19.33/19.53	YES
19.33/19.53	
19.33/19.53	Problem 1: 
19.33/19.53	
19.33/19.53	(VAR v_NonEmpty:S x1:S)
19.33/19.53	(RULES
19.33/19.53	b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	)
19.33/19.53	
19.33/19.53	Problem 1: 
19.33/19.53	
19.33/19.53	Dependency Pairs Processor:
19.33/19.53	-> Pairs:
19.33/19.53	 B(b(a(a(x1:S)))) -> B(b(x1:S))
19.33/19.53	 B(b(a(a(x1:S)))) -> B(x1:S)
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
19.33/19.53	-> Rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	
19.33/19.53	Problem 1: 
19.33/19.53	
19.33/19.53	SCC Processor:
19.33/19.53	-> Pairs:
19.33/19.53	 B(b(a(a(x1:S)))) -> B(b(x1:S))
19.33/19.53	 B(b(a(a(x1:S)))) -> B(x1:S)
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
19.33/19.53	-> Rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	->Strongly Connected Components:
19.33/19.53	->->Cycle:
19.33/19.53	->->-> Pairs:
19.33/19.53	 B(b(a(a(x1:S)))) -> B(b(x1:S))
19.33/19.53	 B(b(a(a(x1:S)))) -> B(x1:S)
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
19.33/19.53	->->-> Rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	
19.33/19.53	Problem 1: 
19.33/19.53	
19.33/19.53	Reduction Pair Processor:
19.33/19.53	-> Pairs:
19.33/19.53	 B(b(a(a(x1:S)))) -> B(b(x1:S))
19.33/19.53	 B(b(a(a(x1:S)))) -> B(x1:S)
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
19.33/19.53	-> Rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	-> Usable rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	->Interpretation type:
19.33/19.53	 Linear
19.33/19.53	->Coefficients:
19.33/19.53	 Natural Numbers
19.33/19.53	->Dimension:
19.33/19.53	 1
19.33/19.53	->Bound:
19.33/19.53	 2
19.33/19.53	->Interpretation:
19.33/19.53	 
19.33/19.53	[b](X) = 2.X + 1
19.33/19.53	[a](X) = 2.X + 1
19.33/19.53	[B](X) = 2.X
19.33/19.53	
19.33/19.53	Problem 1: 
19.33/19.53	
19.33/19.53	SCC Processor:
19.33/19.53	-> Pairs:
19.33/19.53	 B(b(a(a(x1:S)))) -> B(x1:S)
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
19.33/19.53	-> Rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	->Strongly Connected Components:
19.33/19.53	->->Cycle:
19.33/19.53	->->-> Pairs:
19.33/19.53	 B(b(a(a(x1:S)))) -> B(x1:S)
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
19.33/19.53	->->-> Rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	
19.33/19.53	Problem 1: 
19.33/19.53	
19.33/19.53	Reduction Pair Processor:
19.33/19.53	-> Pairs:
19.33/19.53	 B(b(a(a(x1:S)))) -> B(x1:S)
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
19.33/19.53	-> Rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	-> Usable rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	->Interpretation type:
19.33/19.53	 Linear
19.33/19.53	->Coefficients:
19.33/19.53	 Natural Numbers
19.33/19.53	->Dimension:
19.33/19.53	 1
19.33/19.53	->Bound:
19.33/19.53	 2
19.33/19.53	->Interpretation:
19.33/19.53	 
19.33/19.53	[b](X) = 2.X + 1
19.33/19.53	[a](X) = 2.X + 1
19.33/19.53	[B](X) = 2.X
19.33/19.53	
19.33/19.53	Problem 1: 
19.33/19.53	
19.33/19.53	SCC Processor:
19.33/19.53	-> Pairs:
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
19.33/19.53	-> Rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	->Strongly Connected Components:
19.33/19.53	->->Cycle:
19.33/19.53	->->-> Pairs:
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
19.33/19.53	->->-> Rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	
19.33/19.53	Problem 1: 
19.33/19.53	
19.33/19.53	Reduction Pair Processor:
19.33/19.53	-> Pairs:
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
19.33/19.53	-> Rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	-> Usable rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	->Interpretation type:
19.33/19.53	 Linear
19.33/19.53	->Coefficients:
19.33/19.53	 Natural Numbers
19.33/19.53	->Dimension:
19.33/19.53	 1
19.33/19.53	->Bound:
19.33/19.53	 2
19.33/19.53	->Interpretation:
19.33/19.53	 
19.33/19.53	[b](X) = 2.X + 2
19.33/19.53	[a](X) = 2.X + 2
19.33/19.53	[B](X) = 2.X
19.33/19.53	
19.33/19.53	Problem 1: 
19.33/19.53	
19.33/19.53	SCC Processor:
19.33/19.53	-> Pairs:
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
19.33/19.53	-> Rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	->Strongly Connected Components:
19.33/19.53	->->Cycle:
19.33/19.53	->->-> Pairs:
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
19.33/19.53	->->-> Rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	
19.33/19.53	Problem 1: 
19.33/19.53	
19.33/19.53	Reduction Pair Processor:
19.33/19.53	-> Pairs:
19.33/19.53	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
19.33/19.53	-> Rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	-> Usable rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	->Interpretation type:
19.33/19.53	 Linear
19.33/19.53	->Coefficients:
19.33/19.53	 Natural Numbers
19.33/19.53	->Dimension:
19.33/19.53	 2
19.33/19.53	->Bound:
19.33/19.53	 1
19.33/19.53	->Interpretation:
19.33/19.53	 
19.33/19.53	[b](X) = [0;1]
19.33/19.53	[a](X) = [0 1;0 0].X
19.33/19.53	[B](X) = [1 0;1 1].X
19.33/19.53	
19.33/19.53	Problem 1: 
19.33/19.53	
19.33/19.53	SCC Processor:
19.33/19.53	-> Pairs:
19.33/19.53	 Empty
19.33/19.53	-> Rules:
19.33/19.53	 b(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
19.33/19.53	 b(a(b(b(x1:S)))) -> b(a(a(a(x1:S))))
19.33/19.53	->Strongly Connected Components:
19.33/19.53	 There is no strongly connected component
19.33/19.53	
19.33/19.53	The problem is finite.
19.33/56.89	EOF