0.00/0.12	YES
0.00/0.12	
0.00/0.12	Problem 1: 
0.00/0.12	
0.00/0.12	(VAR v_NonEmpty:S x1:S)
0.00/0.12	(RULES
0.00/0.12	a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.12	a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.12	b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.12	)
0.00/0.12	
0.00/0.12	Problem 1: 
0.00/0.12	
0.00/0.12	Dependency Pairs Processor:
0.00/0.12	-> Pairs:
0.00/0.12	 A(a(a(a(x1:S)))) -> B(a(a(a(x1:S))))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(a(a(b(x1:S))))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(a(b(x1:S)))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.12	 A(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.12	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.12	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.12	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.12	-> Rules:
0.00/0.12	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.12	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.12	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.12	
0.00/0.12	Problem 1: 
0.00/0.12	
0.00/0.12	SCC Processor:
0.00/0.12	-> Pairs:
0.00/0.12	 A(a(a(a(x1:S)))) -> B(a(a(a(x1:S))))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(a(a(b(x1:S))))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(a(b(x1:S)))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.12	 A(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.12	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.12	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.12	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.12	-> Rules:
0.00/0.12	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.12	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.12	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.12	->Strongly Connected Components:
0.00/0.12	->->Cycle:
0.00/0.12	->->-> Pairs:
0.00/0.12	 A(a(a(a(x1:S)))) -> B(a(a(a(x1:S))))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(a(a(b(x1:S))))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(a(b(x1:S)))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.12	 A(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.12	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.12	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.12	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.12	->->-> Rules:
0.00/0.12	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.12	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.12	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.12	
0.00/0.12	Problem 1: 
0.00/0.12	
0.00/0.12	Reduction Pair Processor:
0.00/0.12	-> Pairs:
0.00/0.12	 A(a(a(a(x1:S)))) -> B(a(a(a(x1:S))))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(a(a(b(x1:S))))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(a(b(x1:S)))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.12	 A(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.12	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.12	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.12	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.12	-> Rules:
0.00/0.12	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.12	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.12	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.12	-> Usable rules:
0.00/0.12	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.12	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.12	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.12	->Interpretation type:
0.00/0.12	 Linear
0.00/0.12	->Coefficients:
0.00/0.12	 Natural Numbers
0.00/0.12	->Dimension:
0.00/0.12	 1
0.00/0.12	->Bound:
0.00/0.12	 2
0.00/0.12	->Interpretation:
0.00/0.12	 
0.00/0.12	[a](X) = 2.X + 2
0.00/0.12	[b](X) = 2.X + 1
0.00/0.12	[A](X) = 2.X + 1
0.00/0.12	[B](X) = 2.X
0.00/0.12	
0.00/0.12	Problem 1: 
0.00/0.12	
0.00/0.12	SCC Processor:
0.00/0.12	-> Pairs:
0.00/0.12	 A(a(b(a(x1:S)))) -> A(a(a(b(x1:S))))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(a(b(x1:S)))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.12	 A(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.12	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.12	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.12	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.12	-> Rules:
0.00/0.12	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.12	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.12	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.12	->Strongly Connected Components:
0.00/0.12	->->Cycle:
0.00/0.12	->->-> Pairs:
0.00/0.12	 A(a(b(a(x1:S)))) -> A(a(a(b(x1:S))))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(a(b(x1:S)))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.12	 A(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.12	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.12	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.12	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.12	->->-> Rules:
0.00/0.12	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.12	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.12	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.12	
0.00/0.12	Problem 1: 
0.00/0.12	
0.00/0.12	Reduction Pair Processor:
0.00/0.12	-> Pairs:
0.00/0.12	 A(a(b(a(x1:S)))) -> A(a(a(b(x1:S))))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(a(b(x1:S)))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.12	 A(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.12	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.12	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.12	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.12	-> Rules:
0.00/0.12	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.12	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.12	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.12	-> Usable rules:
0.00/0.12	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.12	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.12	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.12	->Interpretation type:
0.00/0.12	 Linear
0.00/0.12	->Coefficients:
0.00/0.12	 Natural Numbers
0.00/0.12	->Dimension:
0.00/0.12	 1
0.00/0.12	->Bound:
0.00/0.12	 2
0.00/0.12	->Interpretation:
0.00/0.12	 
0.00/0.12	[a](X) = 2.X + 2
0.00/0.12	[b](X) = 2.X + 1
0.00/0.12	[A](X) = 2.X + 1
0.00/0.12	[B](X) = 2.X + 2
0.00/0.12	
0.00/0.12	Problem 1: 
0.00/0.12	
0.00/0.12	SCC Processor:
0.00/0.12	-> Pairs:
0.00/0.12	 A(a(b(a(x1:S)))) -> A(a(b(x1:S)))
0.00/0.12	 A(a(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.12	 A(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.12	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.12	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.12	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.12	-> Rules:
0.00/0.12	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.13	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.13	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.13	->Strongly Connected Components:
0.00/0.13	->->Cycle:
0.00/0.13	->->-> Pairs:
0.00/0.13	 A(a(b(a(x1:S)))) -> A(a(b(x1:S)))
0.00/0.13	 A(a(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.13	 A(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.13	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.13	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.13	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.13	->->-> Rules:
0.00/0.13	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.13	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.13	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	Reduction Pair Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 A(a(b(a(x1:S)))) -> A(a(b(x1:S)))
0.00/0.13	 A(a(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.13	 A(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.13	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.13	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.13	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.13	-> Rules:
0.00/0.13	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.13	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.13	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.13	-> Usable rules:
0.00/0.13	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.13	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.13	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.13	->Interpretation type:
0.00/0.13	 Linear
0.00/0.13	->Coefficients:
0.00/0.13	 Natural Numbers
0.00/0.13	->Dimension:
0.00/0.13	 1
0.00/0.13	->Bound:
0.00/0.13	 2
0.00/0.13	->Interpretation:
0.00/0.13	 
0.00/0.13	[a](X) = 2.X + 2
0.00/0.13	[b](X) = 2.X + 2
0.00/0.13	[A](X) = 2.X + 2
0.00/0.13	[B](X) = 2.X + 2
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	SCC Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 A(a(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.13	 A(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.13	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.13	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.13	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.13	-> Rules:
0.00/0.13	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.13	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.13	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.13	->Strongly Connected Components:
0.00/0.13	->->Cycle:
0.00/0.13	->->-> Pairs:
0.00/0.13	 A(a(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.13	 A(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.13	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.13	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.13	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.13	->->-> Rules:
0.00/0.13	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.13	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.13	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	Reduction Pair Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 A(a(b(a(x1:S)))) -> A(b(x1:S))
0.00/0.13	 A(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.13	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.13	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.13	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.13	-> Rules:
0.00/0.13	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.13	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.13	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.13	-> Usable rules:
0.00/0.13	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.13	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.13	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.13	->Interpretation type:
0.00/0.13	 Linear
0.00/0.13	->Coefficients:
0.00/0.13	 Natural Numbers
0.00/0.13	->Dimension:
0.00/0.13	 1
0.00/0.13	->Bound:
0.00/0.13	 2
0.00/0.13	->Interpretation:
0.00/0.13	 
0.00/0.13	[a](X) = 2.X + 1
0.00/0.13	[b](X) = 2.X
0.00/0.13	[A](X) = 2.X + 2
0.00/0.13	[B](X) = 2.X + 2
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	SCC Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 A(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.13	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.13	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.13	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.13	-> Rules:
0.00/0.13	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.13	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.13	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.13	->Strongly Connected Components:
0.00/0.13	->->Cycle:
0.00/0.13	->->-> Pairs:
0.00/0.13	 A(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.13	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.13	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.13	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.13	->->-> Rules:
0.00/0.13	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.13	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.13	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	Reduction Pair Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 A(a(b(a(x1:S)))) -> B(x1:S)
0.00/0.13	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.13	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.13	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.13	-> Rules:
0.00/0.13	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.13	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.13	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.13	-> Usable rules:
0.00/0.13	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.13	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.13	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.13	->Interpretation type:
0.00/0.13	 Linear
0.00/0.13	->Coefficients:
0.00/0.13	 Natural Numbers
0.00/0.13	->Dimension:
0.00/0.13	 1
0.00/0.13	->Bound:
0.00/0.13	 2
0.00/0.13	->Interpretation:
0.00/0.13	 
0.00/0.13	[a](X) = 2.X + 2
0.00/0.13	[b](X) = 2.X + 2
0.00/0.13	[A](X) = 2.X + 2
0.00/0.13	[B](X) = 2.X + 2
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	SCC Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 B(b(a(b(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.13	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
0.00/0.13	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.13	-> Rules:
0.00/0.13	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.13	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.13	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.13	->Strongly Connected Components:
0.00/0.13	->->Cycle:
0.00/0.13	->->-> Pairs:
0.00/0.13	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.13	->->-> Rules:
0.00/0.13	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.13	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.13	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	Subterm Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 B(b(a(b(x1:S)))) -> B(b(x1:S))
0.00/0.13	-> Rules:
0.00/0.13	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.13	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.13	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.13	->Projection:
0.00/0.13	 pi(B) = 1
0.00/0.13	
0.00/0.13	Problem 1: 
0.00/0.13	
0.00/0.13	SCC Processor:
0.00/0.13	-> Pairs:
0.00/0.13	 Empty
0.00/0.13	-> Rules:
0.00/0.13	 a(a(a(a(x1:S)))) -> b(a(a(a(x1:S))))
0.00/0.13	 a(a(b(a(x1:S)))) -> a(a(a(b(x1:S))))
0.00/0.13	 b(b(a(b(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.13	->Strongly Connected Components:
0.00/0.13	 There is no strongly connected component
0.00/0.13	
0.00/0.13	The problem is finite.
0.00/0.13	EOF