0.00/0.31	YES
0.00/0.31	
0.00/0.31	Problem 1: 
0.00/0.31	
0.00/0.31	(VAR v_NonEmpty:S x1:S)
0.00/0.31	(RULES
0.00/0.31	a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	)
0.00/0.31	
0.00/0.31	Problem 1: 
0.00/0.31	
0.00/0.31	Dependency Pairs Processor:
0.00/0.31	-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> A(a(b(x1:S)))
0.00/0.31	 A(a(a(x1:S))) -> A(b(x1:S))
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 A(a(a(x1:S))) -> B(x1:S)
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	 B(a(x1:S)) -> B(x1:S)
0.00/0.31	 B(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.31	-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	
0.00/0.31	Problem 1: 
0.00/0.31	
0.00/0.31	SCC Processor:
0.00/0.31	-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> A(a(b(x1:S)))
0.00/0.31	 A(a(a(x1:S))) -> A(b(x1:S))
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 A(a(a(x1:S))) -> B(x1:S)
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	 B(a(x1:S)) -> B(x1:S)
0.00/0.31	 B(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.31	-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	->Strongly Connected Components:
0.00/0.31	->->Cycle:
0.00/0.31	->->-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> A(a(b(x1:S)))
0.00/0.31	 A(a(a(x1:S))) -> A(b(x1:S))
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 A(a(a(x1:S))) -> B(x1:S)
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	 B(a(x1:S)) -> B(x1:S)
0.00/0.31	 B(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.31	->->-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	
0.00/0.31	Problem 1: 
0.00/0.31	
0.00/0.31	Reduction Pair Processor:
0.00/0.31	-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> A(a(b(x1:S)))
0.00/0.31	 A(a(a(x1:S))) -> A(b(x1:S))
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 A(a(a(x1:S))) -> B(x1:S)
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	 B(a(x1:S)) -> B(x1:S)
0.00/0.31	 B(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.31	-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	-> Usable rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	->Interpretation type:
0.00/0.31	 Linear
0.00/0.31	->Coefficients:
0.00/0.31	 Natural Numbers
0.00/0.31	->Dimension:
0.00/0.31	 1
0.00/0.31	->Bound:
0.00/0.31	 2
0.00/0.31	->Interpretation:
0.00/0.31	 
0.00/0.31	[a](X) = X + 2
0.00/0.31	[b](X) = X + 1
0.00/0.31	[A](X) = X + 1
0.00/0.31	[B](X) = X
0.00/0.31	
0.00/0.31	Problem 1: 
0.00/0.31	
0.00/0.31	SCC Processor:
0.00/0.31	-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> A(b(x1:S))
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 A(a(a(x1:S))) -> B(x1:S)
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	 B(a(x1:S)) -> B(x1:S)
0.00/0.31	 B(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.31	-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	->Strongly Connected Components:
0.00/0.31	->->Cycle:
0.00/0.31	->->-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> A(b(x1:S))
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 A(a(a(x1:S))) -> B(x1:S)
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	 B(a(x1:S)) -> B(x1:S)
0.00/0.31	 B(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.31	->->-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	
0.00/0.31	Problem 1: 
0.00/0.31	
0.00/0.31	Reduction Pair Processor:
0.00/0.31	-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> A(b(x1:S))
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 A(a(a(x1:S))) -> B(x1:S)
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	 B(a(x1:S)) -> B(x1:S)
0.00/0.31	 B(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.31	-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	-> Usable rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	->Interpretation type:
0.00/0.31	 Linear
0.00/0.31	->Coefficients:
0.00/0.31	 Natural Numbers
0.00/0.31	->Dimension:
0.00/0.31	 1
0.00/0.31	->Bound:
0.00/0.31	 2
0.00/0.31	->Interpretation:
0.00/0.31	 
0.00/0.31	[a](X) = X + 2
0.00/0.31	[b](X) = X + 1
0.00/0.31	[A](X) = 2.X + 2
0.00/0.31	[B](X) = 2.X
0.00/0.31	
0.00/0.31	Problem 1: 
0.00/0.31	
0.00/0.31	SCC Processor:
0.00/0.31	-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 A(a(a(x1:S))) -> B(x1:S)
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	 B(a(x1:S)) -> B(x1:S)
0.00/0.31	 B(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.31	-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	->Strongly Connected Components:
0.00/0.31	->->Cycle:
0.00/0.31	->->-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 A(a(a(x1:S))) -> B(x1:S)
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	 B(a(x1:S)) -> B(x1:S)
0.00/0.31	 B(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.31	->->-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	
0.00/0.31	Problem 1: 
0.00/0.31	
0.00/0.31	Reduction Pair Processor:
0.00/0.31	-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 A(a(a(x1:S))) -> B(x1:S)
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	 B(a(x1:S)) -> B(x1:S)
0.00/0.31	 B(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.31	-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	-> Usable rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	->Interpretation type:
0.00/0.31	 Linear
0.00/0.31	->Coefficients:
0.00/0.31	 Natural Numbers
0.00/0.31	->Dimension:
0.00/0.31	 1
0.00/0.31	->Bound:
0.00/0.31	 2
0.00/0.31	->Interpretation:
0.00/0.31	 
0.00/0.31	[a](X) = X + 2
0.00/0.31	[b](X) = X + 1
0.00/0.31	[A](X) = X + 1
0.00/0.31	[B](X) = X
0.00/0.31	
0.00/0.31	Problem 1: 
0.00/0.31	
0.00/0.31	SCC Processor:
0.00/0.31	-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	 B(a(x1:S)) -> B(x1:S)
0.00/0.31	 B(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.31	-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	->Strongly Connected Components:
0.00/0.31	->->Cycle:
0.00/0.31	->->-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	 B(a(x1:S)) -> B(x1:S)
0.00/0.31	 B(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.31	->->-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	
0.00/0.31	Problem 1: 
0.00/0.31	
0.00/0.31	Reduction Pair Processor:
0.00/0.31	-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	 B(a(x1:S)) -> B(x1:S)
0.00/0.31	 B(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.31	-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	-> Usable rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	->Interpretation type:
0.00/0.31	 Linear
0.00/0.31	->Coefficients:
0.00/0.31	 Natural Numbers
0.00/0.31	->Dimension:
0.00/0.31	 1
0.00/0.31	->Bound:
0.00/0.31	 2
0.00/0.31	->Interpretation:
0.00/0.31	 
0.00/0.31	[a](X) = X + 2
0.00/0.31	[b](X) = X + 1
0.00/0.31	[A](X) = 2.X + 2
0.00/0.31	[B](X) = 2.X
0.00/0.31	
0.00/0.31	Problem 1: 
0.00/0.31	
0.00/0.31	SCC Processor:
0.00/0.31	-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	 B(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.31	-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	->Strongly Connected Components:
0.00/0.31	->->Cycle:
0.00/0.31	->->-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	 B(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.31	->->-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	
0.00/0.31	Problem 1: 
0.00/0.31	
0.00/0.31	Reduction Pair Processor:
0.00/0.31	-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	 B(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.31	-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	-> Usable rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	->Interpretation type:
0.00/0.31	 Linear
0.00/0.31	->Coefficients:
0.00/0.31	 Natural Numbers
0.00/0.31	->Dimension:
0.00/0.31	 1
0.00/0.31	->Bound:
0.00/0.31	 2
0.00/0.31	->Interpretation:
0.00/0.31	 
0.00/0.31	[a](X) = X + 2
0.00/0.31	[b](X) = X + 1
0.00/0.31	[A](X) = 2.X + 2
0.00/0.31	[B](X) = 2.X
0.00/0.31	
0.00/0.31	Problem 1: 
0.00/0.31	
0.00/0.31	SCC Processor:
0.00/0.31	-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	->Strongly Connected Components:
0.00/0.31	->->Cycle:
0.00/0.31	->->-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	->->-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	
0.00/0.31	Problem 1: 
0.00/0.31	
0.00/0.31	Reduction Pair Processor:
0.00/0.31	-> Pairs:
0.00/0.31	 A(a(a(x1:S))) -> B(a(a(b(x1:S))))
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	-> Usable rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	->Interpretation type:
0.00/0.31	 Linear
0.00/0.31	->Coefficients:
0.00/0.31	 All rationals
0.00/0.31	->Dimension:
0.00/0.31	 1
0.00/0.31	->Bound:
0.00/0.31	 2
0.00/0.31	->Interpretation:
0.00/0.31	 
0.00/0.31	[a](X) = X + 2
0.00/0.31	[b](X) = X + 1/2
0.00/0.31	[A](X) = X + 1
0.00/0.31	[B](X) = X
0.00/0.31	
0.00/0.31	Problem 1: 
0.00/0.31	
0.00/0.31	SCC Processor:
0.00/0.31	-> Pairs:
0.00/0.31	 B(a(x1:S)) -> A(b(x1:S))
0.00/0.31	-> Rules:
0.00/0.31	 a(a(a(x1:S))) -> b(a(a(b(x1:S))))
0.00/0.31	 b(a(x1:S)) -> a(b(x1:S))
0.00/0.31	 b(b(b(b(x1:S)))) -> a(x1:S)
0.00/0.31	->Strongly Connected Components:
0.00/0.31	 There is no strongly connected component
0.00/0.31	
0.00/0.31	The problem is finite.
0.00/0.31	EOF