
0.00/0.20	 There is no strongly connected component
0.00/0.20	
0.00/0.20	The problem is finite.
0.00/0.20	EOF