21.97/22.13	YES
21.97/22.13	
21.97/22.13	Problem 1: 
21.97/22.13	
21.97/22.13	(VAR v_NonEmpty:S x1:S)
21.97/22.13	(RULES
21.97/22.13	a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	)
21.97/22.13	
21.97/22.13	Problem 1: 
21.97/22.13	
21.97/22.13	Dependency Pairs Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(x1:S))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(x1:S))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> A(a(x1:S))
21.97/22.13	 B(b(b(b(x1:S)))) -> A(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	
21.97/22.13	Problem 1: 
21.97/22.13	
21.97/22.13	SCC Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(x1:S))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(x1:S))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> A(a(x1:S))
21.97/22.13	 B(b(b(b(x1:S)))) -> A(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Strongly Connected Components:
21.97/22.13	->->Cycle:
21.97/22.13	->->-> Pairs:
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(x1:S))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(x1:S))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> A(a(x1:S))
21.97/22.13	 B(b(b(b(x1:S)))) -> A(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	->->-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	
21.97/22.13	Problem 1: 
21.97/22.13	
21.97/22.13	Reduction Pair Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(x1:S))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(x1:S))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> A(a(x1:S))
21.97/22.13	 B(b(b(b(x1:S)))) -> A(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	-> Usable rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Interpretation type:
21.97/22.13	 Linear
21.97/22.13	->Coefficients:
21.97/22.13	 Natural Numbers
21.97/22.13	->Dimension:
21.97/22.13	 1
21.97/22.13	->Bound:
21.97/22.13	 2
21.97/22.13	->Interpretation:
21.97/22.13	 
21.97/22.13	[a](X) = 2.X + 2
21.97/22.13	[b](X) = 2.X + 2
21.97/22.13	[A](X) = X + 2
21.97/22.13	[B](X) = 2.X + 2
21.97/22.13	
21.97/22.13	Problem 1: 
21.97/22.13	
21.97/22.13	SCC Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(x1:S))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> A(a(x1:S))
21.97/22.13	 B(b(b(b(x1:S)))) -> A(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Strongly Connected Components:
21.97/22.13	->->Cycle:
21.97/22.13	->->-> Pairs:
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(x1:S))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> A(a(x1:S))
21.97/22.13	 B(b(b(b(x1:S)))) -> A(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	->->-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	
21.97/22.13	Problem 1: 
21.97/22.13	
21.97/22.13	Reduction Pair Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(x1:S))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> A(a(x1:S))
21.97/22.13	 B(b(b(b(x1:S)))) -> A(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	-> Usable rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Interpretation type:
21.97/22.13	 Linear
21.97/22.13	->Coefficients:
21.97/22.13	 Natural Numbers
21.97/22.13	->Dimension:
21.97/22.13	 1
21.97/22.13	->Bound:
21.97/22.13	 2
21.97/22.13	->Interpretation:
21.97/22.13	 
21.97/22.13	[a](X) = 2.X + 1
21.97/22.13	[b](X) = 2.X + 1
21.97/22.13	[A](X) = X + 2
21.97/22.13	[B](X) = 2.X + 2
21.97/22.13	
21.97/22.13	Problem 1: 
21.97/22.13	
21.97/22.13	SCC Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(x1:S))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> A(a(x1:S))
21.97/22.13	 B(b(b(b(x1:S)))) -> A(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Strongly Connected Components:
21.97/22.13	->->Cycle:
21.97/22.13	->->-> Pairs:
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(x1:S))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> A(a(x1:S))
21.97/22.13	 B(b(b(b(x1:S)))) -> A(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	->->-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	
21.97/22.13	Problem 1: 
21.97/22.13	
21.97/22.13	Reduction Pair Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 A(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(x1:S))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> A(a(x1:S))
21.97/22.13	 B(b(b(b(x1:S)))) -> A(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	-> Usable rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Interpretation type:
21.97/22.13	 Linear
21.97/22.13	->Coefficients:
21.97/22.13	 Natural Numbers
21.97/22.13	->Dimension:
21.97/22.13	 1
21.97/22.13	->Bound:
21.97/22.13	 2
21.97/22.13	->Interpretation:
21.97/22.13	 
21.97/22.13	[a](X) = X + 1
21.97/22.13	[b](X) = X + 1
21.97/22.13	[A](X) = 2.X + 2
21.97/22.13	[B](X) = 2.X + 2
21.97/22.13	
21.97/22.13	Problem 1: 
21.97/22.13	
21.97/22.13	SCC Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	 B(b(a(a(x1:S)))) -> A(b(x1:S))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> A(a(x1:S))
21.97/22.13	 B(b(b(b(x1:S)))) -> A(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Strongly Connected Components:
21.97/22.13	->->Cycle:
21.97/22.13	->->-> Pairs:
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	->->-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->->Cycle:
21.97/22.13	->->-> Pairs:
21.97/22.13	 B(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	->->-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	
21.97/22.13	
21.97/22.13	The problem is decomposed in 2 subproblems.
21.97/22.13	
21.97/22.13	Problem 1.1: 
21.97/22.13	
21.97/22.13	Reduction Pair Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 A(b(a(a(x1:S)))) -> A(b(a(b(x1:S))))
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	-> Usable rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Interpretation type:
21.97/22.13	 Linear
21.97/22.13	->Coefficients:
21.97/22.13	 Natural Numbers
21.97/22.13	->Dimension:
21.97/22.13	 2
21.97/22.13	->Bound:
21.97/22.13	 1
21.97/22.13	->Interpretation:
21.97/22.13	 
21.97/22.13	[a](X) = [0 1;1 0].X + [1;1]
21.97/22.13	[b](X) = [1 0;1 0].X + [1;0]
21.97/22.13	[A](X) = [1 1;1 1].X
21.97/22.13	
21.97/22.13	Problem 1.1: 
21.97/22.13	
21.97/22.13	SCC Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 Empty
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Strongly Connected Components:
21.97/22.13	 There is no strongly connected component
21.97/22.13	
21.97/22.13	The problem is finite.
21.97/22.13	
21.97/22.13	Problem 1.2: 
21.97/22.13	
21.97/22.13	Reduction Pair Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 B(b(a(a(x1:S)))) -> B(a(b(x1:S)))
21.97/22.13	 B(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	-> Usable rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Interpretation type:
21.97/22.13	 Linear
21.97/22.13	->Coefficients:
21.97/22.13	 Natural Numbers
21.97/22.13	->Dimension:
21.97/22.13	 1
21.97/22.13	->Bound:
21.97/22.13	 2
21.97/22.13	->Interpretation:
21.97/22.13	 
21.97/22.13	[a](X) = X + 1
21.97/22.13	[b](X) = X + 1
21.97/22.13	[B](X) = X
21.97/22.13	
21.97/22.13	Problem 1.2: 
21.97/22.13	
21.97/22.13	SCC Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 B(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Strongly Connected Components:
21.97/22.13	->->Cycle:
21.97/22.13	->->-> Pairs:
21.97/22.13	 B(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	->->-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	
21.97/22.13	Problem 1.2: 
21.97/22.13	
21.97/22.13	Reduction Pair Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 B(b(a(a(x1:S)))) -> B(x1:S)
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	-> Usable rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Interpretation type:
21.97/22.13	 Linear
21.97/22.13	->Coefficients:
21.97/22.13	 Natural Numbers
21.97/22.13	->Dimension:
21.97/22.13	 1
21.97/22.13	->Bound:
21.97/22.13	 2
21.97/22.13	->Interpretation:
21.97/22.13	 
21.97/22.13	[a](X) = X + 1
21.97/22.13	[b](X) = X + 1
21.97/22.13	[B](X) = X
21.97/22.13	
21.97/22.13	Problem 1.2: 
21.97/22.13	
21.97/22.13	SCC Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Strongly Connected Components:
21.97/22.13	->->Cycle:
21.97/22.13	->->-> Pairs:
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	->->-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	
21.97/22.13	Problem 1.2: 
21.97/22.13	
21.97/22.13	Reduction Pair Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 B(b(b(b(x1:S)))) -> B(a(a(x1:S)))
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	-> Usable rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Interpretation type:
21.97/22.13	 Linear
21.97/22.13	->Coefficients:
21.97/22.13	 Natural Numbers
21.97/22.13	->Dimension:
21.97/22.13	 1
21.97/22.13	->Bound:
21.97/22.13	 2
21.97/22.13	->Interpretation:
21.97/22.13	 
21.97/22.13	[a](X) = 2
21.97/22.13	[b](X) = 2.X + 1
21.97/22.13	[B](X) = 2.X
21.97/22.13	
21.97/22.13	Problem 1.2: 
21.97/22.13	
21.97/22.13	SCC Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Strongly Connected Components:
21.97/22.13	->->Cycle:
21.97/22.13	->->-> Pairs:
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	->->-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	
21.97/22.13	Problem 1.2: 
21.97/22.13	
21.97/22.13	Reduction Pair Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 B(b(b(b(x1:S)))) -> B(b(a(a(x1:S))))
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	-> Usable rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Interpretation type:
21.97/22.13	 Linear
21.97/22.13	->Coefficients:
21.97/22.13	 Natural Numbers
21.97/22.13	->Dimension:
21.97/22.13	 1
21.97/22.13	->Bound:
21.97/22.13	 2
21.97/22.13	->Interpretation:
21.97/22.13	 
21.97/22.13	[a](X) = 2
21.97/22.13	[b](X) = 2.X + 2
21.97/22.13	[B](X) = 2.X
21.97/22.13	
21.97/22.13	Problem 1.2: 
21.97/22.13	
21.97/22.13	SCC Processor:
21.97/22.13	-> Pairs:
21.97/22.13	 Empty
21.97/22.13	-> Rules:
21.97/22.13	 a(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(a(a(x1:S)))) -> a(b(a(b(x1:S))))
21.97/22.13	 b(b(b(b(x1:S)))) -> b(b(a(a(x1:S))))
21.97/22.13	->Strongly Connected Components:
21.97/22.13	 There is no strongly connected component
21.97/22.13	
21.97/22.13	The problem is finite.
21.97/46.96	EOF