91.67/92.72	YES
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	(VAR v_NonEmpty:S x1:S)
91.67/92.72	(RULES
91.67/92.72	a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	)
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	Dependency Pairs Processor:
91.67/92.72	-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(a(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(x1:S)
91.67/92.72	 A(b(a(b(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	SCC Processor:
91.67/92.72	-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(a(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(x1:S)
91.67/92.72	 A(b(a(b(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	->Strongly Connected Components:
91.67/92.72	->->Cycle:
91.67/92.72	->->-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(a(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(x1:S)
91.67/92.72	 A(b(a(b(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	->->-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	Reduction Pair Processor:
91.67/92.72	-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(a(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(x1:S)
91.67/92.72	 A(b(a(b(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	-> Usable rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	->Interpretation type:
91.67/92.72	 Linear
91.67/92.72	->Coefficients:
91.67/92.72	 Natural Numbers
91.67/92.72	->Dimension:
91.67/92.72	 1
91.67/92.72	->Bound:
91.67/92.72	 2
91.67/92.72	->Interpretation:
91.67/92.72	 
91.67/92.72	[a](X) = 0
91.67/92.72	[b](X) = X + 2
91.67/92.72	[A](X) = 2
91.67/92.72	[B](X) = X
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	SCC Processor:
91.67/92.72	-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(x1:S)
91.67/92.72	 A(b(a(b(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	->Strongly Connected Components:
91.67/92.72	->->Cycle:
91.67/92.72	->->-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(x1:S)
91.67/92.72	 A(b(a(b(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	->->-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	Reduction Pair Processor:
91.67/92.72	-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(a(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(x1:S)
91.67/92.72	 A(b(a(b(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	-> Usable rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	->Interpretation type:
91.67/92.72	 Linear
91.67/92.72	->Coefficients:
91.67/92.72	 Natural Numbers
91.67/92.72	->Dimension:
91.67/92.72	 1
91.67/92.72	->Bound:
91.67/92.72	 2
91.67/92.72	->Interpretation:
91.67/92.72	 
91.67/92.72	[a](X) = 2.X + 2
91.67/92.72	[b](X) = 2.X + 2
91.67/92.72	[A](X) = 2.X
91.67/92.72	[B](X) = 2.X + 1
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	SCC Processor:
91.67/92.72	-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(x1:S)
91.67/92.72	 A(b(a(b(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	->Strongly Connected Components:
91.67/92.72	->->Cycle:
91.67/92.72	->->-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(x1:S)
91.67/92.72	 A(b(a(b(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	->->-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	Reduction Pair Processor:
91.67/92.72	-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(x1:S)
91.67/92.72	 A(b(a(b(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	-> Usable rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	->Interpretation type:
91.67/92.72	 Linear
91.67/92.72	->Coefficients:
91.67/92.72	 Natural Numbers
91.67/92.72	->Dimension:
91.67/92.72	 1
91.67/92.72	->Bound:
91.67/92.72	 2
91.67/92.72	->Interpretation:
91.67/92.72	 
91.67/92.72	[a](X) = 2.X + 2
91.67/92.72	[b](X) = 2.X + 2
91.67/92.72	[A](X) = 2.X + 2
91.67/92.72	[B](X) = 2.X + 2
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	SCC Processor:
91.67/92.72	-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	->Strongly Connected Components:
91.67/92.72	->->Cycle:
91.67/92.72	->->-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	->->-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	Reduction Pair Processor:
91.67/92.72	-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(a(x1:S))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	-> Usable rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	->Interpretation type:
91.67/92.72	 Linear
91.67/92.72	->Coefficients:
91.67/92.72	 Natural Numbers
91.67/92.72	->Dimension:
91.67/92.72	 1
91.67/92.72	->Bound:
91.67/92.72	 2
91.67/92.72	->Interpretation:
91.67/92.72	 
91.67/92.72	[a](X) = 2.X + 2
91.67/92.72	[b](X) = 2.X + 2
91.67/92.72	[A](X) = 2.X
91.67/92.72	[B](X) = 2.X + 2
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	SCC Processor:
91.67/92.72	-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	->Strongly Connected Components:
91.67/92.72	->->Cycle:
91.67/92.72	->->-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	->->-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	Reduction Pair Processor:
91.67/92.72	-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> B(b(a(x1:S)))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	-> Usable rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	->Interpretation type:
91.67/92.72	 Linear
91.67/92.72	->Coefficients:
91.67/92.72	 Natural Numbers
91.67/92.72	->Dimension:
91.67/92.72	 1
91.67/92.72	->Bound:
91.67/92.72	 2
91.67/92.72	->Interpretation:
91.67/92.72	 
91.67/92.72	[a](X) = X + 2
91.67/92.72	[b](X) = X + 2
91.67/92.72	[A](X) = 2.X + 1
91.67/92.72	[B](X) = 2.X + 1
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	SCC Processor:
91.67/92.72	-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 B(b(a(a(x1:S)))) -> A(b(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(a(x1:S))))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(a(x1:S)))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(a(x1:S))
91.67/92.72	 B(b(b(b(x1:S)))) -> A(x1:S)
91.67/92.72	-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	->Strongly Connected Components:
91.67/92.72	->->Cycle:
91.67/92.72	->->-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	->->-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	Reduction Pair Processor:
91.67/92.72	-> Pairs:
91.67/92.72	 A(b(a(a(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	-> Usable rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	->Interpretation type:
91.67/92.72	 Linear
91.67/92.72	->Coefficients:
91.67/92.72	 Natural Numbers
91.67/92.72	->Dimension:
91.67/92.72	 2
91.67/92.72	->Bound:
91.67/92.72	 1
91.67/92.72	->Interpretation:
91.67/92.72	 
91.67/92.72	[a](X) = [1;0]
91.67/92.72	[b](X) = [0 1;1 0].X + [0;1]
91.67/92.72	[A](X) = [0 1;0 1].X
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	SCC Processor:
91.67/92.72	-> Pairs:
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	->Strongly Connected Components:
91.67/92.72	->->Cycle:
91.67/92.72	->->-> Pairs:
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	->->-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	Reduction Pair Processor:
91.67/92.72	-> Pairs:
91.67/92.72	 A(b(a(b(x1:S)))) -> A(b(b(a(x1:S))))
91.67/92.72	-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	-> Usable rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	->Interpretation type:
91.67/92.72	 Linear
91.67/92.72	->Coefficients:
91.67/92.72	 Natural Numbers
91.67/92.72	->Dimension:
91.67/92.72	 2
91.67/92.72	->Bound:
91.67/92.72	 1
91.67/92.72	->Interpretation:
91.67/92.72	 
91.67/92.72	[a](X) = [0 0;1 0].X + [0;1]
91.67/92.72	[b](X) = [0 1;1 0].X + [1;1]
91.67/92.72	[A](X) = [1 0;1 0].X
91.67/92.72	
91.67/92.72	Problem 1: 
91.67/92.72	
91.67/92.72	SCC Processor:
91.67/92.72	-> Pairs:
91.67/92.72	 Empty
91.67/92.72	-> Rules:
91.67/92.72	 a(b(a(a(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 a(b(a(b(x1:S)))) -> a(b(b(a(x1:S))))
91.67/92.72	 b(b(a(a(x1:S)))) -> a(b(a(a(x1:S))))
91.67/92.72	 b(b(b(b(x1:S)))) -> a(a(a(a(x1:S))))
91.67/92.72	->Strongly Connected Components:
91.67/92.72	 There is no strongly connected component
91.67/92.72	
91.67/92.72	The problem is finite.
91.79/138.33	EOF