0.00/0.11	YES
0.00/0.11	
0.00/0.11	Problem 1: 
0.00/0.11	
0.00/0.11	(VAR v_NonEmpty:S x1:S)
0.00/0.11	(RULES
0.00/0.11	a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	)
0.00/0.11	
0.00/0.11	Problem 1: 
0.00/0.11	
0.00/0.11	Dependency Pairs Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 A(b(a(b(x1:S)))) -> A(a(x1:S))
0.00/0.11	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.11	 A(b(a(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.11	 A(b(a(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.11	 A(b(b(b(x1:S)))) -> A(a(b(x1:S)))
0.00/0.11	 A(b(b(b(x1:S)))) -> A(b(x1:S))
0.00/0.11	 A(b(b(b(x1:S)))) -> B(a(a(b(x1:S))))
0.00/0.11	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.11	 B(a(a(a(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.11	-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	
0.00/0.11	Problem 1: 
0.00/0.11	
0.00/0.11	SCC Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 A(b(a(b(x1:S)))) -> A(a(x1:S))
0.00/0.11	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.11	 A(b(a(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.11	 A(b(a(b(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.11	 A(b(b(b(x1:S)))) -> A(a(b(x1:S)))
0.00/0.11	 A(b(b(b(x1:S)))) -> A(b(x1:S))
0.00/0.11	 A(b(b(b(x1:S)))) -> B(a(a(b(x1:S))))
0.00/0.11	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.11	 B(a(a(a(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.11	-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	->Strongly Connected Components:
0.00/0.11	->->Cycle:
0.00/0.11	->->-> Pairs:
0.00/0.11	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.11	 B(a(a(a(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.11	->->-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	->->Cycle:
0.00/0.11	->->-> Pairs:
0.00/0.11	 A(b(a(b(x1:S)))) -> A(a(x1:S))
0.00/0.11	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.11	 A(b(b(b(x1:S)))) -> A(a(b(x1:S)))
0.00/0.11	 A(b(b(b(x1:S)))) -> A(b(x1:S))
0.00/0.11	->->-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	
0.00/0.11	
0.00/0.11	The problem is decomposed in 2 subproblems.
0.00/0.11	
0.00/0.11	Problem 1.1: 
0.00/0.11	
0.00/0.11	Reduction Pair Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 B(a(a(a(x1:S)))) -> B(a(a(x1:S)))
0.00/0.11	 B(a(a(a(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.11	-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	-> Usable rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	->Interpretation type:
0.00/0.11	 Linear
0.00/0.11	->Coefficients:
0.00/0.11	 Natural Numbers
0.00/0.11	->Dimension:
0.00/0.11	 1
0.00/0.11	->Bound:
0.00/0.11	 2
0.00/0.11	->Interpretation:
0.00/0.11	 
0.00/0.11	[a](X) = 2.X + 2
0.00/0.11	[b](X) = 2.X + 2
0.00/0.11	[B](X) = 2.X
0.00/0.11	
0.00/0.11	Problem 1.1: 
0.00/0.11	
0.00/0.11	SCC Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 B(a(a(a(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.11	-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	->Strongly Connected Components:
0.00/0.11	->->Cycle:
0.00/0.11	->->-> Pairs:
0.00/0.11	 B(a(a(a(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.11	->->-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	
0.00/0.11	Problem 1.1: 
0.00/0.11	
0.00/0.11	Reduction Pair Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 B(a(a(a(x1:S)))) -> B(b(a(a(x1:S))))
0.00/0.11	-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	-> Usable rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	->Interpretation type:
0.00/0.11	 Linear
0.00/0.11	->Coefficients:
0.00/0.11	 Natural Numbers
0.00/0.11	->Dimension:
0.00/0.11	 1
0.00/0.11	->Bound:
0.00/0.11	 2
0.00/0.11	->Interpretation:
0.00/0.11	 
0.00/0.11	[a](X) = 2.X + 2
0.00/0.11	[b](X) = 0
0.00/0.11	[B](X) = 2.X
0.00/0.11	
0.00/0.11	Problem 1.1: 
0.00/0.11	
0.00/0.11	SCC Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 Empty
0.00/0.11	-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	->Strongly Connected Components:
0.00/0.11	 There is no strongly connected component
0.00/0.11	
0.00/0.11	The problem is finite.
0.00/0.11	
0.00/0.11	Problem 1.2: 
0.00/0.11	
0.00/0.11	Reduction Pair Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 A(b(a(b(x1:S)))) -> A(a(x1:S))
0.00/0.11	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.11	 A(b(b(b(x1:S)))) -> A(a(b(x1:S)))
0.00/0.11	 A(b(b(b(x1:S)))) -> A(b(x1:S))
0.00/0.11	-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	-> Usable rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	->Interpretation type:
0.00/0.11	 Linear
0.00/0.11	->Coefficients:
0.00/0.11	 Natural Numbers
0.00/0.11	->Dimension:
0.00/0.11	 1
0.00/0.11	->Bound:
0.00/0.11	 2
0.00/0.11	->Interpretation:
0.00/0.11	 
0.00/0.11	[a](X) = X + 2
0.00/0.11	[b](X) = X + 2
0.00/0.11	[A](X) = 2.X
0.00/0.11	
0.00/0.11	Problem 1.2: 
0.00/0.11	
0.00/0.11	SCC Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.11	 A(b(b(b(x1:S)))) -> A(a(b(x1:S)))
0.00/0.11	 A(b(b(b(x1:S)))) -> A(b(x1:S))
0.00/0.11	-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	->Strongly Connected Components:
0.00/0.11	->->Cycle:
0.00/0.11	->->-> Pairs:
0.00/0.11	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.11	 A(b(b(b(x1:S)))) -> A(a(b(x1:S)))
0.00/0.11	 A(b(b(b(x1:S)))) -> A(b(x1:S))
0.00/0.11	->->-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	
0.00/0.11	Problem 1.2: 
0.00/0.11	
0.00/0.11	Reduction Pair Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 A(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.11	 A(b(b(b(x1:S)))) -> A(a(b(x1:S)))
0.00/0.11	 A(b(b(b(x1:S)))) -> A(b(x1:S))
0.00/0.11	-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	-> Usable rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	->Interpretation type:
0.00/0.11	 Linear
0.00/0.11	->Coefficients:
0.00/0.11	 Natural Numbers
0.00/0.11	->Dimension:
0.00/0.11	 1
0.00/0.11	->Bound:
0.00/0.11	 2
0.00/0.11	->Interpretation:
0.00/0.11	 
0.00/0.11	[a](X) = X + 1
0.00/0.11	[b](X) = X + 1
0.00/0.11	[A](X) = 2.X
0.00/0.11	
0.00/0.11	Problem 1.2: 
0.00/0.11	
0.00/0.11	SCC Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 A(b(b(b(x1:S)))) -> A(a(b(x1:S)))
0.00/0.11	 A(b(b(b(x1:S)))) -> A(b(x1:S))
0.00/0.11	-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	->Strongly Connected Components:
0.00/0.11	->->Cycle:
0.00/0.11	->->-> Pairs:
0.00/0.11	 A(b(b(b(x1:S)))) -> A(a(b(x1:S)))
0.00/0.11	 A(b(b(b(x1:S)))) -> A(b(x1:S))
0.00/0.11	->->-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	
0.00/0.11	Problem 1.2: 
0.00/0.11	
0.00/0.11	Reduction Pair Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 A(b(b(b(x1:S)))) -> A(a(b(x1:S)))
0.00/0.11	 A(b(b(b(x1:S)))) -> A(b(x1:S))
0.00/0.11	-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	-> Usable rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	->Interpretation type:
0.00/0.11	 Linear
0.00/0.11	->Coefficients:
0.00/0.11	 Natural Numbers
0.00/0.11	->Dimension:
0.00/0.11	 1
0.00/0.11	->Bound:
0.00/0.11	 2
0.00/0.11	->Interpretation:
0.00/0.11	 
0.00/0.11	[a](X) = 2.X + 1
0.00/0.11	[b](X) = 2.X + 1
0.00/0.11	[A](X) = 2.X
0.00/0.11	
0.00/0.11	Problem 1.2: 
0.00/0.11	
0.00/0.11	SCC Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 A(b(b(b(x1:S)))) -> A(b(x1:S))
0.00/0.11	-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	->Strongly Connected Components:
0.00/0.11	->->Cycle:
0.00/0.11	->->-> Pairs:
0.00/0.11	 A(b(b(b(x1:S)))) -> A(b(x1:S))
0.00/0.11	->->-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	
0.00/0.11	Problem 1.2: 
0.00/0.11	
0.00/0.11	Subterm Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 A(b(b(b(x1:S)))) -> A(b(x1:S))
0.00/0.11	-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	->Projection:
0.00/0.11	 pi(A) = 1
0.00/0.11	
0.00/0.11	Problem 1.2: 
0.00/0.11	
0.00/0.11	SCC Processor:
0.00/0.11	-> Pairs:
0.00/0.11	 Empty
0.00/0.11	-> Rules:
0.00/0.11	 a(b(a(b(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	 a(b(b(b(x1:S)))) -> b(a(a(b(x1:S))))
0.00/0.11	 b(a(a(a(x1:S)))) -> b(b(a(a(x1:S))))
0.00/0.11	->Strongly Connected Components:
0.00/0.11	 There is no strongly connected component
0.00/0.11	
0.00/0.11	The problem is finite.
0.00/0.11	EOF