0.00/0.09	YES
0.00/0.09	
0.00/0.09	Problem 1: 
0.00/0.09	
0.00/0.09	(VAR v_NonEmpty:S x1:S)
0.00/0.09	(RULES
0.00/0.09	a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	)
0.00/0.09	
0.00/0.09	Problem 1: 
0.00/0.09	
0.00/0.09	Dependency Pairs Processor:
0.00/0.09	-> Pairs:
0.00/0.09	 A(b(a(x1:S))) -> A(a(b(b(a(a(x1:S))))))
0.00/0.09	 A(b(a(x1:S))) -> A(a(x1:S))
0.00/0.09	 A(b(a(x1:S))) -> A(b(b(a(a(x1:S)))))
0.00/0.09	 A(b(a(x1:S))) -> B(a(a(x1:S)))
0.00/0.09	 A(b(a(x1:S))) -> B(b(a(a(x1:S))))
0.00/0.09	 B(a(a(b(x1:S)))) -> B(a(b(x1:S)))
0.00/0.09	-> Rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	
0.00/0.09	Problem 1: 
0.00/0.09	
0.00/0.09	SCC Processor:
0.00/0.09	-> Pairs:
0.00/0.09	 A(b(a(x1:S))) -> A(a(b(b(a(a(x1:S))))))
0.00/0.09	 A(b(a(x1:S))) -> A(a(x1:S))
0.00/0.09	 A(b(a(x1:S))) -> A(b(b(a(a(x1:S)))))
0.00/0.09	 A(b(a(x1:S))) -> B(a(a(x1:S)))
0.00/0.09	 A(b(a(x1:S))) -> B(b(a(a(x1:S))))
0.00/0.09	 B(a(a(b(x1:S)))) -> B(a(b(x1:S)))
0.00/0.09	-> Rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	->Strongly Connected Components:
0.00/0.09	->->Cycle:
0.00/0.09	->->-> Pairs:
0.00/0.09	 B(a(a(b(x1:S)))) -> B(a(b(x1:S)))
0.00/0.09	->->-> Rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	->->Cycle:
0.00/0.09	->->-> Pairs:
0.00/0.09	 A(b(a(x1:S))) -> A(a(b(b(a(a(x1:S))))))
0.00/0.09	 A(b(a(x1:S))) -> A(a(x1:S))
0.00/0.09	 A(b(a(x1:S))) -> A(b(b(a(a(x1:S)))))
0.00/0.09	->->-> Rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	
0.00/0.09	
0.00/0.09	The problem is decomposed in 2 subproblems.
0.00/0.09	
0.00/0.09	Problem 1.1: 
0.00/0.09	
0.00/0.09	Subterm Processor:
0.00/0.09	-> Pairs:
0.00/0.09	 B(a(a(b(x1:S)))) -> B(a(b(x1:S)))
0.00/0.09	-> Rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	->Projection:
0.00/0.09	 pi(B) = 1
0.00/0.09	
0.00/0.09	Problem 1.1: 
0.00/0.09	
0.00/0.09	SCC Processor:
0.00/0.09	-> Pairs:
0.00/0.09	 Empty
0.00/0.09	-> Rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	->Strongly Connected Components:
0.00/0.09	 There is no strongly connected component
0.00/0.09	
0.00/0.09	The problem is finite.
0.00/0.09	
0.00/0.09	Problem 1.2: 
0.00/0.09	
0.00/0.09	Reduction Pair Processor:
0.00/0.09	-> Pairs:
0.00/0.09	 A(b(a(x1:S))) -> A(a(b(b(a(a(x1:S))))))
0.00/0.09	 A(b(a(x1:S))) -> A(a(x1:S))
0.00/0.09	 A(b(a(x1:S))) -> A(b(b(a(a(x1:S)))))
0.00/0.09	-> Rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	-> Usable rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	->Interpretation type:
0.00/0.09	 Linear
0.00/0.09	->Coefficients:
0.00/0.09	 Natural Numbers
0.00/0.09	->Dimension:
0.00/0.09	 1
0.00/0.09	->Bound:
0.00/0.09	 2
0.00/0.09	->Interpretation:
0.00/0.09	 
0.00/0.09	[a](X) = 0
0.00/0.09	[b](X) = 2
0.00/0.09	[A](X) = 2.X
0.00/0.09	
0.00/0.09	Problem 1.2: 
0.00/0.09	
0.00/0.09	SCC Processor:
0.00/0.09	-> Pairs:
0.00/0.09	 A(b(a(x1:S))) -> A(a(x1:S))
0.00/0.09	 A(b(a(x1:S))) -> A(b(b(a(a(x1:S)))))
0.00/0.09	-> Rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	->Strongly Connected Components:
0.00/0.09	->->Cycle:
0.00/0.09	->->-> Pairs:
0.00/0.09	 A(b(a(x1:S))) -> A(a(x1:S))
0.00/0.09	 A(b(a(x1:S))) -> A(b(b(a(a(x1:S)))))
0.00/0.09	->->-> Rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	
0.00/0.09	Problem 1.2: 
0.00/0.09	
0.00/0.09	Reduction Pair Processor:
0.00/0.09	-> Pairs:
0.00/0.09	 A(b(a(x1:S))) -> A(a(x1:S))
0.00/0.09	 A(b(a(x1:S))) -> A(b(b(a(a(x1:S)))))
0.00/0.09	-> Rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	-> Usable rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	->Interpretation type:
0.00/0.09	 Linear
0.00/0.09	->Coefficients:
0.00/0.09	 Natural Numbers
0.00/0.09	->Dimension:
0.00/0.09	 1
0.00/0.09	->Bound:
0.00/0.09	 2
0.00/0.09	->Interpretation:
0.00/0.09	 
0.00/0.09	[a](X) = 0
0.00/0.09	[b](X) = 2
0.00/0.09	[A](X) = 2.X
0.00/0.09	
0.00/0.09	Problem 1.2: 
0.00/0.09	
0.00/0.09	SCC Processor:
0.00/0.09	-> Pairs:
0.00/0.09	 A(b(a(x1:S))) -> A(b(b(a(a(x1:S)))))
0.00/0.09	-> Rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	->Strongly Connected Components:
0.00/0.09	->->Cycle:
0.00/0.09	->->-> Pairs:
0.00/0.09	 A(b(a(x1:S))) -> A(b(b(a(a(x1:S)))))
0.00/0.09	->->-> Rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	
0.00/0.09	Problem 1.2: 
0.00/0.09	
0.00/0.09	Reduction Pair Processor:
0.00/0.09	-> Pairs:
0.00/0.09	 A(b(a(x1:S))) -> A(b(b(a(a(x1:S)))))
0.00/0.09	-> Rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	-> Usable rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	->Interpretation type:
0.00/0.09	 Linear
0.00/0.09	->Coefficients:
0.00/0.09	 All rationals
0.00/0.09	->Dimension:
0.00/0.09	 1
0.00/0.09	->Bound:
0.00/0.09	 2
0.00/0.09	->Interpretation:
0.00/0.09	 
0.00/0.09	[a](X) = 2
0.00/0.09	[b](X) = 1/2.X
0.00/0.09	[A](X) = X
0.00/0.09	
0.00/0.09	Problem 1.2: 
0.00/0.09	
0.00/0.09	SCC Processor:
0.00/0.09	-> Pairs:
0.00/0.09	 Empty
0.00/0.09	-> Rules:
0.00/0.09	 a(b(a(x1:S))) -> a(a(b(b(a(a(x1:S))))))
0.00/0.09	 b(a(a(b(x1:S)))) -> b(a(b(x1:S)))
0.00/0.09	->Strongly Connected Components:
0.00/0.09	 There is no strongly connected component
0.00/0.09	
0.00/0.09	The problem is finite.
0.00/0.09	EOF