0.44/0.57	YES
0.44/0.57	
0.44/0.57	Problem 1: 
0.44/0.57	
0.44/0.57	(VAR v_NonEmpty:S x1:S)
0.44/0.57	(RULES
0.44/0.57	a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.57	b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.57	)
0.44/0.57	
0.44/0.57	Problem 1: 
0.44/0.57	
0.44/0.57	Dependency Pairs Processor:
0.44/0.57	-> Pairs:
0.44/0.57	 A(a(b(x1:S))) -> A(a(a(x1:S)))
0.44/0.57	 A(a(b(x1:S))) -> A(a(x1:S))
0.44/0.57	 A(a(b(x1:S))) -> A(x1:S)
0.44/0.57	 A(a(b(x1:S))) -> B(a(a(a(x1:S))))
0.44/0.57	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.57	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.57	 B(a(b(a(x1:S)))) -> B(x1:S)
0.44/0.57	-> Rules:
0.44/0.57	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.57	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.57	
0.44/0.57	Problem 1: 
0.44/0.57	
0.44/0.57	SCC Processor:
0.44/0.57	-> Pairs:
0.44/0.57	 A(a(b(x1:S))) -> A(a(a(x1:S)))
0.44/0.57	 A(a(b(x1:S))) -> A(a(x1:S))
0.44/0.57	 A(a(b(x1:S))) -> A(x1:S)
0.44/0.57	 A(a(b(x1:S))) -> B(a(a(a(x1:S))))
0.44/0.57	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.57	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.57	 B(a(b(a(x1:S)))) -> B(x1:S)
0.44/0.57	-> Rules:
0.44/0.57	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.57	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.57	->Strongly Connected Components:
0.44/0.57	->->Cycle:
0.44/0.57	->->-> Pairs:
0.44/0.57	 A(a(b(x1:S))) -> A(a(a(x1:S)))
0.44/0.57	 A(a(b(x1:S))) -> A(a(x1:S))
0.44/0.57	 A(a(b(x1:S))) -> A(x1:S)
0.44/0.57	 A(a(b(x1:S))) -> B(a(a(a(x1:S))))
0.44/0.57	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.57	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(x1:S)
0.44/0.58	->->-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	
0.44/0.58	Problem 1: 
0.44/0.58	
0.44/0.58	Reduction Pair Processor:
0.44/0.58	-> Pairs:
0.44/0.58	 A(a(b(x1:S))) -> A(a(a(x1:S)))
0.44/0.58	 A(a(b(x1:S))) -> A(a(x1:S))
0.44/0.58	 A(a(b(x1:S))) -> A(x1:S)
0.44/0.58	 A(a(b(x1:S))) -> B(a(a(a(x1:S))))
0.44/0.58	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(x1:S)
0.44/0.58	-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	-> Usable rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	->Interpretation type:
0.44/0.58	 Linear
0.44/0.58	->Coefficients:
0.44/0.58	 Natural Numbers
0.44/0.58	->Dimension:
0.44/0.58	 1
0.44/0.58	->Bound:
0.44/0.58	 2
0.44/0.58	->Interpretation:
0.44/0.58	 
0.44/0.58	[a](X) = X
0.44/0.58	[b](X) = 2.X + 2
0.44/0.58	[A](X) = X
0.44/0.58	[B](X) = 2.X + 2
0.44/0.58	
0.44/0.58	Problem 1: 
0.44/0.58	
0.44/0.58	SCC Processor:
0.44/0.58	-> Pairs:
0.44/0.58	 A(a(b(x1:S))) -> A(a(x1:S))
0.44/0.58	 A(a(b(x1:S))) -> A(x1:S)
0.44/0.58	 A(a(b(x1:S))) -> B(a(a(a(x1:S))))
0.44/0.58	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(x1:S)
0.44/0.58	-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	->Strongly Connected Components:
0.44/0.58	->->Cycle:
0.44/0.58	->->-> Pairs:
0.44/0.58	 A(a(b(x1:S))) -> A(a(x1:S))
0.44/0.58	 A(a(b(x1:S))) -> A(x1:S)
0.44/0.58	 A(a(b(x1:S))) -> B(a(a(a(x1:S))))
0.44/0.58	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(x1:S)
0.44/0.58	->->-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	
0.44/0.58	Problem 1: 
0.44/0.58	
0.44/0.58	Reduction Pair Processor:
0.44/0.58	-> Pairs:
0.44/0.58	 A(a(b(x1:S))) -> A(a(x1:S))
0.44/0.58	 A(a(b(x1:S))) -> A(x1:S)
0.44/0.58	 A(a(b(x1:S))) -> B(a(a(a(x1:S))))
0.44/0.58	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(x1:S)
0.44/0.58	-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	-> Usable rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	->Interpretation type:
0.44/0.58	 Linear
0.44/0.58	->Coefficients:
0.44/0.58	 Natural Numbers
0.44/0.58	->Dimension:
0.44/0.58	 1
0.44/0.58	->Bound:
0.44/0.58	 2
0.44/0.58	->Interpretation:
0.44/0.58	 
0.44/0.58	[a](X) = X
0.44/0.58	[b](X) = 2.X + 1
0.44/0.58	[A](X) = X + 1
0.44/0.58	[B](X) = 2.X + 2
0.44/0.58	
0.44/0.58	Problem 1: 
0.44/0.58	
0.44/0.58	SCC Processor:
0.44/0.58	-> Pairs:
0.44/0.58	 A(a(b(x1:S))) -> A(x1:S)
0.44/0.58	 A(a(b(x1:S))) -> B(a(a(a(x1:S))))
0.44/0.58	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(x1:S)
0.44/0.58	-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	->Strongly Connected Components:
0.44/0.58	->->Cycle:
0.44/0.58	->->-> Pairs:
0.44/0.58	 A(a(b(x1:S))) -> A(x1:S)
0.44/0.58	 A(a(b(x1:S))) -> B(a(a(a(x1:S))))
0.44/0.58	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(x1:S)
0.44/0.58	->->-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	
0.44/0.58	Problem 1: 
0.44/0.58	
0.44/0.58	Reduction Pair Processor:
0.44/0.58	-> Pairs:
0.44/0.58	 A(a(b(x1:S))) -> A(x1:S)
0.44/0.58	 A(a(b(x1:S))) -> B(a(a(a(x1:S))))
0.44/0.58	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(x1:S)
0.44/0.58	-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	-> Usable rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	->Interpretation type:
0.44/0.58	 Linear
0.44/0.58	->Coefficients:
0.44/0.58	 Natural Numbers
0.44/0.58	->Dimension:
0.44/0.58	 1
0.44/0.58	->Bound:
0.44/0.58	 2
0.44/0.58	->Interpretation:
0.44/0.58	 
0.44/0.58	[a](X) = X
0.44/0.58	[b](X) = 2.X + 2
0.44/0.58	[A](X) = X
0.44/0.58	[B](X) = 2.X + 2
0.44/0.58	
0.44/0.58	Problem 1: 
0.44/0.58	
0.44/0.58	SCC Processor:
0.44/0.58	-> Pairs:
0.44/0.58	 A(a(b(x1:S))) -> B(a(a(a(x1:S))))
0.44/0.58	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(x1:S)
0.44/0.58	-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	->Strongly Connected Components:
0.44/0.58	->->Cycle:
0.44/0.58	->->-> Pairs:
0.44/0.58	 A(a(b(x1:S))) -> B(a(a(a(x1:S))))
0.44/0.58	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(x1:S)
0.44/0.58	->->-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	
0.44/0.58	Problem 1: 
0.44/0.58	
0.44/0.58	Reduction Pair Processor:
0.44/0.58	-> Pairs:
0.44/0.58	 A(a(b(x1:S))) -> B(a(a(a(x1:S))))
0.44/0.58	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(x1:S)
0.44/0.58	-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	-> Usable rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	->Interpretation type:
0.44/0.58	 Linear
0.44/0.58	->Coefficients:
0.44/0.58	 Natural Numbers
0.44/0.58	->Dimension:
0.44/0.58	 1
0.44/0.58	->Bound:
0.44/0.58	 2
0.44/0.58	->Interpretation:
0.44/0.58	 
0.44/0.58	[a](X) = X
0.44/0.58	[b](X) = 2.X + 2
0.44/0.58	[A](X) = X
0.44/0.58	[B](X) = 2.X + 2
0.44/0.58	
0.44/0.58	Problem 1: 
0.44/0.58	
0.44/0.58	SCC Processor:
0.44/0.58	-> Pairs:
0.44/0.58	 A(a(b(x1:S))) -> B(a(a(a(x1:S))))
0.44/0.58	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	->Strongly Connected Components:
0.44/0.58	->->Cycle:
0.44/0.58	->->-> Pairs:
0.44/0.58	 A(a(b(x1:S))) -> B(a(a(a(x1:S))))
0.44/0.58	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	->->-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	
0.44/0.58	Problem 1: 
0.44/0.58	
0.44/0.58	Reduction Pair Processor:
0.44/0.58	-> Pairs:
0.44/0.58	 A(a(b(x1:S))) -> B(a(a(a(x1:S))))
0.44/0.58	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	-> Usable rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	->Interpretation type:
0.44/0.58	 Linear
0.44/0.58	->Coefficients:
0.44/0.58	 All rationals
0.44/0.58	->Dimension:
0.44/0.58	 1
0.44/0.58	->Bound:
0.44/0.58	 4
0.44/0.58	->Interpretation:
0.44/0.58	 
0.44/0.58	[a](X) = X + 2
0.44/0.58	[b](X) = 2/3.X + 2
0.44/0.58	[A](X) = 3.X + 1/3
0.44/0.58	[B](X) = 2.X
0.44/0.58	
0.44/0.58	Problem 1: 
0.44/0.58	
0.44/0.58	SCC Processor:
0.44/0.58	-> Pairs:
0.44/0.58	 B(a(b(a(x1:S)))) -> A(b(b(x1:S)))
0.44/0.58	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	->Strongly Connected Components:
0.44/0.58	->->Cycle:
0.44/0.58	->->-> Pairs:
0.44/0.58	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	->->-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	
0.44/0.58	Problem 1: 
0.44/0.58	
0.44/0.58	Reduction Pair Processor:
0.44/0.58	-> Pairs:
0.44/0.58	 B(a(b(a(x1:S)))) -> B(b(x1:S))
0.44/0.58	-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	-> Usable rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	->Interpretation type:
0.44/0.58	 Linear
0.44/0.58	->Coefficients:
0.44/0.58	 All rationals
0.44/0.58	->Dimension:
0.44/0.58	 1
0.44/0.58	->Bound:
0.44/0.58	 4
0.44/0.58	->Interpretation:
0.44/0.58	 
0.44/0.58	[a](X) = X + 1/4
0.44/0.58	[b](X) = 2/3.X + 2
0.44/0.58	[B](X) = 4.X
0.44/0.58	
0.44/0.58	Problem 1: 
0.44/0.58	
0.44/0.58	SCC Processor:
0.44/0.58	-> Pairs:
0.44/0.58	 Empty
0.44/0.58	-> Rules:
0.44/0.58	 a(a(b(x1:S))) -> b(a(a(a(x1:S))))
0.44/0.58	 b(a(b(a(x1:S)))) -> a(b(b(x1:S)))
0.44/0.58	->Strongly Connected Components:
0.44/0.58	 There is no strongly connected component
0.44/0.58	
0.44/0.58	The problem is finite.
0.44/0.58	EOF