19.05/19.25	YES
19.05/19.25	
19.05/19.25	Problem 1: 
19.05/19.25	
19.05/19.25	(VAR v_NonEmpty:S x1:S)
19.05/19.25	(RULES
19.05/19.25	b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.25	b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.25	b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.25	)
19.05/19.25	
19.05/19.25	Problem 1: 
19.05/19.25	
19.05/19.25	Dependency Pairs Processor:
19.05/19.25	-> Pairs:
19.05/19.25	 B(a(b(a(x1:S)))) -> B(b(a(b(x1:S))))
19.05/19.25	 B(a(b(a(x1:S)))) -> B(a(b(x1:S)))
19.05/19.25	 B(a(b(a(x1:S)))) -> B(x1:S)
19.05/19.25	 B(a(a(a(x1:S)))) -> B(b(x1:S))
19.05/19.25	 B(a(a(a(x1:S)))) -> B(x1:S)
19.05/19.25	-> Rules:
19.05/19.25	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.25	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.25	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.25	
19.05/19.25	Problem 1: 
19.05/19.25	
19.05/19.25	SCC Processor:
19.05/19.25	-> Pairs:
19.05/19.25	 B(a(b(a(x1:S)))) -> B(b(a(b(x1:S))))
19.05/19.25	 B(a(b(a(x1:S)))) -> B(a(b(x1:S)))
19.05/19.25	 B(a(b(a(x1:S)))) -> B(x1:S)
19.05/19.25	 B(a(a(a(x1:S)))) -> B(b(x1:S))
19.05/19.25	 B(a(a(a(x1:S)))) -> B(x1:S)
19.05/19.25	-> Rules:
19.05/19.25	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.25	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.25	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.25	->Strongly Connected Components:
19.05/19.25	->->Cycle:
19.05/19.25	->->-> Pairs:
19.05/19.25	 B(a(b(a(x1:S)))) -> B(b(a(b(x1:S))))
19.05/19.25	 B(a(b(a(x1:S)))) -> B(a(b(x1:S)))
19.05/19.25	 B(a(b(a(x1:S)))) -> B(x1:S)
19.05/19.25	 B(a(a(a(x1:S)))) -> B(b(x1:S))
19.05/19.25	 B(a(a(a(x1:S)))) -> B(x1:S)
19.05/19.25	->->-> Rules:
19.05/19.25	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.25	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.25	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.25	
19.05/19.25	Problem 1: 
19.05/19.25	
19.05/19.25	Reduction Pair Processor:
19.05/19.25	-> Pairs:
19.05/19.25	 B(a(b(a(x1:S)))) -> B(b(a(b(x1:S))))
19.05/19.25	 B(a(b(a(x1:S)))) -> B(a(b(x1:S)))
19.05/19.25	 B(a(b(a(x1:S)))) -> B(x1:S)
19.05/19.25	 B(a(a(a(x1:S)))) -> B(b(x1:S))
19.05/19.25	 B(a(a(a(x1:S)))) -> B(x1:S)
19.05/19.25	-> Rules:
19.05/19.25	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.25	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.25	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.25	-> Usable rules:
19.05/19.25	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.25	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.25	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.25	->Interpretation type:
19.05/19.25	 Linear
19.05/19.25	->Coefficients:
19.05/19.25	 Natural Numbers
19.05/19.25	->Dimension:
19.05/19.25	 1
19.05/19.25	->Bound:
19.05/19.25	 2
19.05/19.25	->Interpretation:
19.05/19.25	 
19.05/19.25	[b](X) = 2.X + 1
19.05/19.25	[a](X) = 2.X + 1
19.05/19.25	[B](X) = 2.X
19.05/19.25	
19.05/19.25	Problem 1: 
19.05/19.25	
19.05/19.25	SCC Processor:
19.05/19.25	-> Pairs:
19.05/19.25	 B(a(b(a(x1:S)))) -> B(b(a(b(x1:S))))
19.05/19.25	 B(a(b(a(x1:S)))) -> B(x1:S)
19.05/19.25	 B(a(a(a(x1:S)))) -> B(b(x1:S))
19.05/19.25	 B(a(a(a(x1:S)))) -> B(x1:S)
19.05/19.25	-> Rules:
19.05/19.25	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.25	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	->Strongly Connected Components:
19.05/19.26	->->Cycle:
19.05/19.26	->->-> Pairs:
19.05/19.26	 B(a(b(a(x1:S)))) -> B(b(a(b(x1:S))))
19.05/19.26	 B(a(b(a(x1:S)))) -> B(x1:S)
19.05/19.26	 B(a(a(a(x1:S)))) -> B(b(x1:S))
19.05/19.26	 B(a(a(a(x1:S)))) -> B(x1:S)
19.05/19.26	->->-> Rules:
19.05/19.26	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.26	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	
19.05/19.26	Problem 1: 
19.05/19.26	
19.05/19.26	Reduction Pair Processor:
19.05/19.26	-> Pairs:
19.05/19.26	 B(a(b(a(x1:S)))) -> B(b(a(b(x1:S))))
19.05/19.26	 B(a(b(a(x1:S)))) -> B(x1:S)
19.05/19.26	 B(a(a(a(x1:S)))) -> B(b(x1:S))
19.05/19.26	 B(a(a(a(x1:S)))) -> B(x1:S)
19.05/19.26	-> Rules:
19.05/19.26	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.26	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	-> Usable rules:
19.05/19.26	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.26	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	->Interpretation type:
19.05/19.26	 Linear
19.05/19.26	->Coefficients:
19.05/19.26	 Natural Numbers
19.05/19.26	->Dimension:
19.05/19.26	 1
19.05/19.26	->Bound:
19.05/19.26	 2
19.05/19.26	->Interpretation:
19.05/19.26	 
19.05/19.26	[b](X) = 2.X + 1
19.05/19.26	[a](X) = 2.X + 1
19.05/19.26	[B](X) = 2.X
19.05/19.26	
19.05/19.26	Problem 1: 
19.05/19.26	
19.05/19.26	SCC Processor:
19.05/19.26	-> Pairs:
19.05/19.26	 B(a(b(a(x1:S)))) -> B(b(a(b(x1:S))))
19.05/19.26	 B(a(a(a(x1:S)))) -> B(b(x1:S))
19.05/19.26	 B(a(a(a(x1:S)))) -> B(x1:S)
19.05/19.26	-> Rules:
19.05/19.26	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.26	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	->Strongly Connected Components:
19.05/19.26	->->Cycle:
19.05/19.26	->->-> Pairs:
19.05/19.26	 B(a(b(a(x1:S)))) -> B(b(a(b(x1:S))))
19.05/19.26	 B(a(a(a(x1:S)))) -> B(b(x1:S))
19.05/19.26	 B(a(a(a(x1:S)))) -> B(x1:S)
19.05/19.26	->->-> Rules:
19.05/19.26	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.26	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	
19.05/19.26	Problem 1: 
19.05/19.26	
19.05/19.26	Reduction Pair Processor:
19.05/19.26	-> Pairs:
19.05/19.26	 B(a(b(a(x1:S)))) -> B(b(a(b(x1:S))))
19.05/19.26	 B(a(a(a(x1:S)))) -> B(b(x1:S))
19.05/19.26	 B(a(a(a(x1:S)))) -> B(x1:S)
19.05/19.26	-> Rules:
19.05/19.26	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.26	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	-> Usable rules:
19.05/19.26	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.26	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	->Interpretation type:
19.05/19.26	 Linear
19.05/19.26	->Coefficients:
19.05/19.26	 Natural Numbers
19.05/19.26	->Dimension:
19.05/19.26	 1
19.05/19.26	->Bound:
19.05/19.26	 2
19.05/19.26	->Interpretation:
19.05/19.26	 
19.05/19.26	[b](X) = X + 1
19.05/19.26	[a](X) = X + 1
19.05/19.26	[B](X) = X
19.05/19.26	
19.05/19.26	Problem 1: 
19.05/19.26	
19.05/19.26	SCC Processor:
19.05/19.26	-> Pairs:
19.05/19.26	 B(a(b(a(x1:S)))) -> B(b(a(b(x1:S))))
19.05/19.26	 B(a(a(a(x1:S)))) -> B(x1:S)
19.05/19.26	-> Rules:
19.05/19.26	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.26	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	->Strongly Connected Components:
19.05/19.26	->->Cycle:
19.05/19.26	->->-> Pairs:
19.05/19.26	 B(a(b(a(x1:S)))) -> B(b(a(b(x1:S))))
19.05/19.26	 B(a(a(a(x1:S)))) -> B(x1:S)
19.05/19.26	->->-> Rules:
19.05/19.26	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.26	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	
19.05/19.26	Problem 1: 
19.05/19.26	
19.05/19.26	Reduction Pair Processor:
19.05/19.26	-> Pairs:
19.05/19.26	 B(a(b(a(x1:S)))) -> B(b(a(b(x1:S))))
19.05/19.26	 B(a(a(a(x1:S)))) -> B(x1:S)
19.05/19.26	-> Rules:
19.05/19.26	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.26	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	-> Usable rules:
19.05/19.26	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.26	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	->Interpretation type:
19.05/19.26	 Linear
19.05/19.26	->Coefficients:
19.05/19.26	 Natural Numbers
19.05/19.26	->Dimension:
19.05/19.26	 1
19.05/19.26	->Bound:
19.05/19.26	 2
19.05/19.26	->Interpretation:
19.05/19.26	 
19.05/19.26	[b](X) = X + 1
19.05/19.26	[a](X) = X + 1
19.05/19.26	[B](X) = X
19.05/19.26	
19.05/19.26	Problem 1: 
19.05/19.26	
19.05/19.26	SCC Processor:
19.05/19.26	-> Pairs:
19.05/19.26	 B(a(b(a(x1:S)))) -> B(b(a(b(x1:S))))
19.05/19.26	-> Rules:
19.05/19.26	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.26	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	->Strongly Connected Components:
19.05/19.26	->->Cycle:
19.05/19.26	->->-> Pairs:
19.05/19.26	 B(a(b(a(x1:S)))) -> B(b(a(b(x1:S))))
19.05/19.26	->->-> Rules:
19.05/19.26	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.26	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	
19.05/19.26	Problem 1: 
19.05/19.26	
19.05/19.26	Reduction Pair Processor:
19.05/19.26	-> Pairs:
19.05/19.26	 B(a(b(a(x1:S)))) -> B(b(a(b(x1:S))))
19.05/19.26	-> Rules:
19.05/19.26	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.26	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	-> Usable rules:
19.05/19.26	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.26	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	->Interpretation type:
19.05/19.26	 Linear
19.05/19.26	->Coefficients:
19.05/19.26	 Natural Numbers
19.05/19.26	->Dimension:
19.05/19.26	 2
19.05/19.26	->Bound:
19.05/19.26	 1
19.05/19.26	->Interpretation:
19.05/19.26	 
19.05/19.26	[b](X) = [0 1;0 0].X + [0;1]
19.05/19.26	[a](X) = [0 0;1 0].X + [0;1]
19.05/19.26	[B](X) = [0 1;0 1].X
19.05/19.26	
19.05/19.26	Problem 1: 
19.05/19.26	
19.05/19.26	SCC Processor:
19.05/19.26	-> Pairs:
19.05/19.26	 Empty
19.05/19.26	-> Rules:
19.05/19.26	 b(a(b(a(x1:S)))) -> b(b(a(b(x1:S))))
19.05/19.26	 b(a(a(b(x1:S)))) -> a(a(a(b(x1:S))))
19.05/19.26	 b(a(a(a(x1:S)))) -> a(a(b(b(x1:S))))
19.05/19.26	->Strongly Connected Components:
19.05/19.26	 There is no strongly connected component
19.05/19.26	
19.05/19.26	The problem is finite.
19.05/19.28	EOF