94.25/95.25	YES
94.25/95.25	
94.25/95.25	Problem 1: 
94.25/95.25	
94.25/95.25	(VAR v_NonEmpty:S x1:S)
94.25/95.25	(RULES
94.25/95.25	a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	)
94.25/95.25	
94.25/95.25	Problem 1: 
94.25/95.25	
94.25/95.25	Dependency Pairs Processor:
94.25/95.25	-> Pairs:
94.25/95.25	 A(a(a(a(x1:S)))) -> A(b(a(x1:S)))
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
94.25/95.25	 B(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	
94.25/95.25	Problem 1: 
94.25/95.25	
94.25/95.25	SCC Processor:
94.25/95.25	-> Pairs:
94.25/95.25	 A(a(a(a(x1:S)))) -> A(b(a(x1:S)))
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
94.25/95.25	 B(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	->Strongly Connected Components:
94.25/95.25	->->Cycle:
94.25/95.25	->->-> Pairs:
94.25/95.25	 A(a(a(a(x1:S)))) -> A(b(a(x1:S)))
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
94.25/95.25	 B(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	->->-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	
94.25/95.25	Problem 1: 
94.25/95.25	
94.25/95.25	Reduction Pair Processor:
94.25/95.25	-> Pairs:
94.25/95.25	 A(a(a(a(x1:S)))) -> A(b(a(x1:S)))
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
94.25/95.25	 B(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	-> Usable rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	->Interpretation type:
94.25/95.25	 Linear
94.25/95.25	->Coefficients:
94.25/95.25	 Natural Numbers
94.25/95.25	->Dimension:
94.25/95.25	 1
94.25/95.25	->Bound:
94.25/95.25	 2
94.25/95.25	->Interpretation:
94.25/95.25	 
94.25/95.25	[a](X) = X + 1
94.25/95.25	[b](X) = X + 1
94.25/95.25	[A](X) = X + 2
94.25/95.25	[B](X) = X + 2
94.25/95.25	
94.25/95.25	Problem 1: 
94.25/95.25	
94.25/95.25	SCC Processor:
94.25/95.25	-> Pairs:
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
94.25/95.25	 B(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	->Strongly Connected Components:
94.25/95.25	->->Cycle:
94.25/95.25	->->-> Pairs:
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
94.25/95.25	 B(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	->->-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	
94.25/95.25	Problem 1: 
94.25/95.25	
94.25/95.25	Reduction Pair Processor:
94.25/95.25	-> Pairs:
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
94.25/95.25	 B(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	-> Usable rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	->Interpretation type:
94.25/95.25	 Linear
94.25/95.25	->Coefficients:
94.25/95.25	 Natural Numbers
94.25/95.25	->Dimension:
94.25/95.25	 1
94.25/95.25	->Bound:
94.25/95.25	 2
94.25/95.25	->Interpretation:
94.25/95.25	 
94.25/95.25	[a](X) = 2.X + 1
94.25/95.25	[b](X) = 2.X + 1
94.25/95.25	[A](X) = 2.X + 2
94.25/95.25	[B](X) = 2.X + 2
94.25/95.25	
94.25/95.25	Problem 1: 
94.25/95.25	
94.25/95.25	SCC Processor:
94.25/95.25	-> Pairs:
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
94.25/95.25	 B(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	->Strongly Connected Components:
94.25/95.25	->->Cycle:
94.25/95.25	->->-> Pairs:
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
94.25/95.25	 B(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	->->-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	
94.25/95.25	Problem 1: 
94.25/95.25	
94.25/95.25	Reduction Pair Processor:
94.25/95.25	-> Pairs:
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(b(a(x1:S)))
94.25/95.25	 B(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	-> Usable rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	->Interpretation type:
94.25/95.25	 Linear
94.25/95.25	->Coefficients:
94.25/95.25	 Natural Numbers
94.25/95.25	->Dimension:
94.25/95.25	 1
94.25/95.25	->Bound:
94.25/95.25	 2
94.25/95.25	->Interpretation:
94.25/95.25	 
94.25/95.25	[a](X) = 2.X + 2
94.25/95.25	[b](X) = 2.X + 2
94.25/95.25	[A](X) = X + 1
94.25/95.25	[B](X) = X + 1
94.25/95.25	
94.25/95.25	Problem 1: 
94.25/95.25	
94.25/95.25	SCC Processor:
94.25/95.25	-> Pairs:
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	->Strongly Connected Components:
94.25/95.25	->->Cycle:
94.25/95.25	->->-> Pairs:
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	->->-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	
94.25/95.25	Problem 1: 
94.25/95.25	
94.25/95.25	Reduction Pair Processor:
94.25/95.25	-> Pairs:
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> B(a(x1:S))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	-> Usable rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	->Interpretation type:
94.25/95.25	 Linear
94.25/95.25	->Coefficients:
94.25/95.25	 Natural Numbers
94.25/95.25	->Dimension:
94.25/95.25	 1
94.25/95.25	->Bound:
94.25/95.25	 2
94.25/95.25	->Interpretation:
94.25/95.25	 
94.25/95.25	[a](X) = 2.X + 2
94.25/95.25	[b](X) = 2.X + 2
94.25/95.25	[A](X) = X + 2
94.25/95.25	[B](X) = X + 2
94.25/95.25	
94.25/95.25	Problem 1: 
94.25/95.25	
94.25/95.25	SCC Processor:
94.25/95.25	-> Pairs:
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	->Strongly Connected Components:
94.25/95.25	->->Cycle:
94.25/95.25	->->-> Pairs:
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	->->-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	
94.25/95.25	Problem 1: 
94.25/95.25	
94.25/95.25	Reduction Pair Processor:
94.25/95.25	-> Pairs:
94.25/95.25	 A(a(a(a(x1:S)))) -> B(a(b(a(x1:S))))
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	-> Usable rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	->Interpretation type:
94.25/95.25	 Linear
94.25/95.25	->Coefficients:
94.25/95.25	 Natural Numbers
94.25/95.25	->Dimension:
94.25/95.25	 2
94.25/95.25	->Bound:
94.25/95.25	 1
94.25/95.25	->Interpretation:
94.25/95.25	 
94.25/95.25	[a](X) = [1 0;1 0].X + [1;0]
94.25/95.25	[b](X) = [0 1;0 1].X + [1;1]
94.25/95.25	[A](X) = [1 1;1 0].X
94.25/95.25	[B](X) = [1 1;1 0].X + [0;1]
94.25/95.25	
94.25/95.25	Problem 1: 
94.25/95.25	
94.25/95.25	SCC Processor:
94.25/95.25	-> Pairs:
94.25/95.25	 B(a(a(a(x1:S)))) -> A(a(b(a(x1:S))))
94.25/95.25	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
94.25/95.25	-> Rules:
94.25/95.25	 a(a(a(a(x1:S)))) -> b(a(b(a(x1:S))))
94.25/95.25	 b(a(a(a(x1:S)))) -> a(a(b(a(x1:S))))
94.25/95.25	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
94.25/95.25	->Strongly Connected Components:
94.25/95.25	 There is no strongly connected component
94.25/95.25	
94.25/95.25	The problem is finite.
94.25/141.30	EOF