31.53/31.79	YES
31.53/31.79	
31.53/31.79	Problem 1: 
31.53/31.79	
31.53/31.79	(VAR v_NonEmpty:S x1:S)
31.53/31.79	(RULES
31.53/31.79	b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	)
31.53/31.79	
31.53/31.79	Problem 1: 
31.53/31.79	
31.53/31.79	Dependency Pairs Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(b(a(b(x1:S)))) -> B(a(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(b(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(x1:S)
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	
31.53/31.79	Problem 1: 
31.53/31.79	
31.53/31.79	SCC Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(b(a(b(x1:S)))) -> B(a(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(b(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(x1:S)
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Strongly Connected Components:
31.53/31.79	->->Cycle:
31.53/31.79	->->-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(b(a(b(x1:S)))) -> B(a(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(b(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(x1:S)
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	->->-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	
31.53/31.79	Problem 1: 
31.53/31.79	
31.53/31.79	Reduction Pair Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(b(a(b(x1:S)))) -> B(a(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(b(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(x1:S)
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	-> Usable rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Interpretation type:
31.53/31.79	 Linear
31.53/31.79	->Coefficients:
31.53/31.79	 Natural Numbers
31.53/31.79	->Dimension:
31.53/31.79	 1
31.53/31.79	->Bound:
31.53/31.79	 2
31.53/31.79	->Interpretation:
31.53/31.79	 
31.53/31.79	[b](X) = 2.X + 2
31.53/31.79	[a](X) = 2.X + 2
31.53/31.79	[B](X) = 2.X
31.53/31.79	
31.53/31.79	Problem 1: 
31.53/31.79	
31.53/31.79	SCC Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(b(a(b(x1:S)))) -> B(a(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(b(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(x1:S)
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Strongly Connected Components:
31.53/31.79	->->Cycle:
31.53/31.79	->->-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(b(a(b(x1:S)))) -> B(a(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(b(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(x1:S)
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	->->-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	
31.53/31.79	Problem 1: 
31.53/31.79	
31.53/31.79	Reduction Pair Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(b(a(b(x1:S)))) -> B(a(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(b(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(x1:S)
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	-> Usable rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Interpretation type:
31.53/31.79	 Linear
31.53/31.79	->Coefficients:
31.53/31.79	 Natural Numbers
31.53/31.79	->Dimension:
31.53/31.79	 1
31.53/31.79	->Bound:
31.53/31.79	 2
31.53/31.79	->Interpretation:
31.53/31.79	 
31.53/31.79	[b](X) = 2.X + 2
31.53/31.79	[a](X) = 2.X + 2
31.53/31.79	[B](X) = 2.X
31.53/31.79	
31.53/31.79	Problem 1: 
31.53/31.79	
31.53/31.79	SCC Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(b(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(x1:S)
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Strongly Connected Components:
31.53/31.79	->->Cycle:
31.53/31.79	->->-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(b(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(x1:S)
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	->->-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	
31.53/31.79	Problem 1: 
31.53/31.79	
31.53/31.79	Reduction Pair Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(b(x1:S))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(x1:S)
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	-> Usable rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Interpretation type:
31.53/31.79	 Linear
31.53/31.79	->Coefficients:
31.53/31.79	 Natural Numbers
31.53/31.79	->Dimension:
31.53/31.79	 1
31.53/31.79	->Bound:
31.53/31.79	 2
31.53/31.79	->Interpretation:
31.53/31.79	 
31.53/31.79	[b](X) = X + 2
31.53/31.79	[a](X) = X + 2
31.53/31.79	[B](X) = 2.X
31.53/31.79	
31.53/31.79	Problem 1: 
31.53/31.79	
31.53/31.79	SCC Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(x1:S)
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Strongly Connected Components:
31.53/31.79	->->Cycle:
31.53/31.79	->->-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(x1:S)
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	->->-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	
31.53/31.79	Problem 1: 
31.53/31.79	
31.53/31.79	Reduction Pair Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(b(a(a(x1:S)))) -> B(x1:S)
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	-> Usable rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Interpretation type:
31.53/31.79	 Linear
31.53/31.79	->Coefficients:
31.53/31.79	 Natural Numbers
31.53/31.79	->Dimension:
31.53/31.79	 1
31.53/31.79	->Bound:
31.53/31.79	 2
31.53/31.79	->Interpretation:
31.53/31.79	 
31.53/31.79	[b](X) = 2.X + 1
31.53/31.79	[a](X) = 2.X + 1
31.53/31.79	[B](X) = 2.X
31.53/31.79	
31.53/31.79	Problem 1: 
31.53/31.79	
31.53/31.79	SCC Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Strongly Connected Components:
31.53/31.79	->->Cycle:
31.53/31.79	->->-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	->->-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	
31.53/31.79	Problem 1: 
31.53/31.79	
31.53/31.79	Reduction Pair Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	-> Usable rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Interpretation type:
31.53/31.79	 Linear
31.53/31.79	->Coefficients:
31.53/31.79	 Natural Numbers
31.53/31.79	->Dimension:
31.53/31.79	 1
31.53/31.79	->Bound:
31.53/31.79	 2
31.53/31.79	->Interpretation:
31.53/31.79	 
31.53/31.79	[b](X) = X + 1
31.53/31.79	[a](X) = X + 2
31.53/31.79	[B](X) = 2.X
31.53/31.79	
31.53/31.79	Problem 1: 
31.53/31.79	
31.53/31.79	SCC Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Strongly Connected Components:
31.53/31.79	->->Cycle:
31.53/31.79	->->-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	->->-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	
31.53/31.79	Problem 1: 
31.53/31.79	
31.53/31.79	Reduction Pair Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(b(a(x1:S)))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	-> Usable rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Interpretation type:
31.53/31.79	 Linear
31.53/31.79	->Coefficients:
31.53/31.79	 Natural Numbers
31.53/31.79	->Dimension:
31.53/31.79	 1
31.53/31.79	->Bound:
31.53/31.79	 2
31.53/31.79	->Interpretation:
31.53/31.79	 
31.53/31.79	[b](X) = 2.X + 2
31.53/31.79	[a](X) = 2.X + 2
31.53/31.79	[B](X) = 2.X
31.53/31.79	
31.53/31.79	Problem 1: 
31.53/31.79	
31.53/31.79	SCC Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Strongly Connected Components:
31.53/31.79	->->Cycle:
31.53/31.79	->->-> Pairs:
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	->->-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->->Cycle:
31.53/31.79	->->-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	->->-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	
31.53/31.79	
31.53/31.79	The problem is decomposed in 2 subproblems.
31.53/31.79	
31.53/31.79	Problem 1.1: 
31.53/31.79	
31.53/31.79	Subterm Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 B(a(a(a(x1:S)))) -> B(a(x1:S))
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Projection:
31.53/31.79	 pi(B) = 1
31.53/31.79	
31.53/31.79	Problem 1.1: 
31.53/31.79	
31.53/31.79	SCC Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 Empty
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Strongly Connected Components:
31.53/31.79	 There is no strongly connected component
31.53/31.79	
31.53/31.79	The problem is finite.
31.53/31.79	
31.53/31.79	Problem 1.2: 
31.53/31.79	
31.53/31.79	Reduction Pair Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 B(b(a(b(x1:S)))) -> B(b(b(a(x1:S))))
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	-> Usable rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Interpretation type:
31.53/31.79	 Linear
31.53/31.79	->Coefficients:
31.53/31.79	 Natural Numbers
31.53/31.79	->Dimension:
31.53/31.79	 2
31.53/31.79	->Bound:
31.53/31.79	 1
31.53/31.79	->Interpretation:
31.53/31.79	 
31.53/31.79	[b](X) = [0 1;0 0].X + [1;0]
31.53/31.79	[a](X) = [0 0;1 0].X
31.53/31.79	[B](X) = [1 0;0 1].X
31.53/31.79	
31.53/31.79	Problem 1.2: 
31.53/31.79	
31.53/31.79	SCC Processor:
31.53/31.79	-> Pairs:
31.53/31.79	 Empty
31.53/31.79	-> Rules:
31.53/31.79	 b(b(a(b(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
31.53/31.79	 b(a(a(a(x1:S)))) -> b(b(b(a(x1:S))))
31.53/31.79	->Strongly Connected Components:
31.53/31.79	 There is no strongly connected component
31.53/31.79	
31.53/31.79	The problem is finite.
31.53/77.33	EOF