0.00/0.28	YES
0.00/0.28	
0.00/0.28	Problem 1: 
0.00/0.28	
0.00/0.28	(VAR v_NonEmpty:S x1:S)
0.00/0.28	(RULES
0.00/0.28	a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	)
0.00/0.28	
0.00/0.28	Problem 1: 
0.00/0.28	
0.00/0.28	Dependency Pairs Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.28	 A(b(a(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	
0.00/0.28	Problem 1: 
0.00/0.28	
0.00/0.28	SCC Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.28	 A(b(a(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Strongly Connected Components:
0.00/0.28	->->Cycle:
0.00/0.28	->->-> Pairs:
0.00/0.28	 A(b(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.28	 A(b(a(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.28	->->-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	
0.00/0.28	Problem 1: 
0.00/0.28	
0.00/0.28	Reduction Pair Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.28	 A(b(a(a(x1:S)))) -> A(b(b(x1:S)))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	-> Usable rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Interpretation type:
0.00/0.28	 Linear
0.00/0.28	->Coefficients:
0.00/0.28	 Natural Numbers
0.00/0.28	->Dimension:
0.00/0.28	 1
0.00/0.28	->Bound:
0.00/0.28	 2
0.00/0.28	->Interpretation:
0.00/0.28	 
0.00/0.28	[a](X) = X + 1
0.00/0.28	[b](X) = X + 1
0.00/0.28	[A](X) = X
0.00/0.28	[B](X) = X
0.00/0.28	
0.00/0.28	Problem 1: 
0.00/0.28	
0.00/0.28	SCC Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Strongly Connected Components:
0.00/0.28	->->Cycle:
0.00/0.28	->->-> Pairs:
0.00/0.28	 A(b(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.28	->->-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	
0.00/0.28	Problem 1: 
0.00/0.28	
0.00/0.28	Reduction Pair Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(b(x1:S))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	-> Usable rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Interpretation type:
0.00/0.28	 Linear
0.00/0.28	->Coefficients:
0.00/0.28	 Natural Numbers
0.00/0.28	->Dimension:
0.00/0.28	 1
0.00/0.28	->Bound:
0.00/0.28	 2
0.00/0.28	->Interpretation:
0.00/0.28	 
0.00/0.28	[a](X) = 2.X + 2
0.00/0.28	[b](X) = 2.X + 2
0.00/0.28	[A](X) = 2.X + 1
0.00/0.28	[B](X) = 2.X + 1
0.00/0.28	
0.00/0.28	Problem 1: 
0.00/0.28	
0.00/0.28	SCC Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Strongly Connected Components:
0.00/0.28	->->Cycle:
0.00/0.28	->->-> Pairs:
0.00/0.28	 A(b(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.28	->->-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	
0.00/0.28	Problem 1: 
0.00/0.28	
0.00/0.28	Reduction Pair Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.28	 A(b(a(a(x1:S)))) -> B(x1:S)
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	-> Usable rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Interpretation type:
0.00/0.28	 Linear
0.00/0.28	->Coefficients:
0.00/0.28	 Natural Numbers
0.00/0.28	->Dimension:
0.00/0.28	 1
0.00/0.28	->Bound:
0.00/0.28	 2
0.00/0.28	->Interpretation:
0.00/0.28	 
0.00/0.28	[a](X) = 2.X + 2
0.00/0.28	[b](X) = 2.X + 2
0.00/0.28	[A](X) = 2.X
0.00/0.28	[B](X) = 2.X
0.00/0.28	
0.00/0.28	Problem 1: 
0.00/0.28	
0.00/0.28	SCC Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(b(a(a(x1:S))))
0.00/0.28	 B(b(a(b(x1:S)))) -> A(x1:S)
0.00/0.28	 B(b(a(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Strongly Connected Components:
0.00/0.28	->->Cycle:
0.00/0.28	->->-> Pairs:
0.00/0.28	 A(b(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	->->-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->->Cycle:
0.00/0.28	->->-> Pairs:
0.00/0.28	 B(b(a(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.28	->->-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	
0.00/0.28	
0.00/0.28	The problem is decomposed in 2 subproblems.
0.00/0.28	
0.00/0.28	Problem 1.1: 
0.00/0.28	
0.00/0.28	Reduction Pair Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(a(a(x1:S)))) -> A(a(b(b(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	-> Usable rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Interpretation type:
0.00/0.28	 Linear
0.00/0.28	->Coefficients:
0.00/0.28	 Natural Numbers
0.00/0.28	->Dimension:
0.00/0.28	 1
0.00/0.28	->Bound:
0.00/0.28	 2
0.00/0.28	->Interpretation:
0.00/0.28	 
0.00/0.28	[a](X) = 1
0.00/0.28	[b](X) = 2.X + 2
0.00/0.28	[A](X) = 2.X
0.00/0.28	
0.00/0.28	Problem 1.1: 
0.00/0.28	
0.00/0.28	SCC Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Strongly Connected Components:
0.00/0.28	->->Cycle:
0.00/0.28	->->-> Pairs:
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	->->-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	
0.00/0.28	Problem 1.1: 
0.00/0.28	
0.00/0.28	Reduction Pair Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	-> Usable rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Interpretation type:
0.00/0.28	 Linear
0.00/0.28	->Coefficients:
0.00/0.28	 Natural Numbers
0.00/0.28	->Dimension:
0.00/0.28	 1
0.00/0.28	->Bound:
0.00/0.28	 2
0.00/0.28	->Interpretation:
0.00/0.28	 
0.00/0.28	[a](X) = 1
0.00/0.28	[b](X) = 2.X + 1
0.00/0.28	[A](X) = 2.X
0.00/0.28	
0.00/0.28	Problem 1.1: 
0.00/0.28	
0.00/0.28	SCC Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Strongly Connected Components:
0.00/0.28	->->Cycle:
0.00/0.28	->->-> Pairs:
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	->->-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	
0.00/0.28	Problem 1.1: 
0.00/0.28	
0.00/0.28	Reduction Pair Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(a(x1:S)))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	-> Usable rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Interpretation type:
0.00/0.28	 Linear
0.00/0.28	->Coefficients:
0.00/0.28	 Natural Numbers
0.00/0.28	->Dimension:
0.00/0.28	 1
0.00/0.28	->Bound:
0.00/0.28	 2
0.00/0.28	->Interpretation:
0.00/0.28	 
0.00/0.28	[a](X) = 2.X + 2
0.00/0.28	[b](X) = 2.X + 2
0.00/0.28	[A](X) = 2.X
0.00/0.28	
0.00/0.28	Problem 1.1: 
0.00/0.28	
0.00/0.28	SCC Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Strongly Connected Components:
0.00/0.28	->->Cycle:
0.00/0.28	->->-> Pairs:
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	->->-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	
0.00/0.28	Problem 1.1: 
0.00/0.28	
0.00/0.28	Reduction Pair Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(b(b(x1:S)))) -> A(a(x1:S))
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	-> Usable rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Interpretation type:
0.00/0.28	 Linear
0.00/0.28	->Coefficients:
0.00/0.28	 Natural Numbers
0.00/0.28	->Dimension:
0.00/0.28	 1
0.00/0.28	->Bound:
0.00/0.28	 2
0.00/0.28	->Interpretation:
0.00/0.28	 
0.00/0.28	[a](X) = 2.X + 2
0.00/0.28	[b](X) = 2.X + 2
0.00/0.28	[A](X) = 2.X
0.00/0.28	
0.00/0.28	Problem 1.1: 
0.00/0.28	
0.00/0.28	SCC Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Strongly Connected Components:
0.00/0.28	->->Cycle:
0.00/0.28	->->-> Pairs:
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	->->-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	
0.00/0.28	Problem 1.1: 
0.00/0.28	
0.00/0.28	Subterm Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 A(b(b(b(x1:S)))) -> A(x1:S)
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Projection:
0.00/0.28	 pi(A) = 1
0.00/0.28	
0.00/0.28	Problem 1.1: 
0.00/0.28	
0.00/0.28	SCC Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 Empty
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Strongly Connected Components:
0.00/0.28	 There is no strongly connected component
0.00/0.28	
0.00/0.28	The problem is finite.
0.00/0.28	
0.00/0.28	Problem 1.2: 
0.00/0.28	
0.00/0.28	Reduction Pair Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 B(b(a(b(x1:S)))) -> B(a(a(x1:S)))
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	-> Usable rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Interpretation type:
0.00/0.28	 Linear
0.00/0.28	->Coefficients:
0.00/0.28	 Natural Numbers
0.00/0.28	->Dimension:
0.00/0.28	 1
0.00/0.28	->Bound:
0.00/0.28	 2
0.00/0.28	->Interpretation:
0.00/0.28	 
0.00/0.28	[a](X) = 2.X + 2
0.00/0.28	[b](X) = 2.X + 2
0.00/0.28	[B](X) = 2.X
0.00/0.28	
0.00/0.28	Problem 1.2: 
0.00/0.28	
0.00/0.28	SCC Processor:
0.00/0.28	-> Pairs:
0.00/0.28	 Empty
0.00/0.28	-> Rules:
0.00/0.28	 a(b(a(a(x1:S)))) -> a(a(b(b(x1:S))))
0.00/0.28	 a(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
0.00/0.28	 b(b(a(b(x1:S)))) -> a(b(a(a(x1:S))))
0.00/0.28	->Strongly Connected Components:
0.00/0.28	 There is no strongly connected component
0.00/0.28	
0.00/0.28	The problem is finite.
0.00/0.29	EOF