152.42/153.95	YES
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	(VAR v_NonEmpty:S x1:S)
152.42/153.95	(RULES
152.42/153.95	a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	)
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	Dependency Pairs Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> A(a(a(x1:S)))
152.42/153.95	 A(b(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(x1:S)))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	SCC Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> A(a(a(x1:S)))
152.42/153.95	 A(b(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(x1:S)))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Strongly Connected Components:
152.42/153.95	->->Cycle:
152.42/153.95	->->-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> A(a(a(x1:S)))
152.42/153.95	 A(b(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(x1:S)))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	->->-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	Reduction Pair Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> A(a(a(x1:S)))
152.42/153.95	 A(b(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(x1:S)))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	-> Usable rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Interpretation type:
152.42/153.95	 Linear
152.42/153.95	->Coefficients:
152.42/153.95	 Natural Numbers
152.42/153.95	->Dimension:
152.42/153.95	 1
152.42/153.95	->Bound:
152.42/153.95	 2
152.42/153.95	->Interpretation:
152.42/153.95	 
152.42/153.95	[a](X) = 2.X + 2
152.42/153.95	[b](X) = 2.X + 2
152.42/153.95	[A](X) = 2.X + 2
152.42/153.95	[B](X) = 2.X + 2
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	SCC Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(x1:S)))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Strongly Connected Components:
152.42/153.95	->->Cycle:
152.42/153.95	->->-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(x1:S)))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	->->-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	Reduction Pair Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(x1:S)))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	-> Usable rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Interpretation type:
152.42/153.95	 Linear
152.42/153.95	->Coefficients:
152.42/153.95	 Natural Numbers
152.42/153.95	->Dimension:
152.42/153.95	 1
152.42/153.95	->Bound:
152.42/153.95	 2
152.42/153.95	->Interpretation:
152.42/153.95	 
152.42/153.95	[a](X) = 2.X + 2
152.42/153.95	[b](X) = 2.X + 2
152.42/153.95	[A](X) = 2.X
152.42/153.95	[B](X) = 2.X
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	SCC Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(x1:S)))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Strongly Connected Components:
152.42/153.95	->->Cycle:
152.42/153.95	->->-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(x1:S)))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	->->-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	Reduction Pair Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(x1:S)))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	-> Usable rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Interpretation type:
152.42/153.95	 Linear
152.42/153.95	->Coefficients:
152.42/153.95	 Natural Numbers
152.42/153.95	->Dimension:
152.42/153.95	 1
152.42/153.95	->Bound:
152.42/153.95	 2
152.42/153.95	->Interpretation:
152.42/153.95	 
152.42/153.95	[a](X) = 2.X + 1
152.42/153.95	[b](X) = 2.X + 1
152.42/153.95	[A](X) = 2.X + 1
152.42/153.95	[B](X) = 2.X + 1
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	SCC Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Strongly Connected Components:
152.42/153.95	->->Cycle:
152.42/153.95	->->-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	->->-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	Reduction Pair Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(x1:S))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	-> Usable rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Interpretation type:
152.42/153.95	 Linear
152.42/153.95	->Coefficients:
152.42/153.95	 Natural Numbers
152.42/153.95	->Dimension:
152.42/153.95	 1
152.42/153.95	->Bound:
152.42/153.95	 2
152.42/153.95	->Interpretation:
152.42/153.95	 
152.42/153.95	[a](X) = 2.X + 2
152.42/153.95	[b](X) = 2.X + 2
152.42/153.95	[A](X) = 2.X + 2
152.42/153.95	[B](X) = 2.X + 2
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	SCC Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Strongly Connected Components:
152.42/153.95	->->Cycle:
152.42/153.95	->->-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	->->-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	Reduction Pair Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	-> Usable rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Interpretation type:
152.42/153.95	 Linear
152.42/153.95	->Coefficients:
152.42/153.95	 Natural Numbers
152.42/153.95	->Dimension:
152.42/153.95	 1
152.42/153.95	->Bound:
152.42/153.95	 2
152.42/153.95	->Interpretation:
152.42/153.95	 
152.42/153.95	[a](X) = 2.X + 2
152.42/153.95	[b](X) = 2.X + 2
152.42/153.95	[A](X) = 2.X + 2
152.42/153.95	[B](X) = 2.X + 2
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	SCC Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Strongly Connected Components:
152.42/153.95	->->Cycle:
152.42/153.95	->->-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	->->-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	Reduction Pair Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> A(b(b(x1:S)))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	-> Usable rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Interpretation type:
152.42/153.95	 Linear
152.42/153.95	->Coefficients:
152.42/153.95	 Natural Numbers
152.42/153.95	->Dimension:
152.42/153.95	 1
152.42/153.95	->Bound:
152.42/153.95	 2
152.42/153.95	->Interpretation:
152.42/153.95	 
152.42/153.95	[a](X) = 2.X + 2
152.42/153.95	[b](X) = 2.X + 2
152.42/153.95	[A](X) = 2.X + 1
152.42/153.95	[B](X) = 2.X + 1
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	SCC Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Strongly Connected Components:
152.42/153.95	->->Cycle:
152.42/153.95	->->-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	->->-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	Reduction Pair Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(b(x1:S))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	-> Usable rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Interpretation type:
152.42/153.95	 Linear
152.42/153.95	->Coefficients:
152.42/153.95	 Natural Numbers
152.42/153.95	->Dimension:
152.42/153.95	 1
152.42/153.95	->Bound:
152.42/153.95	 2
152.42/153.95	->Interpretation:
152.42/153.95	 
152.42/153.95	[a](X) = 2.X + 2
152.42/153.95	[b](X) = 2.X + 2
152.42/153.95	[A](X) = 2.X + 2
152.42/153.95	[B](X) = 2.X + 2
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	SCC Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Strongly Connected Components:
152.42/153.95	->->Cycle:
152.42/153.95	->->-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	->->-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	Reduction Pair Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 A(b(b(a(x1:S)))) -> B(a(a(a(x1:S))))
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	-> Usable rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Interpretation type:
152.42/153.95	 Linear
152.42/153.95	->Coefficients:
152.42/153.95	 Natural Numbers
152.42/153.95	->Dimension:
152.42/153.95	 2
152.42/153.95	->Bound:
152.42/153.95	 1
152.42/153.95	->Interpretation:
152.42/153.95	 
152.42/153.95	[a](X) = [0 0;1 0].X
152.42/153.95	[b](X) = [0 1;0 0].X + [0;1]
152.42/153.95	[A](X) = [1 0;1 1].X + [1;1]
152.42/153.95	[B](X) = [0 0;0 1].X + [1;1]
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	SCC Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 B(a(b(a(x1:S)))) -> A(a(a(a(x1:S))))
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Strongly Connected Components:
152.42/153.95	->->Cycle:
152.42/153.95	->->-> Pairs:
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	->->-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	Reduction Pair Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 B(a(b(b(x1:S)))) -> B(b(b(b(x1:S))))
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	-> Usable rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Interpretation type:
152.42/153.95	 Linear
152.42/153.95	->Coefficients:
152.42/153.95	 Natural Numbers
152.42/153.95	->Dimension:
152.42/153.95	 2
152.42/153.95	->Bound:
152.42/153.95	 1
152.42/153.95	->Interpretation:
152.42/153.95	 
152.42/153.95	[a](X) = [0 1;0 1].X + [1;0]
152.42/153.95	[b](X) = [1 0;1 0].X + [0;1]
152.42/153.95	[B](X) = [1 1;1 1].X
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	SCC Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Strongly Connected Components:
152.42/153.95	->->Cycle:
152.42/153.95	->->-> Pairs:
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	->->-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	Reduction Pair Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 B(b(a(b(x1:S)))) -> B(a(b(b(x1:S))))
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	-> Usable rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Interpretation type:
152.42/153.95	 Linear
152.42/153.95	->Coefficients:
152.42/153.95	 Natural Numbers
152.42/153.95	->Dimension:
152.42/153.95	 2
152.42/153.95	->Bound:
152.42/153.95	 1
152.42/153.95	->Interpretation:
152.42/153.95	 
152.42/153.95	[a](X) = [0 1;0 1].X
152.42/153.95	[b](X) = [1 0;1 0].X + [0;1]
152.42/153.95	[B](X) = [1 1;1 1].X
152.42/153.95	
152.42/153.95	Problem 1: 
152.42/153.95	
152.42/153.95	SCC Processor:
152.42/153.95	-> Pairs:
152.42/153.95	 Empty
152.42/153.95	-> Rules:
152.42/153.95	 a(b(b(a(x1:S)))) -> b(a(a(a(x1:S))))
152.42/153.95	 b(a(b(a(x1:S)))) -> a(a(a(a(x1:S))))
152.42/153.95	 b(a(b(b(x1:S)))) -> b(b(b(b(x1:S))))
152.42/153.95	 b(b(a(b(x1:S)))) -> b(a(b(b(x1:S))))
152.42/153.95	->Strongly Connected Components:
152.42/153.95	 There is no strongly connected component
152.42/153.95	
152.42/153.95	The problem is finite.
152.43/154.00	EOF