23.57/23.82	YES
23.57/23.82	
23.57/23.82	Problem 1: 
23.57/23.82	
23.57/23.82	(VAR v_NonEmpty:S x1:S)
23.57/23.82	(RULES
23.57/23.82	a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	)
23.57/23.82	
23.57/23.82	Problem 1: 
23.57/23.82	
23.57/23.82	Dependency Pairs Processor:
23.57/23.82	-> Pairs:
23.57/23.82	 A(a(b(a(x1:S)))) -> A(b(b(a(x1:S))))
23.57/23.82	 A(a(b(b(x1:S)))) -> A(a(x1:S))
23.57/23.82	 A(a(b(b(x1:S)))) -> A(x1:S)
23.57/23.82	 A(b(b(a(x1:S)))) -> A(b(a(b(x1:S))))
23.57/23.82	 A(b(b(a(x1:S)))) -> A(b(x1:S))
23.57/23.82	-> Rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	
23.57/23.82	Problem 1: 
23.57/23.82	
23.57/23.82	SCC Processor:
23.57/23.82	-> Pairs:
23.57/23.82	 A(a(b(a(x1:S)))) -> A(b(b(a(x1:S))))
23.57/23.82	 A(a(b(b(x1:S)))) -> A(a(x1:S))
23.57/23.82	 A(a(b(b(x1:S)))) -> A(x1:S)
23.57/23.82	 A(b(b(a(x1:S)))) -> A(b(a(b(x1:S))))
23.57/23.82	 A(b(b(a(x1:S)))) -> A(b(x1:S))
23.57/23.82	-> Rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	->Strongly Connected Components:
23.57/23.82	->->Cycle:
23.57/23.82	->->-> Pairs:
23.57/23.82	 A(b(b(a(x1:S)))) -> A(b(a(b(x1:S))))
23.57/23.82	 A(b(b(a(x1:S)))) -> A(b(x1:S))
23.57/23.82	->->-> Rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	->->Cycle:
23.57/23.82	->->-> Pairs:
23.57/23.82	 A(a(b(b(x1:S)))) -> A(a(x1:S))
23.57/23.82	 A(a(b(b(x1:S)))) -> A(x1:S)
23.57/23.82	->->-> Rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	
23.57/23.82	
23.57/23.82	The problem is decomposed in 2 subproblems.
23.57/23.82	
23.57/23.82	Problem 1.1: 
23.57/23.82	
23.57/23.82	Reduction Pair Processor:
23.57/23.82	-> Pairs:
23.57/23.82	 A(b(b(a(x1:S)))) -> A(b(a(b(x1:S))))
23.57/23.82	 A(b(b(a(x1:S)))) -> A(b(x1:S))
23.57/23.82	-> Rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	-> Usable rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	->Interpretation type:
23.57/23.82	 Linear
23.57/23.82	->Coefficients:
23.57/23.82	 Natural Numbers
23.57/23.82	->Dimension:
23.57/23.82	 1
23.57/23.82	->Bound:
23.57/23.82	 2
23.57/23.82	->Interpretation:
23.57/23.82	 
23.57/23.82	[a](X) = 2.X + 1
23.57/23.82	[b](X) = 2.X + 1
23.57/23.82	[A](X) = 2.X
23.57/23.82	
23.57/23.82	Problem 1.1: 
23.57/23.82	
23.57/23.82	SCC Processor:
23.57/23.82	-> Pairs:
23.57/23.82	 A(b(b(a(x1:S)))) -> A(b(a(b(x1:S))))
23.57/23.82	-> Rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	->Strongly Connected Components:
23.57/23.82	->->Cycle:
23.57/23.82	->->-> Pairs:
23.57/23.82	 A(b(b(a(x1:S)))) -> A(b(a(b(x1:S))))
23.57/23.82	->->-> Rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	
23.57/23.82	Problem 1.1: 
23.57/23.82	
23.57/23.82	Reduction Pair Processor:
23.57/23.82	-> Pairs:
23.57/23.82	 A(b(b(a(x1:S)))) -> A(b(a(b(x1:S))))
23.57/23.82	-> Rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	-> Usable rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	->Interpretation type:
23.57/23.82	 Linear
23.57/23.82	->Coefficients:
23.57/23.82	 Natural Numbers
23.57/23.82	->Dimension:
23.57/23.82	 2
23.57/23.82	->Bound:
23.57/23.82	 1
23.57/23.82	->Interpretation:
23.57/23.82	 
23.57/23.82	[a](X) = [0;1]
23.57/23.82	[b](X) = [0 1;1 0].X
23.57/23.82	[A](X) = [0 1;1 1].X
23.57/23.82	
23.57/23.82	Problem 1.1: 
23.57/23.82	
23.57/23.82	SCC Processor:
23.57/23.82	-> Pairs:
23.57/23.82	 Empty
23.57/23.82	-> Rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	->Strongly Connected Components:
23.57/23.82	 There is no strongly connected component
23.57/23.82	
23.57/23.82	The problem is finite.
23.57/23.82	
23.57/23.82	Problem 1.2: 
23.57/23.82	
23.57/23.82	Reduction Pair Processor:
23.57/23.82	-> Pairs:
23.57/23.82	 A(a(b(b(x1:S)))) -> A(a(x1:S))
23.57/23.82	 A(a(b(b(x1:S)))) -> A(x1:S)
23.57/23.82	-> Rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	-> Usable rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	->Interpretation type:
23.57/23.82	 Linear
23.57/23.82	->Coefficients:
23.57/23.82	 Natural Numbers
23.57/23.82	->Dimension:
23.57/23.82	 1
23.57/23.82	->Bound:
23.57/23.82	 2
23.57/23.82	->Interpretation:
23.57/23.82	 
23.57/23.82	[a](X) = 2.X + 2
23.57/23.82	[b](X) = 2.X + 2
23.57/23.82	[A](X) = 2.X
23.57/23.82	
23.57/23.82	Problem 1.2: 
23.57/23.82	
23.57/23.82	SCC Processor:
23.57/23.82	-> Pairs:
23.57/23.82	 A(a(b(b(x1:S)))) -> A(x1:S)
23.57/23.82	-> Rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	->Strongly Connected Components:
23.57/23.82	->->Cycle:
23.57/23.82	->->-> Pairs:
23.57/23.82	 A(a(b(b(x1:S)))) -> A(x1:S)
23.57/23.82	->->-> Rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	
23.57/23.82	Problem 1.2: 
23.57/23.82	
23.57/23.82	Subterm Processor:
23.57/23.82	-> Pairs:
23.57/23.82	 A(a(b(b(x1:S)))) -> A(x1:S)
23.57/23.82	-> Rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	->Projection:
23.57/23.82	 pi(A) = 1
23.57/23.82	
23.57/23.82	Problem 1.2: 
23.57/23.82	
23.57/23.82	SCC Processor:
23.57/23.82	-> Pairs:
23.57/23.82	 Empty
23.57/23.82	-> Rules:
23.57/23.82	 a(a(b(a(x1:S)))) -> a(b(b(a(x1:S))))
23.57/23.82	 a(a(b(b(x1:S)))) -> b(b(a(a(x1:S))))
23.57/23.82	 a(b(b(a(x1:S)))) -> a(b(a(b(x1:S))))
23.57/23.82	->Strongly Connected Components:
23.57/23.82	 There is no strongly connected component
23.57/23.82	
23.57/23.82	The problem is finite.
23.68/69.35	EOF